This preprint formalizes the QSOLKCB/QEC v155.x release arc as a deterministic framework for detecting, classifying, localizing, and proving resistance to identity drift in hash-bound proof artifacts. The v155.x arc extends the v154.x multi-scale invariant compression baseline into a temporal integrity layer: v155.0 introduces deterministic DecayCheckpoint and DecayCheckpointSet artifacts for exact hash-position drift detection. v155.1 introduces DecayThresholdContract and DigitalDecaySignature artifacts for deterministic integer-threshold decay classification. v155.2 introduces subsystem-localized entropy drift receipts across layer, router, mask, shift, and readout receipt families, aggregated into EntropyDriftReceipt. v155.3 introduces DecayResistanceProof, binding clean entropy receipts and deterministic replay-proof hashes into a replay-safe resistance proof artifact. Across the arc, QEC enforces:- canonical JSON serialization- stable SHA-256 hashing- deterministic ordering- self-hash exclusion- explicit failure semantics- exact integer scoring- replay-safe proof construction- recomputed validation The framework is intentionally non-probabilistic. “Decay” is defined as exact hash divergence at explicit artifact positions rather than heuristic anomaly scoring or probabilistic entropy estimation. This work concerns deterministic proof receipts, replay validation, and invariant-driven computation in the QSOLKCB/QEC software system and release lineage. It does not claim to implement physical-layer quantum error correction, stabilizer decoding, syndrome processing, thermodynamic entropy, or quantum hardware control.
This preprint formalizes the QSOLKCB/QEC v155.x release arc as a deterministic framework for detecting, classifying, localizing, and proving resistance to identity drift in hash-bound proof artifacts. The v155.x arc extends the v154.x multi-scale invariant compression baseline into a temporal integrity layer: v155.0 introduces deterministic DecayCheckpoint and DecayCheckpointSet artifacts for exact hash-position drift detection. v155.1 introduces DecayThresholdContract and DigitalDecaySignature artifacts for deterministic integer-threshold decay classification. v155.2 introduces subsystem-localized entropy drift receipts across layer, router, mask, shift, and readout receipt families, aggregated into EntropyDriftReceipt. v155.3 introduces DecayResistanceProof, binding clean entropy receipts and deterministic replay-proof hashes into a replay-safe resistance proof artifact. Across the arc, QEC enforces:- canonical JSON serialization- stable SHA-256 hashing- deterministic ordering- self-hash exclusion- explicit failure semantics- exact integer scoring- replay-safe proof construction- recomputed validation The framework is intentionally non-probabilistic. “Decay” is defined as exact hash divergence at explicit artifact positions rather than heuristic anomaly scoring or probabilistic entropy estimation. This work concerns deterministic proof receipts, replay validation, and invariant-driven computation in the QSOLKCB/QEC software system and release lineage. It does not claim to implement physical-layer quantum error correction, stabilizer decoding, syndrome processing, thermodynamic entropy, or quantum hardware control.
This work introduces QEC, a deterministic, replay-safe reasoning system for quantum error correction and invariant-driven computation. Unlike conventional adaptive systems that rely on stochastic exploration, QEC operates as a deterministic reasoning layer over system evolution, producing proof-carrying state transitions that are fully reproducible and verifiable. The system replaces probabilistic optimization with a structured pipeline of invariant detection, deterministic control, memory accumulation, governance, validation, repair reasoning, and invariant-preserving compression. Each stage produces canonical, hash-stable artifacts, ensuring that identical inputs yield byte-identical outputs across environments. QEC reframes failure as a structural phenomenon ("dark states") and introduces deterministic repair through symmetry breaking, validated via counterfactual replay. The system further demonstrates that reasoning itself can be compressed into minimal canonical forms without loss of replay fidelity. Empirical runs over QLDPC Tanner graph simulations demonstrate zero hash divergence across independent executions and compact proof artifacts (~2–5 KB), supporting the feasibility of deterministic reasoning with proof in complex systems. This work establishes a new paradigm: execution → reasoning → proof
This artifact documents a formally verified optimization in the QSOL-IMC Quantum Error Correction (QEC) framework (v68.4.1). The optimization exploits the algebraic identity that belief propagation decoding using uniformly reweighted min-sum with ρ=1.0 is bitwise identical to baseline min-sum decoding under IEEE 754 double-precision arithmetic. This invariant is proven analytically, validated across all decoder schedules, and confirmed via bitwise equality tests. The optimization removes redundant benchmark computation by reusing baseline results for the ρ=1.0 case without altering outputs, convergence behavior, or test coverage. A secondary improvement eliminates repeated reconstruction of derived data structures through deterministic precomputation. The full test suite (3779 tests) remains unchanged and passes completely. The optimization reduces preview sweep runtime by approximately 43% and overall runtime by approximately 7.6%. This artifact includes formal proof, execution-path validation, safety analysis, and reproducibility guarantees, and serves as a reference for invariant-driven optimization in deterministic QEC benchmarking systems.
