Этот сайт использует файлы cookies. Продолжая просмотр страниц сайта, вы соглашаетесь с использованием файлов cookies. Если вам нужна дополнительная информация, пожалуйста, посетите страницу Политика файлов Cookie
Subscribe
Прямой эфир
Русский Русский  English English
Войти / Регистрация
Cryptocurrencies: 9377 / Markets: 114993
Market Cap: $ 3 712 720 371 656 / 24h Vol: $ 187 913 305 328 / BTC Dominance: 58.97760273029%

Н Новости

  1. Главная
  2. Новости

Математические бланки // Часть 3: математическая реальность

e9eba726a2012847ecdfe99a7596031a.png

В первой части этой серии мы описали проблему математических бланков, и перспективные результаты её решения. Вторая часть показала, что эта проблема упирается в вопрос экземпляров. Он, в свою очередь, может быть решён в рамках модели идеального мира, который должен обладать памятью.

Чтобы подступиться к теме памяти идеального мира, нам нужно с максимальной подробностью разобраться, что такое вообще память, какая она бывает, какие функции выполняет, какими характеристиками обладает, привести подтверждающие примеры.

Исследование низшей математики - это 90% ожидания, 9% отчаяния, и только 1% озарения. Здесь, опустив 99%, можно сразу узнать результат. И в результате, памятью окажется то, что гораздо старше и математики, и самой человеческой истории. И оно всё это время перед глазами. Вот уж точно, хочешь спрятать, прячь на самом виду. Хотите узнать, что это? Не переключайтесь.

Часть 1: введение в проблему
Часть 2: философия

К читателям

Низкий поклон вам, люди, обсуждающие эту серию заметок. Своими комментариями вы даёте бесценную обратную связь, на основании которой можно улучшить тот или иной аспект изложения. Спасибо тем, кто следил за первыми двумя статьями, которые лишь умножали вопросы. В третьей статье пора дать на них ответы.

Вы хороший рассказчик, и мне по прежнему интересно, чем все закончится
Вот вот. Мне кажется, что сейчас идёт замах. Интересно, какой и куда будет удар

Первоначальный план был в постепенном развёртывании рассказа. Но оказывается, аудитория нашла в материале драматизм. Чтобы соответствовать этому новому явлению, пересмотрел план изложения. Статью сделал длиннее, но "тоньше". Мы пройдём с минимальной нагрузкой, кратчайшим путём по всем пунктам нашей стратегии: не только найдём память и время идеального мира, но и создадим там первые объекты и покажем, что они эквивалентны "традиционным" математическим объектам. Потом всё будет по аналогии.

Жду продолжения... Чтобы покритиковать) Пока не ухватить крепко ни за что)))

Излагаемый материал не был придуман. Это результат наблюдений.

И вот так ... вы постулировали ... единицу, единственность, порядок и счёт.

В действительности, нет. Первый человек мог, по желанию, нарисовать на стене пещеры одного оленя, а может двух, то есть уже стадо. При этом он ничего не постулировал. Это означает, что вам не требуются знания о счёте, чтобы нарисовать несколько символов.

Вы же ещё употребляете слово "построение", но даже в общих чертах не описали, что это такое (не говоря уже о строгом определении)

Способность человека писать текст, создавая предложения из слов, сама по себе избавляет от необходимости давать построению формальное определение немедленно: она входит в базовую логику мозга. Специально для Вас это определение будет дано, но позже, когда мы введём необходимые более простые объекты.

Ещё раз: определены будут ВСЕ понятия, которые необходимы и задействованы для рассуждений в области математики. Но не одним куском: в противном случае получится один большой референс-мануал.

Под нуль системой вы подразумеваете максимально вырожденный объект? Настолько не имеющий никаких свойств что по факту не существует?

"Максимально вырожденный" - да. "Не существует" - нет. Существование - это вполне понятная вещь. Чтобы объект существовал, надо, чтобы он был исчерпывающе определён, и не содержал противоречий. Нуль-система отвечает обоим требованиям, поэтому она существует. Хотя само понятие противоречия нам ещё предстоит разобрать и определить, нуль-система, как пустой объект, не содержит ничего, что могло бы образовать противоречие.

Ваша идея в том что бы разобрать математические понятия до атомарных блоков (пока опустим что они из себя представляют) и пересобрать из них эти понятия заново с целью того что бы понять как это вообще происходит, выявить закономерность, так?

Задача разборки ЛЮБОГО объекта заведомо нерешаемая. Разбор объекта - это ВСЕГДА погружение в неизвестность. Неизвестность нельзя взять и отменить. Никак не устранить сомнение, а вдруг ты её не до конца разобрал? Она же что? именно: неизвестность. И совсем другое дело, выполнимая задача - построить конечное и небольшое количество объектов и показать, что из них можно сделать дальше.

Ну и где продолжение?!

Приношу извинения в связи с задержкой третьей части по независящим от автора обстоятельствам.

Микро предисловие

В этой статье мы опишем несколько важных объектов. Подход - дать каждому из них исчерпывающее описание в одной статье сразу - не работает, как показал опыт. Поэтому будем постепенно дополнять сказанное, начав с самого важного и определяющего, и добавляя подробностей и деталей в дальнейших статьях. Критиков прошу учесть этот факт.

