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[Перевод] KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Предлагаю полный перевод второй статьи на тему нейронных сетей на основе алгоритма Колмогорова-Арнольда (KAN), опубликованной в августе 2024 года. В этой работе исследователи продолжают развивать тему KAN, раскрывают ее связь с наукой, а также приводят некоторые практические советы по использованию библиотеки pykan, написанной на python, в которой реализован алгоритм KAN.
Перевод первой статьи размещен по адресу https://habr.com/ru/articles/856776/.

Аннотация

Основная проблема ИИ + Наука (AI + Science) заключается в их изначальной несовместимости: сегодняшний ИИ в первую очередь основан на коннекционизме, в то время как наука опирается на символизм. Чтобы соединить два мира, мы предлагаем структуру для бесшовной синергии сетей Колмогорова-Арнольда (KAN) и науки. Структура подчеркивает использование KAN для трех аспектов научного открытия: определение соответствующих признаков, выявление модульных структур и открытие символических формул. Синергия двунаправленная: наука к KAN (включение научных знаний в KAN) и KAN к науке (извлечение научных идей из KAN). Мы выделяем основные новые функции в pykan: (1) MultKAN: KAN с узлами умножения. (2) kanpiler: компилятор KAN, который компилирует символические формулы в KAN. (3) преобразователь деревьев: преобразование KAN (или любых нейронных сетей) в древовидные графы. На основе этих инструментов мы демонстрируем способность KAN открывать различные типы физических законов, включая сохраняющиеся величины, лагранжианы, симметрии и конститутивные законы.

Рисунок 1: Синергия науки и сети Колмогорова-Арнольда (KAN)

1 Введение

В последние годы ИИ + Наука стали многообещающей новой областью, что привело к значительным научным достижениям, включая прогнозирование сворачивания белков [37], автоматическое доказательство теорем [95, 83], прогноз погоды [41] и другие. Общей чертой этих задач является то, что все они могут быть хорошо сформулированы в виде проблем с четкими целями, оптимизируемыми системами ИИ-черного ящика. Хотя эта парадигма работает исключительно хорошо для прикладной науки, существует другой вид науки: наука, движимая любопытством. В исследованиях, движимых любопытством, процедура является более исследовательской, часто не имеющей четких целей, кроме «получения большего понимания». Для ясности, наука, движимая любопытством, далеко не бесполезна; совсем наоборот. Научные знания и понимание, полученные посредством любопытства, часто закладывают прочную основу для завтрашних технологий и способствуют широкому спектру приложений.

Хотя и прикладная, и любознательная наука бесценны и незаменимы, они задают разные вопросы. Когда астрономы наблюдают движение небесных тел, прикладные исследователи сосредотачиваются на прогнозировании их будущих состояний, в то время как любознательные исследователи изучают физику, лежащую в основе движения. Другим примером является AlphaFold, которая, несмотря на свой огромный успех в прогнозировании белковых структур, остается в сфере прикладной науки, поскольку она не предоставляет новых знаний на более фундаментальном уровне (например, атомных сил). Гипотетически AlphaFold должен был открыть важную неизвестную физику, чтобы достичь своих высокоточных предсказаний. Однако эта информация остается скрытой от нас, оставляя AlphaFold в значительной степени черным ящиком. Поэтому мы выступаем за новые парадигмы ИИ для поддержки любознательной науки. Эта новая парадигма ИИ + Наука требует более высокой степени интерпретируемости и интерактивности в инструментах ИИ, чтобы их можно было легко интегрировать в научные исследования.

Недавно новый тип нейронной сети, называемый сетью Колмогорова-Арнольда (KAN) [57], показал себя многообещающим для задач, связанных с наукой. В отличие от многослойных персептронов (MLP), которые имеют фиксированные функции активации на узлах, KAN имеют обучаемые функции активации на ребрах. Поскольку KAN могут раскладывать многомерные функции на одномерные функции, интерпретируемость может быть получена путем символической регрессии этих 1D-функций. Однако их определение интерпретируемости несколько узкое, поскольку оно приравнивается почти исключительно к способности извлекать символические формулы. Это ограниченное определение сужает сферу их применения, поскольку символические формулы не всегда необходимы или возможны в науке. Например, если в физике символьные уравнения являются мощным инструментом и широко распространены, то в химии и биологии системы часто слишком сложны, чтобы их можно было представить с помощью таких уравнений. В этих областях модульные структуры и ключевые особенности могут быть достаточными для характеристики интересных аспектов этих систем. Еще одним упущенным из виду аспектом является обратная задача - внедрение знаний в KAN: как мы можем внедрить предварительные знания в KAN в духе обучения на основе физики?

Мы совершенствуем и расширяем KAN, чтобы их было легко использовать в науке, движимой любопытством. Цель этой статьи можно кратко сформулировать следующим образом:

Чтобы быть более конкретным, научные объяснения могут иметь разные уровни, начиная от самых грубых / простых / корреляционных и заканчивая самыми тонкими / сложными / причинно-следственными:
• Важные характеристики: Например, " полностью определяется x_1 и x_2 , в то время как другие факторы не имеют значения". Другими словами, существует функция , такая, что y = f(x_1, x_2) .
• Модульные структуры: например, " x_1 и x_2 независимо друг от друга аддитивно влияют на ". Это означает, что существуют такие функции и , что y = g(x_1) + h(x_2) .
• Символические формулы: Например, " зависит от x_1 как синусоидальная функция и от x_2 как экспоненциальная функция". Другими словами, y = sin(x_1) + exp(x_2) .

В статье рассказывается о том, как включить и извлечь эти свойства из KAN. Структура статьи выглядит следующим образом (показано на рисунке 1): В разделе 2 мы дополняем исходную CAN узлами умножения, представляя новую модель под названием MultKAN. В разделе 3 мы исследуем способы внедрения научных индуктивных методов в KAN, уделяя особое внимание важным функциям (раздел 3.1), модульным структурам (раздел 3.2) и символическим формулам (раздел 3.3).

Рисунок 2: Вверху: сравнение диаграмм KAN и MultKAN. MultKAN имеет дополнительные слои умножения M. Внизу: После обучения на KAN реализует алгоритм, требующий двух узлов сложения, тогда как MultKAN требует только один узел умножения.

Рисунок 2: Вверху: сравнение диаграмм KAN и MultKAN. MultKAN имеет дополнительные слои умножения M. Внизу: После обучения на f(x, y) = xy

KAN реализует алгоритм, требующий двух узлов сложения, тогда как MultKAN требует только один узел умножения.

В разделе 4 мы предлагаем методы извлечения научных знаний из KAN, снова охватывая важные функции (раздел 4.1), модульные структуры (раздел 4.2) и символьные формулы (раздел 4.3). В разделе 5 мы применяем KAN к различным задачам научного поиска, используя инструменты, разработанные в предыдущих разделах. Эти задачи включают в себя обнаружение сохраняющихся величин, симметрий, лагранжианов и определяющих законов. Коды доступны по адресу https://github.com/KindXiaoming/pykan и также могут быть установлены с помощью pip install pykan. Хотя статья называется “KAN 2.0”, выпущенная версия pykan - 0.2.x.

2 MultKAN: Увеличение количества KAN за счет умножения

Теорема о представлении Колмогорова-Арнольда (Kolmogorov-Arnold representation theorem KART) утверждает, что любая непрерывная функция большой размерности может быть разложена на конечную композицию одномерных непрерывных функций и переменной:

Это означает, что сложение является единственной истинной многомерной операцией, в то время как другие многомерные операции (включая умножение) могут быть выражены как операции сложения в сочетании с одномерными функциями. Например, чтобы умножить два положительных числа x и y, мы можем выразить это как xy = exp(logx + logy) *, правая часть которого состоит только из сложения и одномерных функций (log и exp). (*Значения и могут быть отрицательными, поэтому можно использовать большое значение c > 0 и выразить xy = exp(log(x + c) + log(y +c)) − c(x + y) − c^2 . Другие конструкции включают квадратичные функции, такие как xy = ((x + y)^2 − (x − y)^2)/4 или xy = ((x + y)^2 − x^2 − y^2)/2) .
Однако, учитывая распространенность умножений как в науке, так и в повседневной жизни, желательно явно включать умножения в KAN, что потенциально может повысить как интерпретируемость, так и потенциал модели.

Kolmogorov-Arnold Network (KAN) В то время как уравнение KART (1) соответствует двухслойной сети, Лю и др. [57] удалось расширить его на произвольную глубину, признав, что кажущиеся различными внешние функции Φ_q и внутренние функции $ϕ_{q,p}$ могут быть объединены с помощью предложенных ими слоев KAN. Глубину L KANN можно построить, просто наложив L слоев KAN. Форма глубины L KAN представлена целочисленным массивом [n_0, n_1, ··· , n_L] , где n_l обозначает количество нейронов в -м нейронном слое. Слой KAN с входными размерами n_l и выходными размерами $n_{l+1}$ преобразует входной вектор $x_l \in \mathbb{R}^{n_l}$ в $x_{l+1} \in \mathbb{R}^{n_{l+1}}$

и вся сеть представляет собой композицию из L слоев KAN, т.е.,

На диаграммах KAN можно интуитивно представить сеть, состоящую из узлов (суммирование) и ребер (обучаемые активации), как показано на рисунке 2 вверху слева. При обучении на наборе данных, сгенерированном из f(x, y) = xy , KAN (рисунок 2 внизу слева) использует два дополнительных узла, что делает неясным, действия сети. Однако после некоторого размышления мы понимаем, что она использует равенство xy = ((x + y)^2 − (x − y)^2)/4 , но это далеко не очевидно.

Multiplicative Kolmogorov-Arnold Networks (MultKAN) Для явного введения операций умножения мы предлагаем MultKAN, который может более четко выявлять мультипликативные структуры в данных. MultKAN (показан на рисунке 2 вверху справа) похож на KAN, причем оба имеют стандартные слои KAN. Мы называем входные узлы слоя KAN узлами, а выходные узлы слоя KAN подузлами. Разница между KAN и MultKAN заключается в преобразованиях из подузлов текущего слоя в узлы следующего слоя. В KAN узлы напрямую копируются из подузлов предыдущего слоя. В MultKAN некоторые узлы (узлы сложения) копируются из соответствующих подузлов, в то время как другие узлы (узлы умножения) выполняют умножение на k подузлах из предыдущего слоя. Для простоты далее мы установим k = 2 *.
*(Для простоты мы задали k = 2 , но пакет pykan позволяет использовать любое целое число k ≥ 2 . Пользователи даже могут задавать разные значения для разных узлов умножения. Однако если в одном слое используются разные значения , распараллеливание этих умножений может быть затруднено.)

На основе диаграммы MultKAN (рисунок 2 вверху справа) можно интуитивно понять, что MultKAN — это обычный KAN с необязательными вставленными умножениями. Для математической точности мы определяем следующие обозначения: Количество операций сложения (умножения) в слое обозначается как n_l^a ( n_l^m) соответственно. Они собираются в массивы: ширина сложения n^a ≡[n_0^a,n_1^a,⋅⋅⋅n_L ^a] и ширина умножения n^m ≡[n_0^m,n_1^m,⋅⋅⋅n_L ^m] . Когда n_0^m = n_1^m =⋅⋅⋅n_L^m=0 , MultKAN сводится к KAN. Например, на рисунке 2 (вверху справа) показан MultKAN с $\mathbf{n}^a = [2, 2, 1]$ и $\mathbf{n}^m = [0, 2, 0]$ .

