Francisco Angulo De Lafuente, Vladimir Veselov, Richard Goodman
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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 by Richard (Apoth3osis) using Lean 4 and Mathlib. This formalization provides 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 (validating the 92.19% claim), and Physical Unclonable Function (PUF) distinguishability witnesses. The formalization is publicly available with interactive proof visualizations. Vladimir Veselov's hierarchical number system theory explains why early-round information contains predictive power. Comparative analysis demonstrates that while prior algorithmic approaches achieved only 1-3% early-abort rates, our thermodynamic approach achieves 88-92%. 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-now with mathematical rigor at the gold standard of formal verification.
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