Другая особенность материала - это ссылки вперёд. Некоторые вещи относятся к категории интуитивно понятных, что позволяет нам до какого-то момента отложить их формальное определение. Мы будем активно пользоваться этой возможностью. Например, когда мы даём определение сложности, мы используем понятие числа, хотя его строгое определение будет дано в более поздних статьях.

Впрочем, это всё равно больше, чем предлагает традиционная математика. Так, Математическая энциклопедия вовсе не даёт определение таких вещей, как например, равенство или истина, определение которых будет предъявлено в рамках нейроматематики.

Энциклопедия памяти

Разберём термины и понятия, так или иначе связанные с памятью.

ОСНОВНЫЕ ПОНЯТИЯ

Есть термины, которые применимы к любой памяти. Термин ХРАНЕНИЕ является синонимом понятия памяти как таковой. Признаком хранения является возможность так или иначе получить (ЧТЕНИЕ) то, что хранится в памяти (ОБЪЕКТ). Хранению предшествует помещение объекта в память (ЗАПИСЬ). Эти термины характерно определяют абсолютно любую память.

Исследуя аналогичные вопросы, Алан Тьюринг не счёл нужным формализовать указанные понятия, и тем не менее, его машина (МТ) признана математиками. Также и мы получаем, по прецеденту, возможность продолжать рассуждения, оставив формализацию этих понятий на потом.

МУЛЬТИПАМЯТЬ

Некоторые виды памяти, например, триггер, способны хранить один-единственный объект. Другие (RAM, нейросеть) предназначены для хранения множественных экземпляров. В реальной жизни мы сталкиваемся с обоими типами памяти, и так же будет в этой работе. У мультипамяти всегда имеется некоторое многообразие МЕСТ, куда может быть помещён запоминаемый объект: нейроны, ячейки, и т.п..

АДРЕС

Как правило, у мультипамяти место может быть сопоставлено с некоторым показателем, называемым АДРЕСОМ. Иными словами, адрес - ответ на вопрос "ГДЕ?". В рамках данной работы, этот ответ будем называть ИНФОРМАЦИЕЙ. То есть информация, это всегда какое-то значение какого-то адреса в какой-то памяти.

ЛОКАЛЬНОСТЬ

Под локальностью мы понимаем возможность сопоставить конкретный сложный объект с одним конкретным адресом в памяти. Лента/RAM - да, нейросеть - нет.

БОГАТСТВО

Коль скоро объект располагается в некотором месте памяти, это место в некоторых случаях может быть изменено, т.е. объект может быть перемещён. Количество принципиальных способов переместить объект в памяти будем называть её БОГАТСТВОМ. Лента/RAM - один, т.е. объекты могут быть сдвинуты вправо/влево, нейросеть - ноль, т.к. перемещение объекта в нейросети не определено.

БЕСКОНЕЧНОСТЬ

Физически существующие устройства памяти, естественно, являются конечными, но в математике это не так: лента бесконечна. По понятным причинам, память идеального мира также должна быть бесконечна.

НЕПРЕРЫВНОСТЬ

Многие распространённые виды памяти имеют дискретную природу - лента, мозг и нейросеть. Разум человека может рассматривать непрерывные объекты, анализируя их структуру, но непосредственно хранить их в памяти он не может. Таким образом, непрерывность предоставляет памяти расширенные возможности в области математики.

ИТОГ

Изложенное можно свести в таблицу:

#

Лента

Нейросеть

Объекты

Числа

?

Мультипамять

Да

Да

Адрес

Да

Да

Локальность

Да

Нет

Богатство

1

0

Бесконечность

Да

Нет

Непрерывность

Нет

Нет

Итак, мы подобрали все понятия, важные для рассуждений о памяти. Из таблицы видно, что ни лента, ни, в ещё большей степени, нейросеть не пригодны в качестве памяти идеального мира. До того, как мы сможем её найти, остался буквально один шаг.

Коллектор

Два экземпляра, которые мы записали в предыдущей статье, ещё не образуют новый объект.

5abe772c0e1d5ddb41d593a20f67dd45.png

Это видно и по коду, который создаёт экземпляры:

empty x_1 = new();
empty x_2 = new();

Чтобы, наконец, создать наш первый объект из этих экземпляров, определим новое имя КОЛЛЕКТОР, и его структуру выразим в коде вот так:

collector
{
    empty x_1 = new();
    empty x_2 = new();
}

Теперь мы можем создать экземпляр коллектора:

collector x_0 = new();

На картинке эта структура будет выражена вот так:

Элементы коллектора
Элементы коллектора

Так должен выглядеть первый сложный объект, сконструированный из экземпляров \underline{\alpha}. Других исходных материалов у нас пока нет, поэтому коллектор состоит из трёх пустых элементов (примитивов). Порядок конструирования коллектора следующий: сначала создаётся x_0, затем одновременно x_1 и x_2. Первый примитив коллектора (и любого сложного объекта) называется его БАЗИСОМ, примитивы x_1 иx_2 его ПОЛЮСАМИ.