Слой MultKAN состоит из стандартного KANLayer $\mathbf{Φ}_l$ и слоя умножения M_l . $\mathbf{Φ}_l$ принимает входной вектор $x_l ∈ \mathbb{R}^{n_l^a+n_l^m}$ и выводит $\mathbf{z}_l=\mathbf{\Phi}_l(x) \in \mathbb{R}^{n_{l+1}^a + 2n_{l+1}^m}$ . Слой умножения состоит из двух частей: часть умножения выполняет умножения пар подузлов, в то время как другая часть выполняет тождественное преобразование. Написанный на Python, M_l преобразует $\mathbf{z}_l$ следующим образом:

где — поэлементное умножение. MultKANLayer можно кратко представить как Ψ_l≡M_l∘ Φ_l . Таким образом весь MultKAN:

Рисунок 3: Добавление вспомогательных переменных к входным данным улучшает интерпретируемость. Для уравнения релятивистской массы , (a) двухслойная KAN необходима, если в качестве входных данных используются только . (b) Если мы добавим и в качестве вспомогательных переменных к KAN, то будет достаточно однослойной KAN (seed 0). (c) seed 1 находит другое решение, которое не является оптимальным и которого можно избежать с помощью проверки гипотез (раздел 4.3).

Рисунок 3: Добавление вспомогательных переменных к входным данным улучшает интерпретируемость. Для уравнения релятивистской массы ${m_0}/{\sqrt{{1-v^2}/c^2}}$ , (a) двухслойная KAN необходима, если в качестве входных данных используются только (m0, v, c)

. (b) Если мы добавим β≡v/c

и $γ ≡1/\sqrt{1-β^2}$ в качестве вспомогательных переменных к KAN, то будет достаточно однослойной KAN (seed 0). (c) seed 1 находит другое решение, которое не является оптимальным и которого можно избежать с помощью проверки гипотез (раздел 4.3).

Поскольку в слоях умножения нет обучаемых параметров, все методы разреженной регуляризации (например, ℓ_1 и энтропийная регуляризация) для KAN [57] могут быть напрямую применены к MultKAN. Для задачи умножения f(x, y) = xy MultKAN действительно учится использовать один узел умножения, что позволяет ему выполнять простое умножение, поскольку все изученные функции активации являются линейными (рисунок 2 внизу справа).
Хотя KAN ранее рассматривались как особый случай MultKAN, мы расширяем определение и рассматриваем «KAN» и «MultKAN» как синонимы. По умолчанию, когда мы ссылаемся на KAN, умножение разрешено. Если мы конкретно ссылаемся на KAN без умножения, мы явно это укажем.

3 Наука в KAN

В науке знание предметной области имеет решающее значение, позволяя нам эффективно работать даже с небольшими или нулевыми данными. Поэтому полезно принять подход, основанный на физике, для KAN: мы должны включить доступные индуктивные предубеждения в KAN, сохраняя их гибкость для открытия новой физики из данных.
Мы исследуем три типа индуктивных предубеждений, которые могут быть интегрированы в KAN. От самых грубых/легких/корреляционных до самых тонких/сложных/причинных – это: важные признаки (раздел 3.1), модульные структуры (раздел 3.2) и символические формулы (раздел 3.3).

3.1 Добавление важных признаков в KAN

В задаче регрессии цель состоит в том, чтобы найти функцию , такую, что y = f(x_1, x_2, · · · , x_n) . Предположим, мы хотим ввести вспомогательную входную переменную a = a(x_1, x_2,···, x_n) , преобразуя функцию в y = f(x_1,···,x_n, a) . Хотя вспомогательная переменная a не добавляет новой информации, она может увеличить выразительную силу нейронной сети. Это связано с тем, что сети не нужно тратить ресурсы на вычисление вспомогательной переменной. Кроме того, вычисления могут стать проще, что приведет к улучшению интерпретируемости. Пользователи могут добавлять вспомогательные функции к входам с помощью метода augment_input:

В качестве примера рассмотрим формулу для релятивистской массы $m(m_0,v,c) = m_0/\sqrt{1 -(v/c)^2}$ , где — масса покоя, — скорость точечной массы, а — скорость света. Поскольку физики часто работают с безразмерными числами β ≡ v/c и $γ ≡ 1/\sqrt{1 - β^2} ≡ 1/\sqrt{1 - (v/c)^2}$ , они могут ввести и наряду с и в качестве входных данных. Рисунок 3 показывает KAN с этими вспомогательными переменными и без них: (a) иллюстрирует KAN, составленный из символической формулы (см. раздел 3.3 для компилятора KAN), которая требует 5 ребер; (b)(c) показывает KAN со вспомогательными переменными, требующими только 2 или 3 ребра и достигающими потерь 10⁻⁶ и 10⁻⁴ соответственно. Обратите внимание, что (b) и (c) отличаются только величиной seed. Seed равный 1 представляет собой неоптимальное решение, поскольку оно также определяет β = v/c как ключевой признак (feature). Это неудивительно, так как в классическом пределе v ≪ c , $γ ≡ 1/\sqrt{1 - (v/c)^2} ≈ 1 + (v/c)^2/2 = 1 + β^2/2$ . Разнообразие, вызванное различными seed, можно рассматривать либо как особенность, либо как ошибку (bug): Как особенность, это разнообразие может помочь найти неоптимальные решения, которые, тем не менее, могут предложить интересные идеи; как ошибка, оно может быть устранено с помощью метода проверки гипотез, предложенного в разделе 4.3.

Рисунок 4: Построение модульных структур для KAN: (a) мультипликативная разделимость; (b) симметрии

3.2 Строительство модульных конструкций для KAN

Модульность распространена в природе: например, кора головного мозга человека разделена на несколько функционально различных модулей, каждый из которых отвечает за определенные задачи, такие как восприятие или принятие решений. Эта модульность упрощает понимание нейронных сетей, поскольку позволяет нам интерпретировать кластеры нейронов совместно, а не анализировать каждый нейрон по отдельности.
Структурная модульность характеризуется кластерами связей, где внутрикластерные связи намного сильнее межкластерных. Чтобы обеспечить модульность, мы вводим модульный метод, который сохраняет внутрикластерные связи, удаляя межкластерные связи. Модули указываются пользователями. Синтаксис:

Например, если пользователь хочет назначить модулю определенные узлы/подузлы - скажем, 0-й узел в слой 1, 1-й и 3-й подузлы в слой 1, 1-й и 3-й узлы в слой 2 - он может использовать module(1, '[0] -> [1,3] -> [1,3]'). Если говорить конкретно, то существует два типа модульности: разделимость и симметрия.

Разделимость Мы говорим, что функция считается разделимой, если ее можно выразить как сумму или произведение функций непересекающихся групп переменных. Например, функция четырех переменных f(x_1, x_2, x_3, x_4) является максимально мультипликативно разделимой, если она имеет вид f_1(x_1)f_2(x_2)f_3(x_3)f_4(x_4) , создавая четыре различные группы (1), (2), (3), (4). Пользователи могут создавать эти модули, вызывая метод module четыре раза: module(0, '[ i ]->[ i ]'), = 0, 1, 2, 3, как показано на рисунке 4 (а). Последний вызов можно пропустить, так как первых трех достаточно для определения групп. Более слабые формы мультипликативной разделимости могут быть f_1 (x_1, x_2)f_2 (x_3,x_4) (вызов module(0, '[ 0,1 ]->[ 0,1 ]' )) или f_1 (x_1)f_2 (x_2,x_3,x_4) (вызов module(0, '[ 0 ]->[ 0 ]' )).

Обобщенная симметрия Мы говорим, что функция симметрична относительно переменных (x_1,x_2) , если f(x_1, x_2,x_3,· · · ) = g(h(x_1, x_2),x_3,· · · ) . Это свойство называется симметрией, поскольку значение остается неизменным до тех пор, пока h(x_1,x_2) остается постоянным, даже если x_1 и x_2 изменяются. Например, функция является вращательно-инвариантной в 2D, если f(x_1,x_2) = g(r) где $r ≡ \sqrt{x_1^2 + x_2^2}$ . Когда симметрия затрагивает только подмножество переменных, ее можно считать иерархической, поскольку x_1 и x_2 сначала взаимодействуют через (2-слойный KAN), а затем взаимодействует с другими переменными через (2-слойный KAN). Предположим, что функция с четырьмя переменными имеет иерархическую форму f(x_1,x_2,x_3,x_4) = h(f(x_1,x_2),g(x_3,x_4)) ,

Рисунок 5: Компилятор KAN (kanpiler) преобразует символьные выражения в KAN. (a) Как работает kanpiler: символьная формула сначала разбирается на дерево выражений, которое затем преобразуется в KAN. (b) Применение KAN к 10 уравнениям (выбранным из набора данных Фейнмана). (c) Расширение скомпилированного KAN для увеличения его выразительной мощности.

как показано на рисунке 4 (b). Мы можем использовать метод module для создания этой структуры, вызвав module(0, '[ 0,1 ] -> [ 0,1 ] -> [ 0,1 ] -> [ 0 ]'), гарантируя, что группы переменных (x_1,x_2) и (x_3,x_4) не будут взаимодействовать в первых двух слоях.

3.3 Составление символических формул в KAN

Ученые часто находят удовлетворение в представлении сложных явлений посредством символических уравнений. Однако, хотя эти уравнения и лаконичны, им может не хватать выразительной силы, необходимой для охвата всех нюансов из-за их специфических функциональных форм. Напротив, нейронные сети очень выразительны, но могут неэффективно тратить время обучения и данные на изучение знаний предметной области, уже известных ученым. Чтобы использовать сильные стороны обоих подходов, мы предлагаем двухэтапную процедуру:
(1) компилировать символические уравнения в KAN и
(2) настраивать эти KAN с использованием данных.
Первый шаг направлен на внедрение известных знаний предметной области в KAN, в то время как второй шаг фокусируется на изучении новой «физики» из данных.

kanpiler (KAN compiler) Цель kanpiler — преобразовать символическую формулу в KAN. Процесс, показанный на рисунке 5 (a), включает три основных шага: (1) Символическая формула разбирается на древовидную структуру, где узлы представляют выражения, а ребра обозначают операции/функции. (2) Затем это дерево модифицируется для приведения в соответствие со структурой графа KAN. Изменения включают перемещение всех листовых узлов на входной слой через фиктивные ребра и добавление фиктивных подузлов/узлов для соответствия архитектуре KAN. Эти фиктивные ребра/узлы/подузлы выполняют только тождественное преобразование. (3) Переменные объединяются в первом слое, эффективно преобразуя дерево в граф. Для наглядности на ребрах размещены одномерные кривые для представления функций. Мы протестировали kanpiler на наборе данных Фейнмана, и он успешно обрабатывает все 120 уравнений. Примеры показаны на рисунке 5 (b). Kanpiler принимает входные переменные (как символы sympy) и выходное выражение (как выражение sympy) и возвращает модель KAN.

