Mnemosyne: Post-Quantum Distributed AI Infrastructure via Physical Security Barriers, Speculative Consensus, and Proof-of-Useful-Work on Heterogeneous Edge Networks

Mnemosyne: Post-Quantum Distributed AI Infrastructure via Physical Security Barriers, Speculative Consensus, and Proof-of-Useful-Work on Heterogeneous Edge Networks Overview Mnemosyne is a theoretical framework and system design for running large language model (LLM) inference on heterogeneous edge devices — from Raspberry Pi to high-end workstations — with privacy guarantees that remain valid even after quantum computers break all existing cryptographic assumptions. This paper presents 14 original theorems and 3 new network protocols, spanning five interconnected layers: Layer 1 — OS-Level Memory Management (Ch. 3. 1) Formalizes a 6-tuple system model covering semantic-aware LRU page replacement, zero-copy mmap, and delta encoding. Defines four system invariants verified via TLA+ specification. Layer 2 — Information-Theoretic Compression (Ch. 3. 2–3. 4, Theorems 5. 1–5. 3) Proves that delta encoding of LLM embedding sequences achieves a lower differential entropy bound when adjacent vector correlation ρ > 0. 5. Static analysis of LLaMA-2-7B confirms ρ ≈ 0. 85, yielding a theoretical compression gain of ~10. 88× over FP16. Full invertibility and floating-point stability bounds are proven. Layer 3 — Thermodynamic Privacy Guarantee (Ch. 5–6, Theorems 7. 1–8. 4) The core contribution of this paper. Mnemosyne's privacy guarantee is grounded in Landauer's Principle and the Second Law of Thermodynamics, not computational hardness assumptions. Theorem 8. 3 proves that exhaustive reconstruction of compressed embeddings requires a minimum energy of 10^38, 778 joules — approximately 10^38, 709× the total energy of the observable universe. This makes Mnemosyne the first federated learning system, to our knowledge, whose privacy bound is elevated to the level of a physical law. The system is formally characterized as an Inverse Maxwell's Demon: it actively amplifies entropy to make information reconstruction thermodynamically infeasible, rather than computationally difficult. Layer 4 — Distributed Consensus (Ch. 7, Theorems 9. 1–9. 2) Proves the existence and feasibility of a Global Decentralized Compute Grid (GDCG) across heterogeneous hardware. Introduces a Byzantine Fault-Tolerant (BFT) extension of the MESI protocol with three new states (RS, PF, EC), enabling zero-copy memory sharing across devices. Theorem 9. 2 proves that the system-recognized Modified state exists in at most one node among all nodes (including Byzantine nodes) at any time. Layer 5 — Economic Incentive Model (Ch. 7. 4, Protocol 2) Defines Proof-of-Useful-Work (PoUW), a five-dimensional incentive function replacing wasteful Proof-of-Work mining with verifiable AI inference contributions. Projected annual reward: USD 100–500 per edge device. Key Contributions First federated learning system with privacy guarantee grounded in the Second Law of Thermodynamics 14 original theorems spanning information theory, thermodynamics, distributed systems, and formal verification 3 new network protocols (BFT-MESI extension, PoUW, QClock consensus) Formal verification via TLA+ and Z3 SMT Solver Minimum hardware requirement: 8 GB RAM (ARM Cortex-A76 class), enabling LLaMA-2-7B inference on commodity edge devices Keywords Edge AI · LLM Inference · Landauer's Principle · Post-Quantum Security · Delta Encoding · Product Quantization · Byzantine Fault Tolerance · Distributed Systems · Information Thermodynamics · Maxwell's Demon · Proof-of-Useful-Work · Federated Learning