Итого код и рисунок. По какой-то причине, именно рисунок изначально воспринимался как нечто крайне важное. Он годами присутствовал на доске, пока шли многочисленные попытки конструировать что-то ещё более сложное. Кое-что удавалось, но вопрос "что такое память" всё ещё не был решён. Однако, упорство и труд в конце концов вознаграждаются. И однажды, глядя на рисунок на доске, вы вдруг понимаете:

Эврика! Доска - это и есть память

Разумеется, речь идёт об абстрактной доске. Доска на стене - это материальная проекция идеальной доски, бесконечной и непрерывной. Быстрый взгляд на доску позволяет внести её в таблицу памяти, и убедиться, насколько она хороша в этой роли.

#

Лента

Нейросеть

Доска

Объекты

Числа

?

Графические символы

Мультипамять

Да

Да

Да

Адрес

Да

Да

Да

Локальность

Да

Нет

Да

Богатство

1

0

2

Бесконечность

Да

Нет

Да

Непрерывность

Нет

Нет

Да

Прежде чем мы продолжим, два важных замечания.

Первое: используя доску как память, мы не делаем ничего принципиально нового по сравнению с лентой машины Тьюринга. Мы добавили дополнительное измерение и убрали ограничение дискретности, но в целом, прецедент использования некого протяжённого объекта в качестве памяти уже создан Тьюрингом.

Второе: рассматривая доску, мы ограничиваемся только теми её аспектами, которые были понятны ещё доисторическим людям - место, направления и ориентации, передвинуть и повернуть, точка, линия. Мы можем сделать такой вывод, глядя на наскальные рисунки.

Основные аспекты плоскости были понятны ещё предкам человека
Основные аспекты плоскости были понятны ещё предкам человека

Переходим теперь к символам. В математике есть понятие символов, но они рассматриваются в отрыве от своего начертания. О двух символах в математике можно сказать только то, различны они или нет [1, с.12]. Именно в таком смысле символы фигурируют в машине Тьюринга. Символы же на доске являются графическими фигурами, и несут в себе значительно больше смысла.

Доска обладает богатством 2, т.к. имеет два способа переместить изображение - сдвиг и поворот. Замечательный факт: поворот добавляется за счёт второго измерения, но добавление ещё одного измерения (плоскость -> пространство) не добавляет богатства, т.к. в пространстве те же два вида перемещения, что и на плоскости.

А теперь то, что мы получаем бонусом. Рассмотрение доски как памяти позволяет сделать вывод о том, что временем идеального мира должен выступать очевидный второй компонент письма в дополнение к доске - маркер (обобщённое средство написания). Доску и маркер совместно будем называть МАТЕМАТИЧЕСКАЯ РЕАЛЬНОСТЬ.

Структура доски

СИНТАКСИС

Для описания доски в программной нотации нам потребуется оригинальный синтаксис. В рамках этого синтаксиса, информацию (значение адреса) будем обозначать символом @. При описании структуры объекта, фигурные скобки обозначают неупорядоченные элементы, квадратные скобки - упорядоченные элементы.

Несмотря на то, что этот синтаксис хорош при описании структуры доски, маркера (и вообще алгоритмов), а также нескольких простых объектов, его возможности ограничены и уступают в выразительности графическим диаграммам ФОРАОН. В следующей статье мы столкнёмся как раз с таким случаем. Это объясняется тем, что программный синтаксис - линейный, он не задействует измерения, присутствующие на доске.

ОПРЕДЕЛЕНИЕ ДОСКИ

Итак, наше программное определение доски будет содержать следующие понятия:

board
{
    @location;
    direction { @positive; @negative; }
    orientation { @primary; @secondary; }

    shift;
    rotatation;
}

В соответствии с ним, в структуру доски входят:

  • место или точка (@location)

  • направления (direction) - положительное (@positive) и отрицательное (@negative)

  • ориентации (orientation) - первичная (@primary) и вторичная (@secondary)

  • сдвиг (shift)

  • поворот (rotation)

Элементы доски
Элементы доски

Схематично указанные элементы доски изображены на рисунке. Символы p и s означают первичную и вторичную ориентации (горизонтальную и вертикальную, соответственно), а плюс и минус это синонимы положительного (вправо/вверх/против часовой) и отрицательного (наоборот) направлений (выбор ориентаций и направлений произвольный).

Прямые стрелочки выражают сдвиг, изогнутые - вращение. Преобразования на доске будем обозначать (буквы греческие): вращение (\Pi), сдвиг (A). Для них также введём собирательный термин ДВИЖЕНИЕ (K). Если известно направление движения, будем приписывать его верхним индексом к обозначению: \Pi^+, K^-. Для сдвига также можно приписать нижний индекс ориентации: A_p, A^+_s, если она известна.

Примем, что если ориентация поворота не рассматривается, по умолчанию его величина равна \pi, если задана - то величина равна \pi/2.

Коллектор (продолжение)

Теперь, когда память найдена, можно "узаконить" нашу графическую нотацию. Это означает, что графическое изображение становится полностью легальным способом определения структурного и информационного наполнения объекта.