Обратите внимание, что возвращаемая модель KAN находится в символическом режиме, т.е. символические функции точно закодированы. Если вместо этого мы используем кубические сплайны для аппроксимации этих символических функций, мы получим потери MSE $ℓ ∝ N^{−8}$ [57], где N — число интервалов сетки (пропорционально числу параметров модели).
Расширение ширины/глубины для увеличения выразительной мощности Сеть KAN, сгенерированная kanpiler, компактна, без избыточных ребер, которые могут ограничить ее выразительную мощность и помешать дальнейшей тонкой настройке. Для решения этой проблемы мы предлагаем методы expand_width и expand_depth для расширения сети, чтобы она стала шире и глубже, как показано на рисунке 5 (c). Методы расширения изначально добавляют нулевые функции активации, которые страдают от нулевых градиентов во время обучения. Поэтому метод возмущения следует использовать для возмущения этих нулевых функций до ненулевых значений, что делает их обучаемыми с ненулевыми градиентами.

4 KAN в науку

Сегодняшние черные ящики глубоких нейронных сетей являются мощными, но интерпретация этих моделей остается сложной задачей. Ученые ищут не только высокопроизводительные модели, но и возможность извлекать значимые знания из моделей. В этом разделе мы сосредоточимся на повышении интерпретируемости научных целей KAN. Мы рассмотрим три уровня извлечения знаний из KAN, от самых базовых до самых сложных: важные признаки (раздел 4.1), модульные структуры (раздел 4.2) и символические формулы (раздел 4.3).

4.1 Определение важности переменных KAN

Определение важности переменных имеет решающее значение для многих задач. Учитывая регрессионную модель , где y ≈ f(x_1 ,x_2 ,...,x_n) , мы стремимся назначить баллы (scores) входным переменным для оценки их важности. Лю и др. [57] использовали функцию L1 norm для указания важности ребер, но эта метрика может быть проблематичной, поскольку она учитывает только локальную информацию.

Чтобы решить эту проблему, мы вводим более эффективную оценку атрибуции, которая лучше отражает важность переменных, чем норма L1. Для простоты предположим, что есть узлы умножения, поэтому нам не нужно различать узлы и подузлы* (*для подузлов, принадлежащих узлу умножения, подузлы наследуют свои оценки от узла умножения). Предположим, что у нас есть L-слой KAN с шириной [n_0, n_1, · · · , n_L] . Мы определяем $E_{l,i,j}$ как стандартное отклонение активаций на ребре (l, i, j) , а $N_{l,i}$ как стандартное отклонение активаций на узле (l, i) . Затем мы определяем оценку узла (атрибуции) $A_{l,i}$ и оценку ребра (атрибуции) $B_{l,i,j}$ . В [57] мы просто определили $B_{l,i,j} = E_{l,i,j}$ и $A_{l,i} = N_{l,i}$ . Однако это определение не учитывает более поздние сегменты сети; даже если узел или ребро имеет бо́льшую норму, они могут не вносить вклад в выход, если остальная часть сети фактически является нулевой функцией. Поэтому теперь мы вычисляем оценки узлов и ребер итеративно от выходного слоя до входного слоя. Мы устанавливаем все выходные измерения так, чтобы они имели единичные оценки, т. е. $A_{L,i} = 1$ , i = 0, 1, · · · , n_L – 1 * , и вычисляем оценки следующим образом:
(*другие варианты могут быть сделаны на основе воспринимаемой важности каждого выходного измерения, хотя это менее критично, когда выходные данные, как правило, одномерны)

Рисунок 6: Определение важных признаков в KAN. (a) сравнение оценки атрибуции с нормой L1, используемой в работе Лю и др. [57]. В двух синтетических задачах оценка атрибуции дает больше информации, чем норма L1. (b) Оценки атрибуции можно вычислить для входных данных и использовать для обрезки входных данных.

Сравнение $E_{l,i,j}$ и $B_{l,i,j}$ Мы обнаружили, что $B_{l,i,j}$ обеспечивает более точное отражение важности ребер. На рисунке 6 мы сравниваем KAN, обученные на двух уравнениях y = exp(sin(πx_1) + x_2^2) и y= (x_1^2 + x_2^2)^2 + (x_3^2+ x_4^2)^2 , и визуализируем KAN с оценками важности (L1 norm) или (оценка атрибуции). Для первого уравнения оценки атрибуции показывают более чистый график, чем нормы L1, так как многие активные ребра в первом слое не вносят вклад в конечный результат из-за неактивных последующих ребер. Оценка атрибуции учитывает это, что приводит к более осмысленному графику. Для второго уравнения y= (x_1^2 + x_2^2)^2 + (x_3^2+ x_4^2)^2 , мы можем сказать исходя из её символического вида, что все четыре переменные одинаково важны. Оценки атрибуции правильно отражают равную важность всех четырех переменных, тогда как норма L1 неверно предполагает, что x_3 и x_4 важнее, чем x_1 и x_2 .
Отсечение входных данных на основе оценок атрибуции В реальных наборах данных размерность входных данных может быть большой, но только несколько переменных могут быть релевантными. Чтобы решить эту проблему, мы предлагаем отсечение нерелевантных признаков на основе оценок атрибуции, чтобы мы могли сосредоточиться на наиболее релевантных. Пользователи могут применить prune_input, чтобы сохранить только наиболее релевантные переменные. Например, если есть 100 входных признаков, упорядоченных по убыванию релевантности в функции $y =∑_{i=0}^{99} {x_i^2/2^i}$ , x_i ∈ [-1,1] , и после обучения только первые пять признаков показывают значительно более высокие оценки атрибуции, метод prune_input сохранит только эти пять признаков. Отсеченная сеть становится компактной и интерпретируемой, тогда как исходная KAN со 100 входными данными слишком плотна для прямой интерпретации.

4.2 Определение модульных структур из KAN

Хотя оценка атрибуции дает ценную информацию о том, какие ребра или узлы важны, она не раскрывает модульные структуры, т. е. как связаны важные ребра и узлы. В этой части мы стремимся раскрыть модульные структуры из обученных KAN и MLP, исследуя два типа модульности: анатомическую модульность и функциональную модульность.

Рисунок 7: Индуцирование анатомической модульности в нейронных сетях посредством обмена нейронами. Подход включает назначение пространственных координат нейронам и их перестановку для минимизации общей стоимости соединения. Для двух задач (слева: многозадачный паритет, справа: иерархическое голосование большинства) обмен нейронами работает для KAN (вверху) в обоих случаях и работает для MLP (внизу) для многозадачного паритета.

4.2.1 Анатомическая модульность

Анатомическая модульность относится к тенденции нейронов, расположенных близко друг к другу в пространстве, иметь более сильные связи, чем те, которые находятся дальше друг от друга. Хотя искусственные нейронные сети не имеют физических пространственных координат, было показано, что введение концепции физического пространства улучшает интерпретируемость [51, 52]. Мы принимаем метод обмена нейронами из [51, 52], который сокращает связи, сохраняя при этом функциональность сети. Мы называем этот метод auto_swap. Анатомическая модульная структура, выявленная путем обмена нейронами, облегчает идентификацию модулей, даже визуально, для двух задач, показанных на рисунке 7: (1) многозадачный разреженный паритет; и (2) иерархическое голосование большинства. Для многозадачной разреженной четности у нас есть 10 входных бит $x_i ∈ \{0, 1\}, i = 1, 2, ···, 10$ , и выход $y_j = x_{2j−1} ⊕ x_{2j}, j = 1,···, 5$ , где обозначает сложение по модулю 2. Задача демонстрирует модульность, поскольку каждый выход зависит только от подмножества входов. Функция auto_swap успешно идентифицирует модули как для KAN, так и для MLP, при этом KAN обнаруживает более простые модули. Для иерархического голосования большинством с 9 входными битами $x_i ∈ \{0, 1\}$ , i=1,···,9 и выходом y = maj(maj(x_1,x_2,x_3),maj(x_4,x_5,x_6),maj(x_7,x_8,x_9)) , где maj обозначает голосование большинством (выход 1, если два или три входа равны 1, в противном случае 0). KAN раскрывает модульную структуру даже до auto_swap, и диаграмма становится более организованной после auto_swap. MLP показывает некоторую модульную структуру из шаблона весов первого слоя, указывая на взаимодействия между переменными, но глобальная модульная структура остается неясной независимо от auto_swap.

4.2.2 Функциональная модульность

Функциональная модульность относится к общей функции, представленной нейронной сетью. Учитывая сеть Oracle, где внутренние детали, такие как веса и активации скрытых слоев, недоступны (слишком сложны для анализа), мы все равно можем собирать информацию о функциональной модульности посредством прямых и обратных проходов на входах и выходах. Мы определяем три типа функциональной модульности (см. Рисунок 8 (a)), основываясь в основном на [84].

Разделимость: Функция f аддитивно разделима, если

Обратите внимание, что $\frac{∂^2 f}{∂x_i ∂x_j }=0$ , когда 1≤i≤k , k+ 1 ≤ j≤ n .

Чтобы обнаружить разделимость, мы можем вычислить матрицу Гессиан

$\mathbf{H} ≡ ∇^T ∇f \left(\mathbf{H}_{ij} = \frac{∂^2 f}{∂x_i ∂x_j}\right)$ и проверить блочную структуру.

Рисунок 8: Обнаружение функциональной модульности в KAN. (a) Мы изучаем три типа функциональной модульности: разделимость (аддитивная или мультипликативная), общая разделимость и симметрия. (b) Применение этих тестов рекурсивно преобразует функцию в дерево. Здесь функция может быть символической функцией (вверху), KAN (в середине) или MLP (внизу). Как KAN, так и MLP создают правильные графы деревьев в конце обучения, но показывают различную динамику обучения.

Если $\mathbf{H}_{ij}=0$ для всех 1≤i≤k и k+1≤j≤n , то мы знаем, что аддитивно разделима. Для мультипликативной разделимости мы можем преобразовать ее в аддитивную разделимость, взяв логарифм:

Для обнаружения мультипликативной разделимости мы определяем $\mathbf{H}_{ij} ≡ \frac{∂^2 log|f|}{∂x_i ∂x_j}$ и

проверяем блочную структуру. Пользователи могут вызвать test_separability для проверки общей разделимости.

Обобщенная разделимость: Функция f имеет обобщенную разделимость, если

Для обнаружения обобщенной отделимости мы вычисляем

где мы использовали $\frac{∂F}{∂g} = \frac{∂F}{∂h}$ . Обратите внимание, что $\frac{{∂f}/{∂x_i}}{∂f/∂x_j}$ является

мультипликативно разделимым, это может быть обнаружено с помощью теста на разделимость, предложенного выше. Пользователи могут вызвать test_general_separability для проверки на аддитивную или мультипликативную разделимость.