QECTOR-Decoder-v3 is a high-throughput, multi-backend quantum error correction (QEC) decoding suite implemented in compiled native Rust with native Python bindings via PyO3. Designed for high-performance computing (HPC) environments, low-latency quantum hardware pipelines, and offline zero-egress research, the engine bridges theoretical stabilizer formalisms with hardware-level decoding execution. This archival release includes the formal technical specification, architectural reference manual, cryptographic proof suite, and reproducible Linux/x86_64 verification harness for version 1.0.0. Key Architectural Components Native Compiled Core: High-performance Rust backend exposing zero-copy FFI bindings to Python (CPython 3.9–3.13) via PyO3. Multi-Backend Decoding Library: Includes implementations of Blossom Minimum Weight Perfect Matching (MWPM), FastUnionFind, Belief Propagation with Ordered Statistics Decoding (BP-OSD), Belief-Matching, and an AutoDecoder multi-tier fallback architecture. Hardware Interoperability: Drop-in compatibility with standard QEC formats and frameworks (Stim, PyMatching, Sinter) with Rayon multi-threading and CUDA/OpenCL acceleration hooks. Model Context Protocol (MCP) Integration: Native stdio JSON-RPC tool surfaces supporting automated syndrome decoding, check-matrix validation, and real-time telemetry profiling. Included Proof Artifacts & Verification Bundle This release contains the complete, cryptographic proof suite validating numerical correctness, memory layout, and statistical bounds: certified_proof.json & certified_proof.json.sha256: Tamper-evident execution logs confirming 100% syndrome faithfulness (H⋅c=s) across all evaluation checkpoints. wilson_interval.png / .svg: Exact 95% Wilson score confidence interval statistical sweeps across code distance ranges (d=3 through d=7). syndrome_faithfulness.png / .svg: High-resolution visual parity validation and check-matrix verification charts. workspace_strides.png / .svg: Cache-line memory alignment and SIMD stride profiling diagnostics. certified_report.pdf & certified_report.md: Formal verification report and reproduction methodology. verify_artifacts.py & test_qector_decoder_v3_proofs_linux.py: Automated Python/Linux validation scripts to independently recompute and verify SHA-256 signatures and artifact integrity. Reproduction & Verification To verify the included artifact bundle locally: Bash python3 verify_artifacts.py python3 test_qector_decoder_v3_proofs_linux.py Licensing & Metadata License: PolyForm Noncommercial / Proprietary Commercial (iD01t Productions) PyPI Distribution: qector-decoder-v3 Keywords: Quantum Error Correction, Surface Codes, Rust, PyO3, Stabilizer Decoders, MWPM, BP-OSD, Union-Find, Fault-Tolerant Quantum Computing, Model Context Protocol (MCP). License terms. The software, scripts, and code in this record (including the Python verification scripts and the inlined pure-Python ground truth) are licensed under the PolyForm Noncommercial License 1.0.0: noncommercial use only. Any commercial use requires a separate commercial license from iD01t Productions. Documentation, reports, and figures in this record are made available under the Creative Commons Attribution 4.0 International License (CC-BY-4.0) with credit to Guillaume Lessard / iD01t Productions. Copyright (c) 2026 Guillaume Lessard / iD01t Productions. All rights reserved except as expressly granted above.