В этой нотации можно закончить определение коллектора, как на следующем рисунке:

Полная структура коллектора
Полная структура коллектора

Полюсы коллектора x_1 и x_2 располагаются в положительном и отрицательном направлении от его базиса x_0. Сами эти направления изображены двумя линиями между примитивами. Эти же линии также являются эквивалентом скобок в коде коллектора, обозначая целостность объекта. В формулах будем обозначать коллектор как \underline{\omega}.

С учётом графической нотации, программный код коллектора дополним адресами:

collector
{
    empty x_1 = new() @positive;
    empty x_2 = new() @negative;
}

Если коллектор создаётся, как указано выше collector x_0 = new();, то в графической нотации его можно изображать по горизонтали или по вертикали, эти изображения будут эквивалентны. Можно также рассмотреть и более подробное описание:

collector x_3 = new() @primary;
collector x_4 = new() @secondary;

В этом случае, когда ориентация коллекторов рассматривается, графическая нотация выразит их с двойной линией, показывающей ориентацию:

Ориентированный коллектор
Ориентированный коллектор

Маркер

Прежде чем разбирать маркер, необходимо сказать несколько слов о ВРЕМЕНИ как таковом. Время относится к непосредственным понятиям, которые для понимания должны быть показаны. По счастью, сам мозг работает во времени, и у него не возникнет проблем распознать последнее, когда ему будет продемонстрировано какое-либо изменение (альтер-эго времени) в физическом мире.

Как сказано выше, идею маркера как времени мы получили бонусом к идее доски. Вместе с тем, маркер как средство совершения ДЕЙСТВИЙ не является чем-то принципиально новым по сравнению с головкой машины Тьюринга. Фактически, маркер это аналог головки: активное устройство, выполняющее действия.

При отыскании структуры маркера необходимо учитывать тот факт, что он находится в идеальном мире, где нет рук, которые бы им двигали. Следовательно, маркер должен обладать всем необходимым для самостоятельного совершения действий.

Говоря об элементарных действиях, перечислим их:

  • чтение

  • изменение

  • запись или удаление

Представим гипотетический сценарий, когда мы хотим записать идеальным маркером на доске какой-то символ. Поскольку маркер выполняет всё сам, ему надо передать информацию о символе. Прочтя её из источника, маркер может произвести запись на доске (приёмнике) самостоятельно. Т.к. мы хотим, чтобы маркер умел преобразовывать данные, место для такого преобразования - между чтением и записью.

Указанная последовательность описана в этом коде:

marker
{
    x; // данные
    f; // преобразование

    read;
    write;

    invoke(previous, next) // действие маркера
    [
        x = read(previous);
        x = f(x);
        write(next, x);
    ]
}

Этот код отражает описанный сценарий и достаточно понятен. Действие маркера, обозначенное как invoke, имеет аргументы previous и next, которые называются КОММУТАТОРАМИ маркера. В качестве коммутаторов могут выступать любые объекты, включая другие маркеры (об этом позже). То же самое относится и к преобразованию f.

Самое простое из возможных преобразований - естественно, сама нуль-система \underline{\alpha}. Если f пустая, то такое преобразование не вносит никаких изменений: \underline{\alpha}(x) = x.

Нейроматематика (начало)

Нейроматематика начинается с нескольких вещей, что интуитивно понятны каждому, но тем не менее, никак формально не определены в традиционной математике (буквально, отсутствуют в математической энциклопедии [2]). Более того, эти вещи не только интуитивно понятны, но и повсеместно используются в рассуждениях, являясь мощнейшим инструментом мышления. В рамках нейроматематики, мы не имеем права пройти мимо них, а значит надо сначала предъявить их определения.

ВАЖНО: определения даются в рамках нейроматематики, которая пишется с чистого листа.

ИЗМЕРЕНИЕ ОБЪЕКТОВ

Вещи могут быть более или менее сложны. Но что это значит? Космическая ракета много сложнее, чем велосипед, но даже миллиард велосипедов не сложнее ракеты, хотя много тяжелее её. "Больше/меньше" в отношении сложности означает, что сложность - это число. Но как её померить? В рамках традиционной математики, это сделать невозможно, потому что нет исчерпывающей структуры любых объектов. Что сложнее - 2 или i?

Спойлер

Они равны по сложности - как будет показано в следующих статьях

Для нейроматематики, где структура всего задаётся явно, это становится возможным. Итак, СЛОЖНОСТЬЮ \mathcal{C}(x) будем называть рекурсивно посчитанное количество уникальных имён во внутренней структуре x. Сложность нуль-системы \mathcal{C}(\underline{\alpha}), очевидно 0, т.к. в определении empty { } нет никаких внутренних имён. Сложность же коллектора \mathcal{C}(\underline{\omega})=1, поскольку в его структуру входит единственное имя empty. Когда мы в следующей статье создадим более сложные объекты, мы сможем проиллюстрировать данное определение более подробно. В целом, сложность показывает, сколько надо разных понятий, чтобы сконструировать тот или иной объект.

Если определена сложность, то автоматом получаем определение простоты. Число \mathcal{S}(x)=-\mathcal{C}(x) будем называть ПРОСТОТОЙ x. Что, в общем-то, логично: чем больше сложность, тем меньше простота, и сходятся они в точке \mathcal{S}(\underline{\alpha})=\mathcal{C}(\underline{\alpha})=0.