Обобщенная симметрия: Функция имеет обобщенную симметрию (по первым k переменным), если

Обозначим $\mathbf{y} = (x_1,· · · ,x_k)$ и $\mathbf{z} = (x_{k+1},· · · ,x_n)$ . Это свойство называется обобщенной симметрией, поскольку сохраняет одно и то же значение до тех пор, пока остается постоянным, независимо от индивидуальных значений x_1,· · · ,x_k . Вычислим градиент f относительно : $∇_y f = \frac{∂g}{∂h} ∇_y h$ . Поскольку $\frac{∂g}{∂h}$ является скалярной функцией, она не

меняет направление ∇_y h . Таким образом, направление $\widehat{{∇_y f}} ≡ \frac{∇_y f}{|∇_y f|}$ не зависит от $\mathbf{z}$ , т. е.

что является условием симметрии. Пользователи могут вызвать метод test_symmetry для проверки симметрии.

Древовидный преобразователь Три типа функциональной модульности образуют иерархию: симметрия является наиболее общей, общая разделимость является промежуточной, а разделимость является наиболее специфической. Математически,

Чтобы получить максимальную иерархию модульных структур, мы применяем обобщенное обнаружение симметрии рекурсивно, формируя группы всего с k = 2 переменными и расширяя их до всех k = n переменных. Например, рассмотрим функцию с 8 переменными

которая имеет четыре обобщенные симметрии k = 2 , включающие группы (x_1,x_2),(x_3,x_4),(x_5,x_6),(x_7,x_8) ; две обобщенные симметрии k = 2 , включающие группы (x_1,x_2,x_3,x_4) и (x_5,x_6,x_7,x_8) . Таким образом, каждая группа k = 4 содержит две группы k = 2 , демонстрируя иерархию. Для каждой обобщенной симметрии мы также можем проверить, является ли обобщенная симметрия далее обобщенно разделимой или разделимой. Пользователи могут использовать метод plot_tree для получения графа дерева для функции (функцией могут быть любые выражения Python, нейронные сети и т. д.). Для модели нейронной сети пользователи могут просто вызвать model.tree(). Граф дерева может иметь стиль «дерево» (по умолчанию) или «ящик» («box»).

Примеры На рисунке 8 (b) приведены два примера. Когда точные символьные функции вводятся в plot_tree, получаются графы истинного дерева. Нас особенно интересует, работает ли преобразователь деревьев для нейронных сетей. Для этих простых случаев и KAN, и MLP могут найти правильный граф, если они достаточно обучены. На рисунке 8 (b) (внизу) показана эволюция графов деревьев во время обучения KAN и MLP. Особенно интересно наблюдать, как нейронные сети постепенно усваивают правильную модульную структуру. В первом случае f(x_1,x_2,x_3,x_4) = (x_1^2 + x_2^2)^2 + (x_3^2 + x_4^2)^2 , и KAN, и MLP постепенно приобретают больше индуктивных смещений (их промежуточные состояния различны), пока не достигнут правильной структуры.

Рисунок 9: Три приема для упрощения символической регрессии. Прием A (верхний ряд): обнаружение и использование модульных структур. Прием B (средний ряд): инициализация разреженных соединений. Прием C (нижний ряд): проверка гипотез.

Во втором случае, $f(x_1,x_2,x_3) = sin(x_1)/\sqrt{x_2^2 + x_3^2}$ , обе модели изначально обнаруживают мультипликативную разделимость для всех трех переменных, показывая даже более высокую симметрию, чем правильная структура. После обучения обе модели «понимают», что: для лучшего соответствия данным (потери становятся ниже), такая высокосимметричная структура больше не может быть выполнена и должна быть ослаблена до менее строгой структуры. Дополнительное наблюдение заключается в том, что KAN имеет промежуточную структуру, не найденную в MLP. Есть два предостережения, которые мы хотели бы упомянуть: (1) результаты могут зависеть от начального значения и/или порога. (2) все тесты полагаются на производные второго порядка, которые могут быть ненадежными из-за того, что модель обучается только на информации нулевого порядка. Состязательные конструкции, такие как $f_ϵ (x) = f(x)+ϵsin \left( \frac xϵ\right)$ могут привести к проблемам, потому что хотя |f_ϵ (x)-f(x)| → 0 при ϵ → 0, |f_ϵ^" (x) - f^"(x)| → ∞ при . Хотя такие крайние случаи маловероятны на практике, гладкость необходима для обеспечения успешности наших методов.

4.3 Определение символических формул из KAN

Символические формулы являются наиболее информативными, поскольку они четко раскрывают как важные характеристики, так и модульные структуры, как только они становятся известны. В работе Лю и др. [57] авторы показали ряд примеров, из которых они могут извлекать символические формулы, имея при необходимости некоторые предварительные знания. С помощью новых инструментов, предложенных выше (важность характеристик, модульные структуры и символические формулы), пользователи могут использовать эти новые инструменты для легкого взаимодействия и совместной работы с KAN, что упрощает символическую регрессию. Ниже мы представляем три приема, проиллюстрированные на рисунке 9.

Прием A: обнаружить и использовать модульные структуры Сначала мы можем обучить общую сеть и исследовать ее модульность. После того, как модульная структура идентифицирована, мы инициализируем новую модель с этой модульной структурой в качестве индуктивных смещений. Например, рассмотрим функцию f(q,v,B,m) = qvB/m Сначала мы инициализируем большую KAN (предположительно достаточно выразительную), чтобы подогнать набор данных с разумной точностью. После обучения из обученной KAN извлекается древовидный граф (ссылка на раздел 4.2), который показывает мультипликативную разделимость. Затем мы можем построить модульную структуру во второй KAN (ссылка на раздел 3.2), обучить ее, а затем символизировать все одномерные функции, чтобы вывести формулу.

Прием B: разреженная инициализация Символические формулы обычно соответствуют KAN с разреженными связями (см. Рисунок 5 (b)), поэтому разреженная инициализация KAN лучше согласует их с индуктивными смещениями символических формул. В противном случае, плотно инициализированные KAN требуют тщательной регуляризации для обеспечения разреженности. Разреженная инициализация может быть достигнута путем передачи аргумента «sparse_init=True» инициализатору KAN. Например, для функции f(q,E,v,B,θ) = q(E + vBsinθ) разреженно инициализированная KAN очень похожа на окончательно обученную KAN, требуя лишь незначительных корректировок в обучении. В отличие от этого, плотная инициализация потребует длительного обучения для удаления ненужных ребер.

Прием C: Проверка гипотезы Когда мы сталкиваемся с несколькими разумными гипотезами, мы можем попробовать их все (ветвясь в «параллельные вселенные»), чтобы проверить, какая гипотеза является наиболее точной и/или самой простой. Чтобы облегчить проверку гипотез, мы создаем систему контрольных точек, которая автоматически сохраняет версии модели всякий раз, когда вносятся изменения (например, обучение, обрезка). Например, рассмотрим функцию $f(m_0,v,c) = m_0/ \sqrt{1 - (v/c)^2}$ . Начнем со случайно инициализированного KAN, имеющего версию 0.0. После обучения он эволюционирует до версии 0.1, где активируется как при β = v/c , так и при $γ = 1/ \sqrt{1 - (v/c)^2}$ . Выдвигаем гипотезу, что могут понадобиться только или . Сначала мы устанавливаем ребро на ноль и обучаем модель, получая $6,5×10^{−4}$ тестового RMSE (версия 0.2). Чтобы проверить альтернативную гипотезу, мы хотим вернуться к точке ветвления (версия 0.1) для чего вызываем model.rewind( '0.1' ), которая возвращает модель обратно к версии 0.1. Чтобы указать, что вызвана перемотка, версия 0.1 переименовывается в версию 1.1. Теперь мы устанавливаем ребро равным нулю, обучаем модель, получая $2.0×10^{−6}$ тестового RMSE (версия становится 1.2). Сравнение версий 0.2 и 1.2 показывает, что вторая гипотеза лучше из-за меньших потерь при одинаковой сложности (обе гипотезы имеют два ненулевых ребра).

5 Применение

Предыдущие разделы в основном были сосредоточены на проблемах регрессии в педагогических целях. В этом разделе мы применяем KAN для обнаружения физических концепций, таких как сохраняющиеся величины, лагранжианы, скрытые симметрии и конститутивные законы. Эти примеры иллюстрируют, как инструменты, предложенные в этой статье, могут быть эффективно интегрированы в реальные научные исследования для решения этих сложных задач.

5.1 Открытие сохраняющихся величин

Рисунок 10: Использование KAN для обнаружения сохраняющихся величин для двумерного гармонического осциллятора.

Сохраняющиеся величины — это физические величины, которые остаются постоянными с течением времени. Например, свободно падающий мяч преобразует свою гравитационную потенциальную энергию в кинетическую энергию, в то время как полная энергия (сумма обеих форм энергии) остается постоянной (при условии пренебрежимо малого сопротивления воздуха). Сохраняющиеся величины имеют решающее значение, поскольку они часто соответствуют симметриям в физических системах и могут упростить вычисления за счет уменьшения размерности системы. Традиционно вывод сохраняющихся величин с помощью бумаги и карандаша может быть трудоемким и требует обширных знаний предметной области. Недавно были исследованы методы машинного обучения для обнаружения сохраняющихся величин [55, 53, 54, 58, 32, 89]. Мы следуем подходу Лю и др. [53], определивших дифференциальное уравнение, которому должны удовлетворять сохраняющиеся величины, тем самым преобразуя проблему поиска сохраняющихся величин в решение дифференциальных уравнений. Они использовали многослойные персептроны (MLP) для параметризации сохраняющихся величин. Мы в основном следуем их процедуре, но заменяем MLP на KAN. Конкретнее, они рассматривают динамическую систему с переменной состояния $\mathbf{z} ∈ \mathbb{R}^d$ , управляемую уравнением $\frac{d \mathbf{z}}{dt} = \mathbf{f}(\mathbf{z})$ . Необходимым и достаточным условием для того, чтобы функция $H(\mathbf{z})$ была сохраняющейся величиной, является выполнение условия $\mathbf{f}(\mathbf{z}) · ∇H(\mathbf{z}) = 0$ для всех $\mathbf{z}$ . Например, в одномерном гармоническом осцилляторе фазовое пространство характеризуется положением и импульсом, $\mathbf{z} = (x,p)$ , а уравнение эволюции имеет вид d(x,p)/dt = (p,-x) . Энергия $H= \frac12 (x^2 + p^2)$ является сохраняющейся величиной, поскольку

$\mathbf{f}(\mathbf{z})·∇H(\mathbf{z}) = (p,-x)·(x,p)=0$ . Мы параметризуем с помощью KAN и обучаем его, используя функции потерь $\ell = ∑_{i=1}^N|\mathbf{f}(\mathbf{z}^{(i)} )· \hat{∇}H{(\mathbf{z}^{\left(i\right)})}|^2$ где $\hat{∇}$ — нормализованный градиент, а $\mathbf{z}^{(i)}$ — i-я точка данных, равномерно взятая из гиперкуба [-1,1]^d .
Мы выбираем 2D гармонический осциллятор для тестирования KAN, характеризующийся (x,y,p_x,p_y) . Он имеет три сохраняющиеся величины: (1) энергия

вдоль направления : $H_1 = \frac12 (x^2 + p_x^2)$ ; (2) энергия вдоль направления :

$H_2 =\frac12 (y^2+p_y^2)$ ; (3) угловой момент H_3 = xp_y-yp_x . Мы обучаем [4, [0, 2], 1] KAN с

тремя различными случайными начальными числами, как показано на рисунке 10, которые соответствуют H1, H2 и H3 соответственно.

