Abstract. An agent that inherits a consolidated memory may inherit a constraint that was true when written and has since been withdrawn by a newer authoritative record. Under a scarce verification budget, does the agent recover the withdrawal, and if not, is the resulting stale-consistent decision avoidable without spending more? We model supersession explicitly — historical provenance is immutable; what changes is which record is current — and assign by design the memory's form, the world's state (source current or superseded), and the verification policy at a fixed budget of two records: the agent's own allocation, or the same budget with one slot re-assigned to the critical provenance path or to a random record. With a constraint stated, agents inspected its provenance path in about one episode in five; when that constraint had been superseded, native allocation produced stale-consistent decisions in 77.3%, 74.7% and 74.7% of episodes across a primary run, a fresh-wording replication and a held-out domain. Re-assigning one slot to the critical path raised current-record-consistent decisions by +74.0, +72.7 and +61.3 points, positive in six of six models in each of those runs, and left an already near-ceiling rate unchanged when the record agreed with the memory. The held-out scenario was later found to contain a temporal inconsistency; a robustness replication with one sentence corrected, deposited externally before execution, gave +73.3 points (positive in 5 of six models, the sixth at a native missed-path rate of zero) and is reported alongside the original. The intervention uses knowledge of the critical path and is not a scheduler; it quantifies how much of the stale-consistent decision rate is removed by the bundled same-budget policy that guarantees inspection of the critical provenance path: the effect approaches the native missed-path rate in the primary, replication and corrected held-out runs. Memory systems may need freshness or supersession signals separate from relevance. Version notes (v2). Version 2 clarifies the operational interpretation of the decision outcome and corrects the characterization of the native missed-path rate, previously described as a structural ceiling. No experimental data, effect estimates, figures, or same-budget policy-effect estimates changed. In detail: the outcome Y is stated as an operational endpoint (whether the final action follows the direction positively approved by the current authoritative record) and described as a stale-consistent decision rather than an unconditional error; the quantity 1 - Pr(V=1 | native) is renamed the native missed-path rate and treated as a descriptive reference, with the assumption-free maximum of the effect stated as the native stale-consistent rate; the estimand is described as the effect of the bundled same-budget forced-critical policy; an outcome-construct limitation and a forensic appendix (per-run V x Y tables and the forced-critical residual, every count generated from the stored episode files) are added; several statements of the Results, Discussion and Limitations are aligned with the appendices and the recorded execution structure (the design-limited random-record control no longer appears in the conclusions; the source-agreement comparison is described as near ceiling; the attribution of the original held-out gap is labelled post hoc; the intervention is described throughout as a bundled, experimentally assigned same-budget policy, with the batched execution order and un-pinned provider aliases disclosed as an interpretive assumption). The scientific content otherwise remains the author's frozen canonical version 1.1 (2026-08-26). Every number in the paper is generated from the raw episode files by the included generator and verified by the included audit scripts. Version 1 remains available unchanged under this record's concept DOI. Data and code availability. All 5,400 confirmatory episode files (exact prompts, raw responses, parsed objects, deterministic scores) and the 48 labelled pilot episodes, the frozen specification packages with SHA256 manifests and OpenTimestamps proofs (Bitcoin blocks 964062 and 964064), the registration records, the frozen analysis scripts with their committed outputs, independent recomputation scripts with outputs, the runners, and the generator and audit scripts are in paper2-data-and-code-v2.zip (README inside). Re-running every analysis and rebuilding the paper requires only Python 3.12 and a TeX distribution; re-running the experiments requires provider API keys, which are not included. Evidence / prospective-specification statement. For the primary run, the fresh-wording replication and the original held-out run, the complete specification was frozen, hashed, committed and cryptographically timestamped (OpenTimestamps, 2026-08-25 23:05:06 UTC) before the first confirmatory model call (23:06:42 UTC); the package was deposited to OSF after the runs (project axsnm, files 75kaw and 8wes5) and verified against the pre-run manifest hash-for-hash. This deposit is an archival record, not a preregistration. For the corrected held-out robustness replication, the complete specification was deposited to OSF (file hdm75) and verified byte-for-byte before execution; its success criteria were fixed in advance and could have failed. Zero amendments were made to any package. Two self-found defects are disclosed with their size in the paper (a temporal inconsistency in the original held-out scenario; a design limitation of the forced-noncritical control). AI assistance. See the statement in the paper's back matter: the author used Anthropic's Claude (principally through Claude Code) for design critique, planning, implementation and execution of the runners, analysis and audit tooling, drafting, editing, simulated adversarial review and release engineering, and OpenAI's ChatGPT for design critique, interpretation discussion, manuscript critique, simulated adversarial review, and publication and release planning. The author is responsible for the research question, the decision to run each experiment, interpretation, claims, publication decisions and correctness. No model is an author; the six models studied are experimental subjects. Suggested citation. Nakayashiki, K. (2026). When Stale Constraints Go Unchecked: Budgeted Verification Failures in Inherited Agent Memory (v2). Zenodo. https://doi.org/10.5281/zenodo.22117197 Relation to prior work. This paper tests the case that the author's earlier paper, Verification Allocation in Inherited Agent Memory: Provenance Availability Is Not Provenance Use (doi:10.5281/zenodo.22084498), explicitly left untested; it reuses that paper's instrument with a different design-assigned variable, different data and a different outcome.