Вернёмся к миллиарду велосипедов. Чтобы отразить их огромность, введём понятие ОБЪЁМА. Объём \mathcal{V}(x) аналогичен сложности, только вместо количества уникальных имён берём их общее число. Отсюда \mathcal{V}(\underline{\alpha})=0, \mathcal{V}(\underline{\omega})=3. Понятие объёма соответствует т.н. колмогоровской сложности в традиционной математике.

По аналогии с простотой, введём противоположную к объёму характеристику: АСКЕТИЧНОСТЬ \mathcal{A}(x) = -\mathcal{V}(x).

РАЗЛИЧИЕ

А и Б похожи, а вот А и К, наоборот, отличаются. Подобная фразеология может встретиться в рассуждениях на абсолютно любую тему. Сходство и различие - одни из самых интуитивно понятных вещей, но в нейроматематике им надо дать формальное определение. Начнём с различия.

Если x и y - произвольные объекты, то РАЗЛИЧИЕ \mathcal{O}(x,y) между ними - это функция двух аргументов, на выходе которой простейший алгоритм \underline{z} такой, что \underline{z}(x) = y. То есть различие возвращает простейший объект, преобразующий x в y. Чем более непохожи x и y, тем более сложным будет преобразование.

Приведём несколько примеров. Пусть будет различие между \underline{\alpha} и \underline{\omega}. Чтобы сделать из примитива (нуль-системы) коллектор, к нему надо приписать x_1 и x_2. Итого \mathcal{O}(\underline{\alpha}, \underline{\omega})=\{x_1; x_2\}. Другой пример (знак числа верхним индексом): \mathcal{O}(1^+, 2^+)=1^+, поскольку простейший способ сделать из единицы двойку - прибавить к ней единицу.

ИСТИНА И РАВЕНСТВО (ОПРЕДЕЛЕНИЕ)

Истина и равенство - широко используются в математике, при этом строгого определения этих понятий нет, нет даже статьи в математической энциклопедии. Что не мешает всем математикам их использовать: предполагается, что любой человек понимает их одинаково. Однако нейроматематика значительно более доскональна. А также она располагает всеми средствами, чтобы в своих рамках эти определения дать.

Пусть рассматривается (записан в память) некоторый объект x. Пусть есть некоторый алгоритм (a.k.a. высказывание) t, на выход которого подана память. После исполнения t его результат записывается в память как y. Если различие \mathcal{O} (x,y), т.е. простейшее преобразование между ними, пусто, то высказывание t будет называться ИСТИНОЙ, а сами объекты x и y будем называть РАВНЫМИ. В противном случае t называется ЛОЖЬЮ.

Приведём пример. Пусть x это некоторый коллектор, записанный, как было выше:

x

Пусть t есть высказывание \{x_2 справа\}, которое, исходя из сказанного выше, порождает такой же коллектор, но с противоположными полюсами, обозначенный как y. К сожалению, преобразование между x и y не пусто, т.к. x надо повернуть, чтобы получить y. По этой причине, t не истинно, т.е. ложно. Соответственно, x \neq y. А вот t' \{x_2 слева\} порождает y' такой, что \underline{\alpha}(x)=y', поэтому t' истинно и x=y'.

ПРОТИВОПОЛОЖНОСТЬ (ОПРЕДЕЛЕНИЕ)

Мы полагаем естественным, что истина и ложь противоположны друг другу. Но какой у этого смысл? ПРОТИВОПОЛОЖНОСТЬ \overline{\alpha} означает, что:

  • есть всего два объекта с нужными свойствами: x_1 и x_2 (противоположная пара)

  • есть всего одно преобразование f, изменяющее x_1 и x_2

  • свойства f таковы: f(x_1) = x_2, f(x_2) = x_1

Проверим, что истина и ложь действительно противоположны.

  • есть всего два истинностных объекта: истина T и ложь F

  • есть всего одно преобразование истинности: отрицание \neg(x)

  • свойства отрицания: \neg(T)=F, \neg(F)=T

Проверим, что направления на доске действительно противоположны.

  • есть всего два направления: положительное + и отрицательное -

  • есть всего одно преобразование направлений: поворот \Pi

  • свойства поворота: \Pi(+)=-, \Pi(-)=+

Проверим, что ориентации на доске действительно противоположны.

  • есть всего два ориентации: первичная p и вторичная s

  • есть всего одно преобразование ориентаций: поворот \Pi

  • свойства поворота: \Pi(p)=s, \Pi(s)=p

Отметим важное свойство противоположности. Объекты противоположной пары обладают связкой друг с другом, так что определив x_1, автоматом получаем x_2 через приставку "не": истина - это которая не ложь, а плюс - это тот, который не минус. Кроме этого, сама противоположность не может быть определена только через x_1 или x_2, но имеет смысл только в связи с противоположной парой.

ИСТИННОСТЬ И ПРОТИВОПОЛОЖНОСТЬ (СТРУКТУРА)

ИСТИННОСТЬ \mathbb{B} будем использовать как собирательный термин для истины и лжи.

