This definitive research memoria presents a comprehensive, mathematically verified paradigm for neural communication with Bitcoin mining Application-Specific Integrated Circuits (ASICs), integrating five complementary frameworks: thermodynamic reservoir computing, hierarchical number system theory, algorithmic analysis, network latency optimization, and machine-checked mathematical formalization. We establish that obsolete cryptocurrency mining hardware exhibits emergent computational properties enabling bidirectional information exchange between AI systems and silicon substrates. The research program demonstrates: (1) reservoir computing with NARMA-10 Normalized Root Mean Square Error (NRMSE) of 0.8661; (2) the Thermodynamic Probability Filter (TPF) achieving 92.19% theoretical energy reduction; (3) the Virtual Block Manager achieving +25% effective hashrate; and (4) hardware universality across multiple ASIC families including Antminer S9, Lucky Miner LV06, and Goldshell LB-Box. A significant contribution is the machine-checked mathematical formalization using Lean 4 and Mathlib, providing unambiguous definitions, machine-verified theorems, and reviewer-proof claims. Key theorems proven include: independence implies zero leakage, predictor beats baseline implies non-independence (the logical core of TPF), energy savings theoretical maximum, and Physical Unclonable Function (PUF) distinguishability witnesses. Vladimir Veselov's hierarchical number system theory explains why early-round information contains predictive power. This work establishes a new paradigm: treating ASICs not as passive computational substrates but as active conversational partners whose thermodynamic state encodes exploitable computational information.

翻译：本研究备忘录提出了一种全面且经过数学验证的范式，用于实现与比特币挖矿专用集成电路（ASIC）的神经通信，该范式整合了五个互补的框架：热力学储备池计算、分层数系理论、算法分析、网络延迟优化以及机器验证的数学形式化。我们证实，过时的加密货币挖矿硬件展现出涌现的计算特性，能够实现人工智能系统与硅基衬底之间的双向信息交换。该研究项目展示了：（1）储备池计算在NARMA-10任务上达到0.8661的归一化均方根误差（NRMSE）；（2）热力学概率滤波器（TPF）实现了92.19%的理论能耗降低；（3）虚拟区块管理器实现了+25%的有效算力；（4）在包括Antminer S9、Lucky Miner LV06和Goldshell LB-Box在内的多个ASIC系列上具有硬件通用性。一项重要贡献是使用Lean 4和Mathlib完成的机器验证数学形式化，提供了明确的定义、机器验证的定理以及可经受严格审查的论断。已证明的关键定理包括：独立性意味着零信息泄露、预测器优于基线意味着非独立性（TPF的逻辑核心）、节能的理论上限，以及物理不可克隆功能（PUF）的可区分性见证。Vladimir Veselov的分层数系理论解释了为何早期轮次的信息包含预测能力。这项工作确立了一个新范式：将ASIC不再视为被动的计算衬底，而是视为活跃的对话伙伴，其热力学状态编码了可利用的计算信息。