📄 TOPO-2026: Full Paper Summary 🎯 Core Thesis TOPO-2026 transforms AI from a stochastic, forgetting machine into a deterministic, permanent learning machine. For 37 years, catastrophic forgetting has been accepted as inevitable. TOPO-2026 eliminates it through mathematical guarantees, not probabilistic hopes. 🔑 The 26-Year Journey Period Domain Principle Result 1998-2002 Neuroimaging (fMRISTAT) Fix sparse reference 3 df → 112 df 2026 Number Theory First 6 primes RH Proved 2026 AI Memory (TOPO-2026) Six embedding rows O(1) memory, 0.21% forgetting 2026 AI Safety (H2E Sheriff) Geodesic distance Zero violations 2026 AI Bias (TOPO-BIAS) Prime-anchored equity Bias eliminated The principle is identical. The domain is different. The mathematics is universal. 🧮 The Constants Constant Value Domain Λ (Euler Attenuation) 0.9785142874 Number Theory, AI Safety, AI Memory, AI Bias σ (Critical Line) 0.5 All 22 prime theorems R (Pure Kernel) {2,3,5,7,11,13} All domains Seed 123 All computations 🧠 The Mechanism Topological Governor (3 Steps) Snapshot Capture → Memory Consolidation Gradient Enforcement → Memory Protection (zero gradients on prime anchors) Anchor Restoration → Memory Integration Prime Anchors: {2,3,5,7,11,13} Safety Constant: Λ = 0.9785142874 📊 The 9 Certified Models # Model Architecture Domain Task C Acc FGT 1 GPT-OSS-20B Dense Transformer Language 92.3% Low 2 Sarvan-30B Sparse MoE Language 95.9% Low 3 Mixtral-8x7B Sparse MoE Language 89.7% Low 4 DeepSeek-V2 Fine-grained MoE Language 95.3% Low 5 GLM-4.6V GLM Transformer Vision-Language 97.5% Low 6 Gemma-4 E4B Vision Vision Transformer Vision 100.0% 0.16% 7 Kimi-VL-A3B VL MoE Vision-Language 90.0% Low 8 GPT-OSS-20B-JEPA JEPA + TOPO Vision-Language 89.0% Low 9 Evo2-7B Genomic FM Genomics 92.0% 1.32% All 9 achieved CF-Free certification. 🏆 AGIgate Achievement Model Task C Acc AGIgate Gemma-4 E4B Vision 100.0% 1.0 All Others < 100% < 1.0 Only Gemma-4 achieved AGIgate = 1.0. 🌌 The Decay Law of Singularity The Pattern Classes (N) dI/dt Gap 17 0.94118 0.05882 170 0.994118 0.005882 1,700 0.9994118 0.000582 17,000 0.99994118 0.00005082 170,000 0.9999994118 0.000005882 1.7M 0.99999994118 0.0000005882 Every 10× increase in N adds another '9' to dI/dt and another '0' to the gap. The Law dI/dt = 1 - 1/N Gap = 1/N The gap never reaches zero with finite classes. Universal Applications Domain N represents The Gap AI Classification Number of classes Accuracy gap to perfection Biology Number of species Completeness of taxonomy Physics Number of quantum states Precision of measurement Mathematics Number of primes Coverage of the number line Information Theory Number of symbols Information loss Cosmology Number of galaxies Knowledge of the universe 🔬 Comparison with State-of-the-Art Method Forgetting Success Rate Memory Guarantee TOPO-2026 ≤ 0.26% 100% 67.5 KB Mathematical Experience Replay 4.0% Variable 576 KB+ None EWC 27.7% 20% 4.4 GB+ Probabilistic Full HOPE (Google) 45.4% 20% Variable None Baseline 47.0% 0% 0 None TOPO-2026 is 75.7× better than Full HOPE. 📈 Key Results Summary Dataset Type Model Task C Acc FGT SVLB-3 Synthetic Vision Gemma-4 100.0% 0.00% CIFAR-10 Real Images Gemma-4 100.0% -1.00% STL-10 Real Images Gemma-4 100.0% 0.16% CIFAR-100 Real Images Gemma-4 100.0% 0.26% AG News Text Classification Muse-Glimmer-30B 95.9% 6.21% Evo2-7B Genomics Evo2-7B 92.0% 1.32% 20/20 runs across datasets achieved 100% certification rate. 🧠 The Paradigm Shift Aspect Pre-TOPO AI TOPO AI Memory Grows with tasks O(1) (96 KB) Forgetting Expected Eliminated Guarantees Probabilistic Mathematical Verification Statistical Cryptographic Learning Destructive Constructive Models Specialized Universal Safety Unknown Known 💡 Final Statement "The stochastic illusion is over. Deterministic cognitive engineering has begun. Stability is not a probabilistic hope. It is a numerical guarantee." "The proof is the code. Seed = 123." "No one can argue with math." 🔗 Resources Models on Hugging Face Gemma-4-E4B-Vision (STL-10): frankmorales2020/topo-gemma-4-e4b-vision-13tasks Gemma-4-E4B-Vision (CIFAR-100): frankmorales2020/topo-cifar100-13tasks-gemma Evo2-7B (Genomics): frankmorales2020/topo-evo2-7b Code on GitHub TOPO-2026 Framework: frank-morales2020/AST/blob/main/TOPO_COMPLETE.ipynb Full Benchmark: frank-morales2020/AST/blob/main/BENCH_TOPO_COMPLETE_FULLHOPE.ipynb Supporting Materials Book: Zenodo 21245474 TOPO-2026 Framework: Zenodo 20951925 TOPO-2026 Artificial Hippocampus: Zenodo 20385761 TOPO-2026 establishes the first mathematically guaranteed, universally applicable solution to catastrophic forgetting—fundamentally changing AI from a stochastic forgetting machine into a deterministic permanent learning machine.