Рассмотрев значения истинности, можно увидеть, что они атомарны: ни T, ни F не содержат внутри себя другие элементы. Иными словами, с точностью до структуры, они эквивалентны \underline{\alpha}. Поскольку структура идентична, различия между \underline{\alpha}, с одной стороны, и T/F, с другой, должны быть информационными.

У нас уже задан объект, в структуру которого укладывается \mathbb{B}. Этот объект - коллектор, который аналогично имеет противоположную пару (полюса). Различием между \underline{\alpha} и T или F является направление + или -, соответственно. Таким образом, по структуре и информации истинность эквивалентны полюсам коллектора: T\equiv x_1, F\equiv x_2.

В отличие от значений истинности, которых два, противоположность только одна, и она задана для некоторой противоположной пары. По данным свойствам, противоположность \overline{\alpha} эквивалентна базису коллектора: \overline{\alpha}\equiv x_0.

Наконец, отрицание. Как было показано выше, отрицание обладает для истинности ровно теми же свойствами, что поворот - для полюсов контракта. По этой причине, мы можем записать: \neg\equiv\Pi. Однако надо отметить, что структура самого поворота ещё не введена, т.к. пока не определены все нужные объекты - это будет сделано в дальнейших статьях.

Итоги

Во второй статье была описана стратегия:

  1. Предложить модель идеального мира.

  2. В рамках этой модели, построить с нуля нужные объекты.

  3. Показать эквивалентность этих объектов объектам "обычной" математики.

  4. Показать преимущества и новые возможности этого подхода.

Как было запланировано выше, мы выполнили эти шаги:

  1. Предложили модель памяти и времени идеального мира (доска и маркер).

  2. Сконструировали с нуля, внутри этой модели, объекты (примитив и коллектор).

  3. Показали эквивалентность частей коллектора истинностным значениям и противоположности, показав структуру последних.

  4. Показали преимущества подхода, предъявив определения объектов, строго не заданных в традиционной математике - истина и равенство.

В дальнейшей работе будет повторяться этот паттерн:

  • Конструирование новых объектов с использованием введённых ранее.

  • Эквивалентность этих конструкций объектам математики.

  • Формализация важных терминов, ранее не определённых строго.

С каждой итерацией, количество строго определённых объектов будет расти, постепенно формируя основу, чтобы формализовать всё, что нам понадобится.

Итого, в рамках нейроматематики появляется возможность дать строгие определения многим понятиям, которые в обычной математике трактуются интуитивно понятными и не имеют определения. Предъявление этих определений ничего не ломает, т.к. они не противоречат уже используемому интуитивному пониманию. Однако, как будет показано позднее, эти и другие определения дают большие возможности как для развития математики, так и для для создания ИИ нового поколения.

ФОРАОН: продолжение

Описав доску и маркер, мы легализовали графическую нотацию ФОРАОН, и задали первые два объекта - примитив и коллектор. В четвёртой статье мы опишем остальные объекты, задающиеся графической нотацией - которых совсем немного, а именно четыре. Вместе с уже заданными, этих объектов, в общем, достаточно, чтобы сделать всё остальное. Не переключайтесь!

Литература

[1] Герасимов А.С. Курс математической логики и теории вычислимости. С-Пб. 2011.

[2] Математическая энциклопедия в 5 томах. Москва. 1982.

Источник

Теги

Категория

Новости

Дата

  • 09.10.25 08:23 pHqghUme

    (select(0)from(select(sleep(15)))v)/*'+(select(0)from(select(sleep(15)))v)+'"+(select(0)from(select(sleep(15)))v)+"*/

  • 09.10.25 08:24 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:24 pHqghUme

    e

  • 09.10.25 08:24 pHqghUme

    can I ask you a question please?-1 waitfor delay '0:0:15' --

  • 09.10.25 08:25 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:25 pHqghUme

    e

  • 09.10.25 08:25 pHqghUme

    e

  • 09.10.25 08:25 pHqghUme

    e

  • 09.10.25 08:25 pHqghUme

    can I ask you a question please?9IDOn7ik'; waitfor delay '0:0:15' --

  • 09.10.25 08:26 pHqghUme

    can I ask you a question please?MQOVJH7P' OR 921=(SELECT 921 FROM PG_SLEEP(15))--

  • 09.10.25 08:26 pHqghUme

    e

  • 09.10.25 08:27 pHqghUme

    can I ask you a question please?64e1xqge') OR 107=(SELECT 107 FROM PG_SLEEP(15))--

  • 09.10.25 08:27 pHqghUme

    can I ask you a question please?ODDe7Ze5')) OR 82=(SELECT 82 FROM PG_SLEEP(15))--

  • 09.10.25 08:28 pHqghUme

    can I ask you a question please?'||DBMS_PIPE.RECEIVE_MESSAGE(CHR(98)||CHR(98)||CHR(98),15)||'

  • 09.10.25 08:28 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:28 pHqghUme

    can I ask you a question please?'"