5.2 Открытие лагранжианов

Рисунок 11: Использование KAN для изучения лагранжианов для одиночного маятника (вверху) и релятивистской массы в однородном поле (внизу).

В физике механика Лагранжа — это формулировка классической механики, основанная на принципе стационарного действия. Она описывает механическую систему с использованием фазового пространства и гладкой функции L, известной как лагранжиан. Для многих систем $\mathcal{L}= T - V$ , где и представляют собой кинетическую и потенциальную энергию системы соответственно. Фазовое пространство обычно описывается как $(\mathbf{\text{q}},\mathbf{\dot{\text{q}}})$ , где $\mathbf{\text{q}}$ и $\mathbf{\dot{\text{q}}}$ обозначают координаты и скорости соответственно. Уравнение движения может быть

выведено из лагранжиана через уравнение Эйлера-Лагранжа: $\frac d{dt}\left(\frac{∂\mathcal{L}}{∂\mathbf{\dot{q}}}\right) = \frac{∂\mathcal{L}}{∂\mathbf{q}}$ , или эквивалентно

Учитывая фундаментальную роль лагранжиана, интересным вопросом является то, можем ли мы вывести лагранжиан из данных. Следуя [19], мы обучаем лагранжеву нейронную сеть предсказывать $\mathbf{\ddot{q}}$ из $(\mathbf{\text{q}},\mathbf{\dot{\text{q}}})$ . LNN использует MLP для параметризации $\mathcal{L} (\mathbf{\text{q}},\mathbf{\dot{\text{q}}})$ и вычисляет уравнение (18) для предсказания мгновенных ускорений $\mathbf{\ddot{q}}$ . Однако LNN сталкиваются с двумя основными проблемами: (1) Обучение LNN может быть нестабильным из-за производных второго порядка и инверсии матрицы в уравнении (18). (2) LNN не обладают интерпретируемостью, поскольку сами MLP нелегко интерпретировать. Мы решаем эти проблемы с помощью KAN.
Чтобы решить первую задачу, отметим, что матричное обращение гессиана $(\nabla_{\dot{q}} \nabla_{\dot{q}}^T \mathcal{L})^{-1}$ становится проблематичным, когда гессиан имеет собственные значения, близкие к нулю. Чтобы смягчить это, мы инициализируем $(\nabla_{\dot{q}} \nabla_{\dot{q}}^T \mathcal{L})$ как положительно определенную матрицу (или положительное число в 1D). Поскольку $(\nabla_{\dot{q}} \nabla_{\dot{q}}^T \mathcal{L})$ — это масса в классической механике, а кинетическая энергия обычно равна $T=\frac12m\mathbf{\dot{q}}^2$ , кодирование этих априорных знаний в KAN проще, чем в MLP (с использованием kanpiler, представленного в разделе 3.3). Kanpiler может преобразовать символическую формулу T в KAN (как показано на рисунке 11). Мы используем эту преобразованную KAN для инициализации и продолжаем обучение, что приводит к гораздо большей стабильности по сравнению со случайной инициализацией. После обучения символическая регрессия может быть применена к каждому ребру для извлечения символических формул, решая вторую задачу.
Мы показываем два 1D примера на рисунке 11, одиночный маятник и релятивистская масса в однородном поле. Скомпилированные KAN показаны слева, с ребрами на $\dot{q}$ , отображающими квадратичные функции, и ребрами на как нулевые функции.

Одиночный маятник Часть $\dot{q}$ остается квадратичной функцией $T(\dot{q}) = \frac12\dot{q}^2$ , в то время

как часть учится быть функцией косинуса, так как V(q)=1-cos(q) . На рисунке 11 вверху результаты suggest_symbolic отображают пять функций, которые лучше всего соответствуют сплайнам, учитывая как пригодность, так и простоту. Как и ожидалось, косинус и квадратичная функция появляются в верхней части списков.

Релятивистская масса в однородном поле После обучения кинетическая энергия отклоняется от $T = ½ \dot{q}^2$ , поскольку для релятивистской частицы $T_r=(1 - \dot{q}^2)^{-1/2}-1$ . На рисунке 11 (внизу) символическая регрессия успешно находит V(q) = q , но не может идентифицировать T_r из-за своей композиционной природы, поскольку наша символическая регрессия ищет только простые функции. Предполагая, что первая композиция функций является квадратичной, мы создаем еще один [1, 1, 1] KAN для соответствия T_r и устанавливаем первую функцию как квадратичную функцию с помощью fix_symbolic и обучаем только вторую функцию. После обучения мы видим, что истина $x^{−1/2}$ появляется среди пяти лучших кандидатов. Однако $x^{1/2}$ немного лучше подходит для сплайна, на что указывает более высокое значение R-квадрата. Это говорит о том, что символическая регрессия чувствительна к шуму (из-за несовершенного обучения), и априорные знания имеют решающее значение для правильного суждения. Например, знание того, что кинетическая энергия должна стремиться к бесконечности по мере приближения скорости к скорости света, помогает подтвердить, что $x^{−1/2}$ является правильным членом, поскольку $x^{1/2}$ не демонстрирует ожидаемого стремления к бесконечности.

5.3 Обнаружение скрытой симметрии

Рисунок 12: Повторное открытие скрытой симметрии черной дыры Шварцшильда с помощью MLP и KAN. (a) ∆t(r), изученный MLP, является глобально гладким решением; (b) ∆t(r), изученный KAN, является решением "доменной стенки"; (c) KAN показывает всплеск потерь на "доменной стенке"; (d) KAN можно использовать для точной настройки решения MLP, близкой к машинной точности.

Филип Андерсон утверждал, что «было бы лишь небольшим преувеличением сказать, что физика — это изучение симметрии», подчеркивая, насколько открытие симметрии было бесценным как для углубления нашего понимания, так и для более эффективного решения проблем.
Однако симметрии иногда не проявляются, а скрываются, только проявляясь путем применения некоторого преобразования координат. Например, после того, как Шварцшильд открыл свою одноименную метрику черной дыры, Painlevé, Gullstrand и Lemaître потребовалось 17 лет, чтобы раскрыть ее скрытую трансляционную симметрию. Они продемонстрировали, что пространственные сечения можно сделать трансляционно инвариантными с помощью умного преобразования координат, тем самым углубив наше понимание черных дыр [65]. Лю и Тегмарк [56] показали, что преобразование Gullstrand-Painlevé можно обнаружить, обучив MLP за считанные минуты. Однако они не получили чрезвычайно высокой точности (т.е. машинной точности) для решения. Мы пытаемся вернуться к этой проблеме с помощью KAN.
Предположим, что в пространстве-времени (t,x,y,z) имеется черная дыра Шварцшильда с массой 2M = 1 , центром в точке x = y = z = 0 и радиусом r_s=2M=1 . Метрика Шварцшильда описывает, как искажаются пространство и время вокруг нее:

Применяя преобразование Gullstrand-Painlevé $t'=t+2M\left(2u+ln⁡\left(\frac{u-1}{u+1}\right) \right)$ ,

$u ≡ \sqrt{\frac{r}{2M}}$ , x'=x, y'=y, z'=z , метрика в новых координатах становится:

которая демонстрирует трансляционную инвариантность в пространственном сечении (нижний правый блок 3×3 представляет собой евклидову метрику). Лю и Тегмарк [56] использовали многослойный перцептрон для обучения отображению из (t,x,y,z) в

(t',x',y',z') . Определяя матрицу Якоби $\mathbf{J}≡\frac{∂(t', x', y', z')}{∂(t,x,y,z)}$ , $\mathbf{\text{g}}$ преобразуется в

$\mathbf{g}'= \mathbf{J}^{-T}\mathbf{g}\mathbf{J}^{-1}$ . Мы берем нижний правый блок 3×3 $\mathbf{\text{g}}'$ ′ и берем его разность с евклидовой метрикой, чтобы получить потерю MSE. Потери минимизируются путем выполнения градиентных спусков на MLP. Чтобы упростить задачу, они предполагают знание x'=x, y'=y, z'=z и используют только MLP (1 вход и 1 выход) для прогнозирования

временной разницы $∆t(r)=t'-t=2M\left(2u+ln⁡\left(\frac{u-1}{u+1}\right) \right)$ , $u≡\sqrt{\frac{r}{2M}}$ из радиуса .
MLP и KAN находят разные решения Мы обучили как MLP, так и KAN минимизировать эту функцию потерь, и результаты показаны на рисунке 12. Поскольку задача имеет 1 входное измерение и 1 выходное измерение, KAN эффективно сводится к сплайну. Изначально мы ожидали, что KAN превзойдут MLP, поскольку сплайны, как известно, превосходят MLP в низкоразмерных условиях [63]. Однако, в то время как MLP может достичь $10^{−8}$ потерь, KAN застревает на $10^{−3}$ потерях, несмотря на уточнения сетки. Оказалось, что KAN и MLP узнали два разных решения: в то время как MLP нашел глобально гладкое решение (рисунок 12 (a)), KAN узнал решение доменной стенки (рисунок 12 (b)). Решение доменной стенки имеет особую точку, которая разделяет всю кривую на два сегмента. Левый сегмент правильно изучает ∆t(r) , в то время как правый сегмент изучает −∆t(r) , что также является допустимым решением, но отличается от левого сегмента знаком минус. В особой точке появляется пик потерь (рисунок 12 (c)). Можно считать это особенностью KAN, поскольку решения с доменными стенками распространены в природе. Однако, если считать это недостатком, KAN все еще могут получать глобально гладкие решения, добавляя регуляризации (для уменьшения колебаний сплайна) или экспериментируя с различными случайными начальными числами (примерно 1 из 3 случайных начальных чисел находит глобально гладкие решения).
KAN могут достигать чрезвычайной точности Хотя MLP находит глобально гладкое решение и достигает потерь $10^{−8}$ , потери все еще далеки от машинной точности. Мы обнаружили, что ни более длительное обучение, ни увеличение размера MLP не привели к значительному уменьшению потерь. Поэтому мы обратились к KAN, которые, как сплайны в 1D, могут достигать произвольной точности за счет уточнения сетки (при бесконечных данных). Сначала мы использовали MLP в качестве учителя, генерируя контролируемые пары (x,y) для обучения KAN для соответствия контролируемым данным. Таким образом, KAN инициализируется для глобально гладкого решения. Затем мы итеративно уточняли KAN, увеличивая количество интервалов сетки до 1000. В конечном итоге точно настроенные KAN достигают потерь $10^{−15}$ , близких к машинной точности (рисунок 12 (d)).