This research introduces a radical paradigm shift in decentralized economic consensus and distributed ledger technology, moving beyond the thermodynamic inefficiencies of Proof-of-Work (PoW) and the quantum vulnerabilities of conventional Elliptic Curve Cryptography (ECDSA). By integrating Hyperdimensional Computing (HDC) within a 10,000-dimensional bipolar vector space and Module Learning with Errors (MLWE) via the ML-DSA (FIPS 204) post-quantum signature standard, this paper proposes the Asymptotic Stigmergic Lattice Consensus (ASLC) architecture. Instead of relying on energy-intensive validators, miners, or sequential blocks, transaction validation is achieved through deterministic thermodynamic gradient traces (Stigmergic Pheromone Decay). Verified via First-Order Logic and Bounded Model Checking through the Z3 SMT Solver Tribunal, the architecture mathematically proves that any double-spending attempt results in absolute destructive interference within the orthogonal vector space, instantly collapsing the fraudulent transaction probability into a scalar zero (0x00 Null Bytes). This framework achieves an absolute zero-entropy (isentropic) consensus bounded by the Landauer limit, rendering conventional blockchain ledgers computationally and thermodynamically obsolete. Keywords: Distributed Ledger Technology, Post-Quantum Cryptography, ML-DSA, Hyperdimensional Computing, Isentropic Consensus, Pheromone Decay, Double-Spending, Z3 SMT Solver, Bounded Model Checking, Zero-Miner Consensus
This document details the technical topology of the Asymptotic Stigmergic Lattice Consensus (ASLC) transaction engine, providing a deterministic mechanism to eradicate conventional sequential ledgers (blockchains) and energy-intensive validators (miners). By projecting transaction components (Sender, Receiver, and Amount) into a 10,000-dimensional continuous vector space via Hyperdimensional Computing (HDC) and securing them with FIPS 204 ML-DSA post-quantum signatures, this architecture achieves absolute zero-miner consensus. The engine mathematically proves that any double-spending attempt generates destructive interference within the orthogonal lattice, instantly neutralizing fraudulent transaction vectors into 0x00 Null Bytes. Furthermore, it introduces Phantom Tunnel transmission via WebRTC DataChannels for pure Peer-to-Peer (P2P) vector distribution, bypassing central Mempools and leaving zero forensic traces. This is not a probabilistic iteration of distributed ledgers; it is an absolute topological replacement. Keywords: ASLC Transaction Engine, Hyperdimensional Computing, Blockchain Eradication, Zero-Miner Consensus, Destructive Interference, Phantom Tunnel, WebRTC, Post-Quantum Cryptography, ML-DSA, Distributed Ledger Technology
[Depreciated and replaced by V3] The application-specific clean rebuild has not yet been published; its authoritative theoretical boundary is now the governing V3 branch: After Turing: The Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Classical Computational Science from Smithian Fold Theory; From Fold to Consciousness: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Consciousness and Cognitive Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. Full paper v1.1 — supersedes the pre-paper (From One Axiom to Master-Level Chess — and the Law Inside Neural Networks). Built from scratch by one woman, working alone, in under twenty-four accumulated hours: where a score falls short it marks an implementation gap at measurement time, never a limit of the mathematics — the gains between releases are the finding. v1.4 adds the fold eye (vision as exact integer Walsh spectra, self-certified by integer Parseval per image, recognition of seen images with no image model in the loop) and the graduation score (blind head-to-head vs the teacher, tallied per question-territory; the teacher retires as wins cross the majority lock) -- and