  • 09.10.25 08:28 pHqghUme

    @@olQP6

  • 09.10.25 08:28 pHqghUme

    (select 198766*667891)

  • 09.10.25 08:28 pHqghUme

    (select 198766*667891 from DUAL)

  • 09.10.25 08:30 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:33 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:34 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:34 pHqghUme

    if(now()=sysdate(),sleep(15),0)

  • 09.10.25 08:35 pHqghUme

    e

  • 09.10.25 08:36 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:36 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:37 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:37 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:37 pHqghUme

    e

  • 09.10.25 08:37 pHqghUme

    e

  • 09.10.25 08:40 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:40 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:41 pHqghUme

    e

  • 09.10.25 08:41 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:42 pHqghUme

    can I ask you a question please?

  • 09.10.25 08:42 pHqghUme

    is it ok if I upload an image?

  • 09.10.25 08:42 pHqghUme

    e

  • 09.10.25 11:05 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

  • 09.10.25 11:05 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

  • 09.10.25 11:05 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

  • 09.10.25 11:05 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

  • 11.10.25 04:41 luciajessy3

    Don’t be deceived by different testimonies online that is most likely wrong. I have made use of several recovery options that got me disappointed at the end of the day but I must confess that the tech genius I eventually found is the best out here. It’s better you devise your time to find the valid professional that can help you recover your stolen or lost crypto such as bitcoins rather than falling victim of other amateur hackers that cannot get the job done. ADAMWILSON . TRADING @ CONSULTANT COM / WHATSAPP ; +1 (603) 702 ( 4335 ) is the most reliable and authentic blockchain tech expert you can work with to recover what you lost to scammers. They helped me get back on my feet and I’m very grateful for that. Contact their email today to recover your lost coins ASAP…

  • 11.10.25 10:44 Tonerdomark

    A thief took my Dogecoin and wrecked my life. Then Mr. Sylvester stepped in and changed everything. He got back €211,000 for me, every single cent of my gains. His calm confidence and strong tech skills rebuilt my trust. Thanks to him, I recovered my cash with no issues. After months of stress, I felt huge relief. I had full faith in him. If a scam stole your money, reach out to him today at { yt7cracker@gmail . com } His help sparked my full turnaround.

  • 12.10.25 01:12 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

  • 12.10.25 01:12 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

  • 12.10.25 19:53 Tonerdomark

    A crook swiped my Dogecoin. It ruined my whole world. Then Mr. Sylvester showed up. He fixed it all. He pulled back €211,000 for me. Not one cent missing from my profits. His steady cool and sharp tech know-how won back my trust. I got my money smooth and sound. After endless worry, relief hit me hard. I trusted him completely. Lost cash to a scam? Hit him up now at { yt7cracker@gmail . com }. His aid turned my life around. WhatsApp at +1 512 577 7957.

  • 12.10.25 21:36 blessing

    Writing this review is a joy. Marie has provided excellent service ever since I started working with her in early 2018. I was worried I wouldn't be able to get my coins back after they were stolen by hackers. I had no idea where to begin, therefore it was a nightmare for me. However, things became easier for me after my friend sent me to [email protected] and +1 7127594675 on WhatsApp. I'm happy that she was able to retrieve my bitcoin so that I could resume trading.

  • 13.10.25 01:11 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

  • 13.10.25 01:11 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

  • 14.10.25 01:15 tyleradams

    Hi. Please be wise, do not make the same mistake I had made in the past, I was a victim of bitcoin scam, I saw a glamorous review showering praises and marketing an investment firm, I reached out to them on what their contracts are, and I invested $28,000, which I was promised to get my first 15% profit in weeks, when it’s time to get my profits, I got to know the company was bogus, they kept asking me to invest more and I ran out of patience then requested to have my money back, they refused to answer nor refund my funds, not until a friend of mine introduced me to the NVIDIA TECH HACKERS, so I reached out and after tabling my complaints, they were swift to action and within 36 hours I got back my funds with the due profit. I couldn’t contain the joy in me. I urge you guys to reach out to NVIDIA TECH HACKERS on their email: [email protected]

  • 14.10.25 08:46 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

  • 14.10.25 08:46 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

  • 14.10.25 08:46 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

  • 15.10.25 18:07 crypto

    Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.

  • 15.10.25 21:52 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

  • 15.10.25 21:52 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

  • 17.10.25 20:17 tyleradams

    As time passes, there are an increasing number of frauds involving Bitcoin and other cryptocurrencies. Although there are many individuals who advertise recovering money online, people should use caution in dealing, especially when money is involved. You can trust NVIDIA TECH HACKERS [[email protected]], I promise. They are the top internet recovery company, and as their names indicate, your money is reclaimed as soon as feasible. My bitcoin was successfully retrieved in large part thanks to NVIDIA TECH HACKERS. Ensure that you get top-notch service; NVIDIA TECH HACKERS provides evidence of its work; and payment is only made when the service has been completed to your satisfaction. Reach them via email: [email protected] on google mail

  • 17.10.25 20:20 lindseyvonn

    Have you gotten yourself involved in a cryptocurrency scam or any scam at all? If yes, know that you are not alone, there are a lot of people in this same situation. I'm a Health Worker and was a victim of a cryptocurrency scam that cost me a lot of money. This happened a few weeks ago, there’s only one solution which is to talk to the right people, if you don’t do this you will end up being really depressed. I was really devastated until went on LinkedIn one evening after my work hours and i saw lots of reviews popped up on my feed about [email protected], I sent an email to the team who came highly recommended - [email protected] I started seeing some hope for myself from the moment I sent them an email. The good part is they made the entire process stress free for me, i literally sat and waited for them to finish and I received what I lost in my wallet