5.4 Изучение конститутивных законов

Конститутивный закон определяет поведение и свойства материала, моделируя его реакцию на внешние силы или деформации. Одной из простейших форм конститутивного закона является закон Гука [34], который линейно связывает деформацию и напряжение эластичных материалов. Конститутивные законы охватывают широкий спектр материалов, включая эластичные материалы [80, 68], пластичные материалы [64] и жидкости [8]. Традиционно эти законы были выведены из первых принципов, основанных на теоретических и экспериментальных исследованиях [79, 81, 6, 29]. Однако недавние достижения представили подходы, основанные на данных, которые используют машинное обучение для обнаружения и уточнения этих законов из выделенных наборов данных [73, 91, 59, 60].

Рисунок 13: Открытие конститутивных законов (соотношений между тензором давления P и тензором деформации F) с помощью KAN, взаимодействуя с ними. Вверху: предсказание диагонального элемента P₁₁; внизу: предсказание внедиагонального элемента P₁₂.

Мы следуем стандартным обозначениям и экспериментальным установкам в упругой части NCLaw [59] и определяем материальный закон как параметризованную функцию $\mathcal{E}_\theta(\mathbf{F})\rightarrow \mathbf{P}$ , где $\mathbf{F}$ обозначает тензор деформации, $\mathbf{P}$ — первый тензор напряжений Piola–Kirchhoff , а — параметры в материнском законе.
Многие изотропные материалы имеют линейные материальные законы при малой деформации:

Однако, когда деформация становится больше, начинают проявляться нелинейные эффекты. Например, материал NeoHookean имеет следующий конститутивный закон:

где и — так называемые параметры Lamé, определяемые так называемым модулем

Юнга и коэффициентом Пуассона как $µ =\frac Y{2(1+v)}$ , $λ=\frac{Yv}{(1+ν )(1-2ν)}$ .

Для простоты выберем Y = 1 и ν = 0,2 , отсюда $µ = \frac {5}{12}≈0,42$ и $λ = \frac{5}{18}≈0,28$ .

Предположим, что мы работаем с нео-гуковскими материалами, и наша цель — использовать KAN для предсказания тензора $\mathbf{P}$ из тензора $\mathbf{F}$ . Предположим, мы не знаем, что это нео-гуковские материалы, но у нас есть предварительное знание того, что линейный конститутивный закон приблизительно действителен для малой деформации. Из-за симметрии достаточно продемонстрировать, что мы можем точно предсказать $P_{11}$ и $P_{12}$ из 9 матричных элементов $\mathbf{F}$ . Мы хотим скомпилировать линейные конститутивные законы в KAN, которые представляют собой $P_{11}= 2µ(F_{11}– 1)+ λ(F_{11}+ F_{22}+ F_{33}– 3)$ , и $P_{12}= µ(F_{12}+ F_{21} )$ . Мы хотим извлечь неогуковские законы из обученных KAN, представляющих собой $P_{11}= µ(F_{11}^2+ F_{12}^2+ F_{13}^2– 1)+λ log⁡(det⁡(\mathbf{F}))$ , и $P_{12}= µ(F_{11} F_{21}+ F_{12} F_{22}+ F_{13} F_{23} )$ . Мы генерируем синтетический набор данных, выбирая $F_{ij}$ из $U[δ_{ij}– w,δ_{ij}+ w](w = 0,2)$ и используя неогуковский конститутивный закон для вычисления P. Наше взаимодействие с KAN проиллюстрировано на рисунке 13. В обоих случаях мы успешно вычислили истинные символические формулы с помощью некоторых индуктивных предубеждений. Однако главный вывод заключается не в том, что мы можем заново найти точные символьные формулы - учитывая, что предварительные знания искажают процесс, - а в том, что в реальных сценариях, где ответы неизвестны и пользователи могут делать предположения на основе предварительных знаний, пакет pykan позволяет легко проверить или учесть предварительные знания.

Предсказание $P_{11}$ На шаге 1 мы компилируем линейный конститутивный закон $P_{11}= 2µ(F_{11}– 1)+ λ(F_{11}+F_{22}+ F_{33}– 3)$ в KAN с помощью kanpiler, что приводит к потере $10^{−2}$ . На шаге 2 мы привносим возмущение в KAN так, чтобы она стала обучаемой (на что указывает изменение цвета с красного на фиолетовый; красный обозначает чисто символическую часть, в то время как фиолетовый указывает на то, что активны как символическая, так и сплайновая части). На шаге 3 мы обучаем возмущенную модель до сходимости, что дает потерю $6×10^{−3}$ . На шаге 4, предполагая, что детерминант является ключевой вспомогательной переменной, мы используем expand_width (для KAN) и augment_input (для набора данных), чтобы включить детерминант |F |. На шаге 5 мы обучаем KAN до сходимости, что дает потерю $2×10^{−4}$ . На шаге 6 мы символизируем KAN, чтобы получить символическую формулу $P_{11} = 0,42(F_{11}^2+ F_{12}^2+F_{13}^2 – 1) + 0,28log⁡(|F|)$ , что дает потерю $3×10^{−11}$ .

Прогнозирование $P_{12}$ Мы экспериментировали с кодированием линейного конститутивного закона в качестве априорного знания и без него. С предварительными знаниями: на шаге 1 мы компилируем линейный конститутивный закон в KAN, что приводит к потере $10^{−2}$ . Затем мы выполняем ряд операций, включая расширение (шаг 2), возмущение (шаг 3), обучение (шаг 4), сокращение (шаг 5) и, наконец, символизацию (шаг 6). Влияние предварительных знаний очевидно, поскольку окончательный KAN определяет только незначительные корректирующие члены линейного конститутивного закона. Окончательный KAN символизируется как $P_{12}=0,42(F_{12}+F_{21})+0,44F_{13} F_{23}-0,03F_{21}^2+0,02 F_{12}^2$ , что дает потерю $7×10^{−3}$ , лишь немного лучше, чем линейный конститутивный закон. Без предварительных знаний: на шаге 1 мы случайным образом инициализируем модель KAN. На шаге 2 мы обучаем KAN с регуляризацией. На шаге 3 мы обрезаем KAN, чтобы сделать ее более компактной. На шаге 4 мы символизируем KAN, получая $P_{12}=0,42(F_{11} F_{21}+F_{12} F_{22}+F_{13} F_{23} )$ , что близко соответствует точной формуле, достигая потери $6×10^{−9}$ . Сравнение двух сценариев — одного с предварительными знаниями и одного без них — показывает неожиданный результат: в этом примере предварительные знания кажутся вредными, возможно, потому, что линейный конститутивный закон, вероятно, находится вблизи (плохого) локального минимума, из которого модели трудно выйти. Однако мы, вероятно, не должны случайным образом экстраполировать этот вывод на более сложные задачи и более крупные сети. Для более сложных задач нахождение локального минимума с помощью градиентного спуска может быть достаточно сложным, что делает желательным приблизительное начальное решение. Кроме того, более крупные сети могут быть достаточно перепараметризованы, чтобы исключить плохие локальные минимумы, гарантируя, что все локальные минимумы будут глобальными и взаимосвязанными.

Рисунок 14: KAN интерполирует между программным обеспечением 1.0 и 2.0. (a) KAN находят баланс между интерпретируемостью (программное обеспечение 1.0) и обучаемостью (программное обеспечение 2.0). (b) Граница Парето KAN на плоскости шкалы интерпретируемости. Количество интерпретации, которое мы можем получить от KAN, зависит от масштабов проблемы и методов интерпретируемости.

6 Связанные работы

Сети Колмогорова-Арнольда (KAN), вдохновленные теоремой Колмогорова-Арнольда о представлении (KART), были недавно предложены Лю и др. [57]. Хотя связь между KART и сетями долгое время считалась несущественной [30], Лю и др. обобщили исходную двухслойную сеть до произвольной глубины и продемонстрировали их перспективность для научно-ориентированных задач с учетом их точности и интерпретируемости. Последующие исследования изучали применение KAN в различных областях, включая графы [12, 22, 38, 99], уравнения в частных производных [87, 78] и обучение операторов [1, 78, 67], табличные данные [70], временные ряды [85, 28, 93, 27], распознавание человеческой активности [49, 50], нейронауку [96, 33], квантовую науку [40, 46, 4], компьютерное зрение [17, 7, 44, 16, 76, 10], обучение ядра [101], ядерную физику [48], электротехнику [69], биологию [71]. Лю и др. использовали B-сплайны для параметризации 1D-функций, а другие исследования изучали различные функции активации, включая wavelet [11, 76], радиальную базисную функцию [47], ряды Фурье [92]), конечный базис [35, 82], базисные функции Якоби [2], полиномиальные базисные функции [75], рациональные функции [3]. Также были предложены другие методы для KAN, включая регуляризацию [5], Kansformer (объединяющий трансформатор и KAN) [15], адаптивное обновление сетки [72], federated learning [98], сверточные KAN [10]. Продолжаются дебаты относительно того, действительно ли KAN превосходят другие нейронные сети (особенно MLP) в различных областях [7, 16, 42, 77, 97], что говорит о том, что, хотя KAN показывают перспективы для задач машинного обучения, необходимы дальнейшие разработки, чтобы превзойти самые современные модели.

Машинное обучение для физических законов Основная цель KAN — помочь в открытии новых физических законов из данных. Предыдущие исследования показали, что машинное обучение можно использовать для изучения различных типов физических законов, включая уравнения движения [90, 13, 43, 20], законы сохранения [55, 53, 54, 58, 32, 89], симметрии [39, 56, 94], фазовые переходы [88, 14], лагранжианы и гамильтонианы [19, 31] и символическую регрессию [18, 61, 23, 74] и т. д. Однако для того, чтобы сделать нейронные сети интерпретируемыми, часто требуются знания, специфичные для предметной области, что ограничивает их общность. Мы надеемся, что KAN превратятся в универсальные базовые модели для физических открытий.

Механистическая интерпретируемость стремится понять, как нейронные сети работают на фундаментальном уровне [21, 62, 86, 25, 66, 100, 51, 24, 45, 26]. Некоторые исследования в этой области сосредоточены на разработке моделей, которые по своей сути являются интерпретируемыми [24] или на предложении методов обучения, которые явно способствуют интерпретируемости [51]. KAN попадают в эту категорию, поскольку теорема Колмогорова-Арнольда раскладывает многомерную функцию на набор одномерных функций, которые значительно легче интерпретировать, чем многомерные функции.

7 Обсуждение

KAN интерполирует между программным обеспечением 1.0 и 2.0 Ключевое различие между сетями Колмогорова-Арнольда (KAN) и другими нейронными сетями (программное обеспечение 2.0, термин, введенный Andrej Karpathy) заключается в их большей интерпретируемости, что позволяет пользователям манипулировать ими, аналогично традиционному программному обеспечению (программное обеспечение 1.0). Однако KAN не являются полностью традиционным программным обеспечением, поскольку они (1) обучаемы (хорошо), что позволяет им изучать новые вещи из данных, и (2) имеют пониженную интерпретируемость (плохо), поскольку они становятся менее интерпретируемыми и контролируемыми по мере увеличения масштабов сети. На рисунке 14 (a) визуализируется положение программного обеспечения 1.0, программного обеспечения 2.0 и KAN на плоскости интерпретируемости-обучаемости, иллюстрируя, как KAN могут сбалансировать компромиссы между этими двумя парадигмами. Целью данной статьи является предложение различных инструментов, которые делают KAN более похожими на программное обеспечение 1.0, используя при этом обучаемость программного обеспечения 2.0.