This compendium presents four revised studies of deterministic computation, reusable intermediate results, and transformation invariants in belief-propagation diagnostics and quantum error-correction software. It connects earlier QSOL-IMC preprints with commit-pinned QEC source snapshots, reproducible experiments, and machine-checked mathematical models. The four studies examine baseline equivalence between min-sum decoding and unit-weight uniformly reweighted belief propagation; trace-indexed reuse of sign vectors and CRC32 values; the interaction of clipping, damping, freezing, and ternary projection in decoder transformation pipelines; and the interpretation of local “dark-state” observables in belief-propagation traces. The deposit contains four revised papers, editable manuscript sources, a dependency-free Lean 4 project, source snapshots, validation scripts, measured results, proof logs, provenance records, and integrity manifests. The formalization comprises 43 compiled theorem declarations. Empirical validation includes 576 paired decoder cases, 80 cached-versus-inline diagnostic comparisons, a reproduced reduction from 81 to 20 sign computations, 204 selected historical tests, and 18 synthetic dark-state scenario runs. The analysis also documents counterexamples and boundary conditions involving CRC32 collisions, cache provenance, source mutation, damping, NaN handling, transformation order, and the distinction between observed local stability and safe computational reuse. The Lean proofs establish properties of the stated exact mathematical models. They do not constitute a complete refinement proof for the Python/NumPy implementations or IEEE-754 arithmetic, nor do they establish physical quantum-hardware correctness or justify skipping live-decoder updates. Historical runtime improvements are identified as previously reported results, separate from the measurements reproduced in this deposit.
Canon² — Trust Layer Research Archive. Ed25519 is the cryptographic foundation of the Lume ecosystem. Every certificate in the Trust Layer's Certificate Fabric, every signal in the Synthetic Organism Runtime's Signal Bus, every state commitment in the deterministic transition graph, and every governance authorization in the GUPAS framework is signed with an Ed25519 key and verified through Ed25519 signature validation [16]. The security of the entire ecosystem—identity anchoring, provenance auditing, governance enforcement, and autonomous organism certification—depends on the computational infeasibility of forging Ed25519 signatures. A sufficiently powerful quantum computer running Shor's algorithm [20] would reduce this computational infeasibility to polynomial-time tractability, rendering every certificate, every identity, and every governance authorization in the ecosystem forgeable. I present a complete quantum-resistant cryptographic architecture for the Lume ecosystem that preserves deterministic semantics, certificate continuity, identity persistence, and governance validity throughout the transition from classical Ed25519 to post-quantum signature schemes. The architecture proceeds through three phases: Phase I (Hybrid), in which every signature operation produces a dual signature combining Ed25519 with a NIST-standardized post-quantum scheme (CRYSTALS-Dilithium [17], Falcon [18], or SPHINCS+ [19]); Phase II (PQ-Primary), in which the post-quantum signature becomes the primary verification target and the Ed25519 signature becomes a backward-compatibility fallback; and Phase III (PQ-Native), in which all new certificates, identities, and governance authorizations are issued exclusively under post-quantum signatures. The architecture integrates with Lume [1] through AST-level cryptographic operation canonicalization, with the Trust Layer [3] through certificate fabric upgrades and identity migration protocols, with Lume-V [4] through envelope-constrained cryptographic transitions, with DAIGS [5] through cognitive substrate extensions for cryptographic reasoning, with LDIR [12] through multilingual cryptographic semantic normalization, with SOR [13] through organism identity preservation, and with GUPAS [2] through governance-safe transition policies. I identify and formalize six failure modes specific to cryptographic transition—identity fragmentation, certificate invalidation, hybrid mismatch, PQ signature drift, governance misalignment, and intent inversion—each with defined detection mechanisms and corrective responses. To my knowledge, this paper presents the first complete quantum-resistant cryptographic architecture for a deterministic, certificate-bound natural-language programming ecosystem.
This document presents a formally validated optimization within the QSOL-IMC Quantum Error Correction (QEC) framework (v68.5.0). The optimization exploits a data-level invariant in belief propagation (BP) dynamics diagnostics: sign vectors and their derived CRC32 signatures are pure, deterministic functions indexed solely by trace position. This invariant enables elimination of redundant computation across multiple diagnostic metrics through trace-level precomputation and reuse. The invariant is proven via slice-level equivalence, byte-level identity, and purity arguments, and validated with deterministic instrumentation. The full test suite remains unchanged and passes completely. The optimization reduces redundant sign computations by 75.3% within BP dynamics analysis while preserving bitwise identity, convergence behavior, and reproducibility guarantees. Scope. This document covers invariant validation and diagnostic-layer optimization only. No algorithmic changes to decoding behavior are introduced.