  • 17.10.25 20:22 richardcharles

    I would recommend NVIDIA TECH HACKERS to anyone that needs this service. I decided to get into crypto investment and I ended up getting my crypto lost to an investor late last year. The guy who was supposed to be managing my account turned out to be a scammer all along. I invested 56,000 USD and at first, my reading and profit margins were looking good. I started getting worried when I couldn’t make withdrawals and realized that I’ve been scammed. I came across some of the testimonials that people said about NVIDIA TECH HACKERS and how helpful he has been in recovering their funds. I immediately contacted him in his mail at [email protected] so I can get his assistance. One week into the recovery process the funds were traced and recovered back from the scammer. I can't appreciate him enough for his professionalism.

  • 17.10.25 20:23 stevekalfman

    If you need a hacker for scam crypto recovery or mobile spy access remotely kindly reach out to [email protected] for quick response, I hired this hacker and he did a nice job. before NVIDIA TECH HACKERS, I met with different hacker's online which turns out to be scam, this NVIDIA TECH HACKERS case was different and he is the trusted hacker I can vote and refer.

  • 17.10.25 21:42 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

  • 17.10.25 21:42 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

  • 17.10.25 21:42 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

  • 21.10.25 08:39 debby131

    Given how swiftly the cryptocurrency market moves, losing USDT may be a terrifying and upsetting experience. Whether you experienced a technical problem, a transaction error, or were the victim of fraud, it is important to understand the potential recovery routes. Marie can assist you in determining the specific actions you can take to attempt to regain your lost USDT when you need guidance and clarification. You can reach her via email at [email protected] and WhatsApp at +1 7127594675.

  • 21.10.25 11:45 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

  • 21.10.25 11:45 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

  • 22.10.25 04:48 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.

  • 22.10.25 07:36 donnacollier

    HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM Hello everyone l’m by name Donna collier I live in urbandale 3 weeks ago was the darkest days of my life, i invested my hard earned money the sum of $123,000 into a crypto currency platform I was introduced to by a friend I met online everything happen so fast I was promised 300% of return of investment when it was time for me to cash out my investment and profit the platform was down I was so diversitated confused and tried to end it all then I came across upswing Ai a renowned expert in crypto currency and digital assets recovery at first it seem impossible after taking up my case within the the next 48 hours they where able to track down those fraud stars and recover my money I can’t recommend them enough to any one facing likewise change I will recommend you contact upswing Ai on Contact Details: WhatsApp +,1,2,0,2,8,1,0,1,4,0,7 E m a i l @Upswing-ai.com Website https: // u psw ing-ai. com/ platform /

  • 22.10.25 11:59 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

  • 22.10.25 11:59 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

  • 22.10.25 16:31 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 $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.

  • 23.10.25 01:52 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

  • 23.10.25 01:52 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

  • 23.10.25 15:47 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 $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.

  • 23.10.25 21:43 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

  • 23.10.25 21:43 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

  • 24.10.25 06:08 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 06:40 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

  • 24.10.25 06:40 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

  • 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

    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

  • 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

    *HOW TO GET BACK YOUR STOLEN BITCOIN FROM SCAMMERS* ⭐️⭐️⭐️⭐️⭐️ Hello everyone, I can see a lot of things going wrong these last few days of investing online and getting scammed. I was in your shoes when I invested in a bogus binary option and was duped out of $87,000 in BTC, but thanks to the assistance of NVIDIA TECH HACKERS. They helped me get back my BTC. I didn’t trust the Hackers at first, but they were recommended to me by a friend whom I greatly respect. I received my refund in two days. I must recommend NVIDIA TECH HACKERS they are fantastic. 📧 [email protected]

  • 25.10.25 00:50 stevekalfman

    If you ever need hacking services, look no further. I found myself in a difficult situation after losing almost $510,000 USD in bitcoin. I was distraught and had no hope of survival because i lost my life savings to this scam, I had no chance of recovering my investment. Until i came across an article on google about ([email protected]). A real-life recovery expert, everything changed completely after contacting him and explaining my ordeal to him and he quickly stepped in and assisted me in recovering 95% of my lost funds. They guarantee their clients and i got the highest level of happiness their services are highly recommended. so I’m putting this here for anyone who require their services too" Email: [email protected]

  • 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

    I suffered a huge money blow when $80,000 slipped away in a bogus crypto plot. It all looked great at first. Then I went to pull out my gains, and poof—my account was gone. I kept telling the cops about it, but they did zip. I felt shattered and lost. That's when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed clear steps, sharp know-how, and real drive to fix it. They tracked my missing cash step by step and pushed hard till they got it back. I swear, I figured it was a lost cause. Their straight-up work and trust brought back my calm. If a scam stole your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 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

Для участия в Чате вам необходим бесплатный аккаунт pro-blockchain.com Войти Регистрация

Похожие новости

Есть вопросы?
С вами на связи 24/7
Поддержка 24/7 Help Icon
Менеджер онлайн Help Icon
Help Icon