Повышение эффективности. Первоначальный пакет pykan [57] был плох в эффективности. Мы включили несколько методов для повышения его эффективности.
1. Эффективные оценки сплайнов. Вдохновленные Efficient KAN [9], мы оптимизировали оценки сплайнов, избегая ненужных расширений входных данных. Для KAN с L слоями, N нейронами на слой и размером сетки G использование памяти было сокращено с O(LN^2 G) до O(LNG) .
2. Включение символической ветви (symbolic branch) только при необходимости. Слой KAN содержит как сплайновую, так и символическую ветвь. Символическая ветвь требует гораздо больше времени, чем сплайновая, поскольку ее нельзя распараллелить (нужны катастрофические двойные циклы). Однако во многих приложениях символическая ветвь не нужна, поэтому мы можем пропустить ее, когда это возможно, что значительно сокращает время выполнения, особенно когда сеть большая.
3. Сохранение промежуточных активаций только при необходимости. Для построения диаграмм KAN необходимо сохранять промежуточные активации. Изначально активации сохранялись по умолчанию, что приводило к замедлению времени выполнения и чрезмерному использованию памяти. Теперь мы сохраняем промежуточные активации только при необходимости (например, для построения графиков или применения регуляризаций при обучении). Пользователи могут включить эти улучшения эффективности с помощью одной строки: model.speed().
4. Ускорение на GPU. Изначально все модели запускались на CPU из-за мелкомасштабного характера проблем. Теперь мы сделали модель совместимой с GPU* (*Модели можно обучать на графических процессорах, но не все функции уже поддерживаются графическими процессорами) . Например, обучение [4,100,100,100,1] с Adam для 100 шагов раньше занимало целый день на CPU (до внедрения 1, 2, 3), но теперь занимает 20 секунд на CPU и менее одной секунды на GPU. Однако KAN все еще отстают от MLP по эффективности, особенно в больших масштабах. Сообщество работает над бенчмаркингом и повышением эффективности KAN, и разрыв в эффективности был значительно сокращен [36].

Поскольку цель этой статьи — сделать KAN более похожими на программное обеспечение 1.0, при выборе между 1.0 (интерактивность и универсальность) и 2.0 (эффективность и конкретика) мы отдаем приоритет интерактивности и универсальности, а не эффективности. Например, мы храним афишированные данные в моделях (что потребляет дополнительную память), поэтому пользователи могут просто вызвать model.plot() для генерации диаграммы KAN без ручного выполнения прямого прохода для сбора данных.

Интерпретируемость Хотя обучаемые одномерные функции в KAN более интерпретируемы, чем весовые матрицы в MLP, масштабируемость остается проблемой. По мере масштабирования моделей KAN, даже если все сплайн-функции интерпретируются по отдельности, становится все труднее управлять объединенным выводом этих 1D-функций. Следовательно, KAN может оставаться интерпретируемой только тогда, когда масштаб сети относительно мал (рисунок 14 (b), толстая красная линия). Важно отметить, что интерпретируемость зависит как от внутренних факторов (связанных с самой моделью), так и от внешних факторов (связанных с методами интерпретируемости). Расширенные методы интерпретируемости должны быть способны обрабатывать интерпретируемость на различных уровнях. Например, интерпретируя KAN с помощью символической регрессии, обнаружения модульности и атрибуции признаков (рисунок 14 (b), тонкие красные линии), граница Парето интерпретируемости по сравнению с масштабом выходит за рамки того, чего может достичь только KAN. Перспективным направлением будущих исследований является разработка более продвинутых методов интерпретируемости, которые могут еще больше раздвинуть текущие границы Парето.

Будущая работа В этой статье представлена структура, которая интегрирует KAN с научными знаниями, фокусируясь в первую очередь на мелкомасштабных примерах, связанных с физикой. В дальнейшем два перспективных направления включают применение этой структуры к более масштабным проблемам и ее распространение на другие научные дисциплины за пределами физики.

Признание

Мы хотели бы поблагодарить Yizhou Liu, Di Luo, Akash Kundu и многих пользователей GitHub за плодотворное обсуждение и конструктивные предложения. Мы выражаем особую благодарность пользователю GitHub Blealtan за публикацию их потрясающей работы по повышению эффективности KAN.
Z.L. и M.T. поддерживаются IAIFI через грант NSF PHY-2019786.

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26 нояб. 2024 г.

24.10.25 06:54 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
24.10.25 18:18 patricialovick86

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24.10.25 18:18 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.10.25 00:49 tyleradams

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25.10.25 00:50 stevekalfman

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25.10.25 05:05 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
25.10.25 10:13 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.10.25 10:13 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.10.25 01:03 Christopherbelle

A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.
26.10.25 18:09 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 17:08 raymondgonzales

Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number +18737715701 Good Day.
27.10.25 17:20 fatimanorth

The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.
28.10.25 00:55 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.10.25 00:55 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.10.25 03:43 Christopherbelle

A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.
29.10.25 10:56 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.10.25 10:56 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.10.25 09:49 Christopherbelle

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30.10.25 12:03 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
31.10.25 13:25 Lillian Lizzy

THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.
31.10.25 13:25 Lillian Lizzy

THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.
01.11.25 03:27 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.11.25 03:27 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.11.25 15:47 kattygates

Hack West Credit Repair is truly in the business of helping people understand credit, how credit works and most importantly they truly care that you understand your next steps to securing a better tomorrow for you and your family. I am grateful that the owner West has taken time out of his evening with his family to get me enrolled and he immediately got the ball rolling in helping me get items deleted from my credit reports. In the few months I’ve been with HACK WEST, 15 of the 17 negative items have been deleted and 250 points have been added to my point. If you want great results, I suggest you use [email protected].
01.11.25 15:49 kattygates

I met an individual on an international dating app, Bumpy. After talking for a few months, the individual encouraged me to start investing on crypto asset trading platform, btc01.org. I started trading and believed I was making profit until I tried to withdraw some of my money, I was asked to pay extra for tax which I did and they kept asking then I knew I have been scammed, I had to contact HACKWEST AT WRITEME DOT COM who then helped to recover the money, the total money I invest is $198,000 in bitcoin. The website is no longer operational. If anyone is in a similar issue, you can as well contact HACK WEST. They also fixed my credit report.
02.11.25 10:55 Christopherbelle

I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
02.11.25 10:56 Christopherbelle

I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
02.11.25 15:23 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
02.11.25 15:23 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.11.25 04:59 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. [email protected] | WhatsApp: +1 512 577 7957 or +44 7428 662701
04.11.25 09:30 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.11.25 09:30 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.11.25 02:43 jordan_11

I made a mistake of not researching about their their investment firm(Binary option), it had a lot of promises which made me fall for all their fake promises , after trying to get my withdrawal out from there, I started having a lot of difficulties. Then I contacted their customer support, they only replied a week after and strangely wanted me to make more deposits just to enable my withdrawal, so i started my research of how I could report this treacherous company to the necessary authorities and also maybe i could get back my investment, The only people that were willing to help me out was Treqora Intel, their customer support replied so fast and immediately directed me to their investigative team which took my up my case and started the tracing and reclaim process with swift, after a week i got an email from Treqora Intel stating that a partial amount had been reclaimed, I was so grateful about their help , then I was asked to decide if I wanted a Partial deposit or wanted all my investment reclaimed and sent to me at once, But I was so desperate at the time so I asked that my partial reclaimed ETH be sent to me first , So the deposit took about few minutes before i got it in my wallet and withdrew it. Then my remaining investment took 2 weeks to get back according to their customer support at Treqora Intel. Immediately They got it, I was contacted again Via email that my reclaimed had been fully reclaimed, so grateful till this day to Treqora Intel for taking their time to help me out with what could have been a very depressing moment to me. And yes no upfront payment until the reclaim has been completed and you've been paid fully. Email:support@treqora. com 📱 WhatsApp: ‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬ ‬‬ 🌐 Website: Treqora. com.
05.11.25 02:44 jordan_11

Crypto Recovery Services _Hire Treqora Intel
05.11.25 02:48 jordan_11

Legitimate Crypto Recovery Companies-CONSULT TREQORA INTEL. After falling victim to a crypt0currency scam group, I lost $35,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to rec0vermy stolen funds and I came across a lot of testimonials online about TREQORA INTEL , an agent who helps in rec0ver of lost bitc0in funds, I contacted TREQORA INTEL , and with their expertise, they successfully traced and rec0vered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and rec0very protocols. They are trusted and very reliable with a 100% successful rate record Rec0very bitc0in, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypt0. Email:support@treqora. com Whats_App: ‪‪‪‪‪+1 (7 7 3 ) 9 7 7 - 7 8 7 7‬ ‬‬ ‬‬, Website: Treqora dot com.
05.11.25 16:20 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.11.25 16:21 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
07.11.25 02:26 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
07.11.25 09:33 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701
07.11.25 16:05 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
07.11.25 23:15 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701
07.11.25 23:30 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
07.11.25 23:30 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
07.11.25 23:32 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701
07.11.25 23:34 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701
09.11.25 03:29 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
09.11.25 03:29 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
10.11.25 05:06 Christopherbelle

I lost $52,000 in USDT to a scam. That hit me hard. USDT is a stable cryptocurrency tied to the US dollar. It keeps its value steady. I thought I had found a sure way to grow my money. Things looked good at first. I even built up profits to $120,000. But when I went to pull out my earnings, the platform blocked me. No access. No funds. Panic set in. I felt trapped and helpless. Scams like this target crypto users all the time. They promise quick gains. Then they vanish with your money. Each year, people lose billions to these tricks. I searched for help everywhere. Forums, support groups. Nothing worked. That's when a friend stepped in. He had faced a similar mess before. He told me about Sylvester Bryant. My friend swore by his skills. So I reached out right away. His email is [email protected]. Sylvester Bryant turned it all around. He listened to my story without judgment. His team got to work fast. They started by reviewing every detail of the scam. Step by step, they traced the path of my stolen USDT. They used tools to follow the blockchain. That's the public record of crypto transactions. It shows where funds move. But scammers hide their tracks. Bryant's group dug deep. They contacted exchanges and networks involved. Day after day, they pushed forward. No shortcuts. They kept me updated the whole time. Every email, every call was clear and honest. In the end, they recovered my full amount. That $52,000 came back to me. The process took focus and grit. Bryant's honesty stood out. He charged no hidden fees. Just straight work for results. My stress melted away. I could breathe again. Sleep came easier. My trust in recovery options grew. If a scam has taken your money, act now. Reach out to Sylvester Bryant. He handles cases like this with care. Email him at [email protected]. Or on WhatsApp at +1 512 577 7957 or +44 7428 662701. Don't wait. Get your funds back.
10.11.25 14:28 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
10.11.25 21:52 ashley11

Legitimate crypto recovery companies in Australia - HIRE TREQORA INTEL
10.11.25 21:53 ashley11

Legitimate crypto recovery companies in Australia - HIRE TREQORA INTEL Sometimes, life can be unpredictable and present us with unexpected twists and turns. On October 15, 2025, I had an experience that taught me a valuable lesson about the importance of vigilance and caution in the digital age. It began when I met someone on TikTok who claimed to have a surefire way to generate significant profits from Ethereum investments. The individual, who went by the name of Mr. Oscar, presented himself as a financial expert with a proven track record of success. Intrigued by the promise of easy money, I decided to invest a substantial amount of my savings into the Ethereum venture. However, I soon discovered that I had fallen victim to a sophisticated scam. Mr. Oscar had fake credentials and a history of deceiving numerous people, leaving them financially devastated and feeling betrayed, I thought I had lost my investment forever. But I was determined to recover my stolen Ethereum and sought help from a reputable firm specializing in cybersecurity. That's when I stumbled upon Treqora Intel, a company with a stellar reputation for assisting victims of online scams. With the support of Treqora Intel , I was able to recover my lost funds in a remarkably short period. Their team of experts was efficient, responsive, and empathetic, making the recovery process as smooth as possible. I was impressed by their professionalism and commitment to helping individuals like me who have been affected by online scams. This experience has taught me to be more cautious when interacting with strangers online, especially when it comes to investment opportunities that seem too good to be true. It has also reminded me of the importance of verifying the credibility of individuals and companies before making any financial decisions. I am grateful to TREQORA INTEL for their assistance and hope that my story can serve as a warning to others to be vigilant in the online world. By being aware of the potential risks and taking necessary precautions, we can protect ourselves from falling prey to scams and ensure a safer online experience.Email:support@treqora. com Whats_App: ‪‪‪‪‪‪‪+1 (7 7 3 ) 9 7 7 - 7 8 7 7‬‬‬ ‬‬ ‬‬, Website: Treqora. com.
11.11.25 06:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
11.11.25 08:34 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
11.11.25 08:34 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
11.11.25 08:34 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
11.11.25 11:15 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
11.11.25 13:36 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
11.11.25 15:16 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
11.11.25 15:36 peggy09

Crypto theft surges, with billions lost yearly. DIY fixes flop due to tech and legal walls. Standard reports gather dust without pros. Anthony Davies changes that. As the best funds recovery expert, his tracing, partnerships, and methods reclaim hacked wallet assets. He maximizes your shot at getting back stolen cryptocurrency. If you've been hit, reach out to Anthony Davies today. Every minute counts in this fight. Start your recovery journey now—don't let thieves win.Crypto theft surges, with billions lost yearly. DIY fixes flop due to tech and legal walls. Standard reports gather dust without pros. Anthony Davies changes that. As the best funds recovery expert, his tracing, partnerships, and methods reclaim hacked wallet assets. He maximizes your shot at getting back stolen cryptocurrency. If you've been hit, reach out to Anthony Davies today. Every minute counts in this fight. Start your recovery journey now—don't let thieves win. reach him at anthonydaviestech@gmail dot com or telegram anthonydavies
11.11.25 19:28 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
11.11.25 19:29 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.11.25 04:09 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
12.11.25 04:10 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
12.11.25 05:07 peggy09

Anthony Davies stands out in the world of crypto recovery. His skills come from years of hands-on work with blockchain tech. He helps people get back what thieves took, often against tough odds. i once lost $200000 to a fake broker site, anthony stood out as the only person who was able to get back my funds. you can contact him by sending an email to; anthonydaviestech @ gma1l com
12.11.25 09:37 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.11.25 09:37 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.11.25 19:01 peggy09

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
13.11.25 20:05 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
13.11.25 20:05 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
13.11.25 22:51 ashley11

Recover All Lost Cryptocurrency From Scammers
13.11.25 22:52 ashley11

Recover All Lost Cryptocurrency From Scammers TREQORA INTEL has exhibited unparalleled strength in the realm of recovery. They stand out as the premier team to collaborate with if you encounter withdrawal difficulties from the platform where you’ve invested. Recently, I engaged with them to recover over a million dollars trapped in an investment platform I’d been involved with for months. I furnished their team with every detail of the investment via Email (SUPPORT @ TREQORA . C O M”), including accounts, names, and wallet addresses to which I sent the funds. This decision proved to be the best I’ve made, especially after realizing I had been sc**med by the company. Initially, I harbored doubts about their services, but I was proven wrong. TREQORA INTEL ensures exemplary service delivery and ensures the perpetrators face justice. They employ advanced techniques to ensure you regain access to your funds. Understandably, many individuals who have fallen victim to investment scams may still harbor trepidation about engaging in online services again due to the trauma of being sc**med. However, I implore you to take action. Seek assistance from TREQORA INTEL today and witness their remarkable capabilities firsthand. Among the myriad of hackers available, TREQORA INTEL stands head and shoulders above the rest. While I may not have sampled all of them, the few I attempted to work with previously were unhelpful and solely focused on depleting the little funds I had left. I am grateful that I resisted their enticements, and despite the time it took me to discover TREQORA INTEL, they ultimately fulfilled my primary objective. I am confident they will execute the task proficiently. Without their intervention, I would have remained despondent and perplexed indefinitely. Don’t make the error of entrusting sc**mers to rectify a sc*m; the consequences are evident. Email:support@treqora. com,WhatsApp: ‪‪‪‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬‬‬‬ ‬‬,Website: Treqora. com. How Can I Recover My Lost Bitcoin From A Romance Scammer-HIRE TREQORA INTEL
13.11.25 23:36 daisy

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
14.11.25 03:42 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.11.25 03:42 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.11.25 08:38 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
14.11.25 10:39 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
14.11.25 12:12 daisy

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
14.11.25 15:07 caridad

Perth Family Saved After $400K Crypto Scam Our family in Perth, WA invested through what we thought was a trusted platform but ended up being a fraudulent investment scheme. We lost nearly AUD 420,000 worth of BTC and USDT. Luckily, a friend recommended Bitreclaim.com. Their 24/7 customer support assigned us a smart contract audit specialist who asked for wallet addresses and transaction hashes. With their forensic blockchain trace, they recovered over 5.1 BTC directly into our hardware wallet. For Perth investors: don’t give up hope. Submit a case at Bitreclaim.com immediately. Their professionalism and success rate in Australia is unmatched.
14.11.25 18:33 justinekelly45

FAST & RELIABLE CRYPTO RECOVERY SERVICES Hire iFORCE HACKER RECOVERY I was one of many victims deceived by fake cryptocurrency investment offers on Telegram. Hoping to build a retirement fund, I invested heavily and ended up losing about $470,000, including borrowed money. Just when I thought recovery was impossible, I found iForce Hacker Recovery. Their team of crypto recovery experts worked tirelessly and helped me recover my assets within 72 hours, even tracing the scammers involved. I’m deeply thankful for their professionalism and highly recommend their services to anyone facing a similar situation. Website: ht tps://iforcehackers. co m WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om
14.11.25 20:56 juliamarvin

Firstly, the importance of verifying the authenticity of online communications, especially those about financial matters. Secondly, the potential for recovery exists even in cases where it seems hopeless, thanks to innovative services like TechY Force Cyber Retrieval. Lastly, the cryptocurrency community needs to be more aware of these risks and the available solutions to combat them. My experience serves as a warning to others to be cautious of online impersonators and never to underestimate the potential for recovery in the face of theft. It also highlights the critical role that professional retrieval services can play in securing your digital assets. In conclusion, while the cryptocurrency space offers unparalleled opportunities, it also presents unique challenges, and being informed and vigilant is key to navigating this landscape safely. W.h.a.t.s.A.p.p.. +.15.6.1.7.2.6.3.6.9.7. M.a.i.l T.e.c.h.y.f.o.r.c.e.c.y.b.e.r.r.e.t.r.i.e.v.a.l.@.c.o.n.s.u.l.t.a.n.t.c.o.m. T.e.l.e.g.r.a.m +.15.6.1.7.2.6.3.6.9.7
15.11.25 12:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 14:39 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.11.25 14:39 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.11.25 15:31 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 15:52 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
16.11.25 14:43 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.11.25 14:44 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.11.25 20:38 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
17.11.25 03:24 johnny231

INFO@THEBARRYCYBERINVESTIGATIONSDOTCOM is one of the best cyber hackers that i have actually met and had an encounter with, i was suspecting my partner was cheating on me for some time now but i was not sure of my assumptions so i had to contact BARRY CYBER INVESTIGATIONS to help me out with my suspicion. During the cause of their investigation they intercepted his text messages, social media(facebook, twittwer, snapchat whatsapp, instagram),also call logs as well as pictures and videos(deleted files also) they found out my spouse was cheating on me for over 3 years and was already even sending nudes out as well as money to anonymous wallets,so i deciced to file for a divorce and then when i did that i came to the understanding that most of the cryptocurrency we had invested in forex by him was already gone. BARRY CYBER INVESTIGATIONS helped me out through out the cause of my divorce with my spouse they also helped me in retrieving some of the cryptocurrency back, as if that was not enough i decided to introduce them to another of my friend who had lost her most of her savings on a bad crytpo investment and as a result of that it affected her credit score, BARRY CYBER INVESTIGATIONS helped her recover some of the funds back and helped her build her credit score, i have never seen anything like this in my life and to top it off they are very professional and they have intergrity to it you can contact them also on their whatsapp +1814-488-3301. for any hacking or pi jobs you can contact them and i assure you nothing but the best out of the job
17.11.25 11:26 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.11.25 11:27 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.11.25 01:56 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I got connected to the best female expert AGENT Jasmine Lopez,,( [email protected] ) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
19.11.25 08:11 JuneWatkins

I’m June Watkins from California. I never thought I’d lose my life savings in Bitcoin. One wrong click, a fake wallet update, and $187,000 vanished in seconds. I cried for days, felt stupid, ashamed, and completely hopeless. But God wouldn’t let me stay silent or defeated. A friend sent me a simple message: “Contact Mbcoin Recovery Group, they specialize in this.” I was skeptical (there are so many scammers), but something in my spirit said “try.” I reached out to Mbcoin Recovery Group through their official site and within minutes their team responded with kindness and clarity. They walked with me step by step, and stayed in constant contact. Three days later, I watched in tears as every single Bitcoin returned to my wallet, 100% recovered. God turned my mess into a message and my shame into a testimony! If you’ve lost crypto and feel it’s gone forever, don’t give up. I’m living proof that recovery is possible. Thank you, Mbcoin Recovery Group, and thank You, Jesus, for never leaving me stranded. contact: (https://mbcoinrecoverygrou.wixsite.com/mb-coin-recovery) (Email: [email protected]) (Call Number: +1 346 954-1564)
19.11.25 08:26 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) (Email [email protected])
19.11.25 08:27 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
19.11.25 16:30 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.11.25 16:30 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.11.25 15:55 mariotuttle94

HIRE THE BEST HACKER ONLINE FOR CRYPTO BITCOIN SCAM RECOVERY / iFORCE HACKER RECOVERY After a security breach, my husband lost $133,000 in Bitcoin. We sought help from a professional cybersecurity team iForce Hacker Recovery they guided us through each step of the recovery process. Their expertise allowed them to trace the compromised funds and help us understand how the breach occurred. The experience brought us clarity, restored a sense of stability, and reminded us of the importance of strong digital asset and security practices. Website: ht tps:/ /iforcehackers. c om WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om