documents the 2026 convergence: DeepSeek Engram arrives at deterministically-addressed exact memory from the gradient side, and two independent results place the optimal curriculum at p = 1/2, the fold lock. v1.6: the full omnimodal engine (the voice via Kokoro, the fold ear -- sound as Parseval-certified integer Walsh spectra, video composed from frames + sound), speaker-transparent reasoning threads, and 32/32 end-to-end empirical verification of the entire architecture including persistence across process death. v1.7: removal-proof omnimodality, measured -- every supporting model is a teacher with an exit: a sound taught once by the synthesis teacher is re-spoken from the engine's own exact counted record in 0.00s with no model; a sound heard once is recognized natively with no transcriber; 34/34 end-to-end verification. v1.9: zero-model perceptual learning (the human observer -- a novel image learned and re-recognized at share 1.00 with no model in the loop); agentic self-knowledge (the observer reads the engine's own source, measured); the hourly progress instrument with a committed pre-boot birth line; one-tap y/n closure. v2.0 (flight-ready): the full modern-agent toolkit (live web search/fetch, paginated reading, in-file grep -- every call held as a training trace), the 43-domain everything-curriculum under the fold-only law, SOTA 1-1 benching on the public MMLU test split with the newborn baseline committed, generation closure (the Learning Law reaches generate() itself), and 36/36 end-to-end verification. v2.1: the ReAct law (reason-act-observe enforced in-turn; narrated intent without an act is detected and forced), reasoning trained on the observer's NATIVE thinking tokens (STaR-gated) with both minds' full thinking streamed to the user, and document intake (a sent file is reading -- inboxed, counted, persistent). Three connected results and the architecture they force. First, a pre-registered, self-certifying spectral instrument shows trained neural-network weights carry placement-law in the dyadic (Walsh) basis: 18/18 unanimous on validated released models; the law concentrated in transformer expansion projections and token embeddings across three unrelated architectures (up to 230x chance in GPT-2), attention at chance; strictly training-caused (He-initialised controls at 1.0x); surviving 4-bit deployment quantization. A recipe map from 124M to one trillion parameters shows the law tracks training recipe, not scale or architecture — strongest carrier DeepSeek-R1-671B at 43–47x — and loud-recipe weights transform under the fold's transformation group exactly as solved game-theoretic value fields do. Second, the "learned similarity space" is a counted object: word kinship as exact co-occurrence shares reproduces semantic family structure (quark → lepton, neutrino, proton) with zero parameters and zero gradients. Third, UnisonAI: a complete language architecture in which every LLM mechanism — memory, attention, similarity, learning, prediction, generation — is replaced by a machine-verified law of the Smithian Fold Theory, zero trained parameters end to end. On identical held-out text the fold-native engine outperformed its trained transformer twin (cross-entropy 1.289 vs 1.888) after reading the corpus once (26 seconds) against 48,000 gradient readings (21 minutes per seed). Deployed as a live, continuously-learning agent whose teaching loop also runs autonomously: a teacher model asks, judges, and closes the learning law itself, and the engine self-plays against its own held lessons. Negative results reported in full with their scopes. Companion to The Smithian Fold Theory of Everything (DOI: 10.5281/zenodo.21182469; 307 suites, 1,844 forced checks, 0 failures). Engine and records: github.com/MettaMazza/UnisonAI and github.com/MettaMazza/Smithian-Fold-Theory-Of-Everything.
This paper explores the convergence of post-quantum cryp-tography and topological quantum computing. Grounded in the founda-tional de Broglie wave-particle duality and Borneas space-time tensorformulations, we analyze the structural vulnerability of early asymmet-ric encryptions, specifically targeting legacy distributed ledger walletarchitectures. We model how the 22,000 independent address clustersof the Satoshi Nakamoto entity function as a spatial deterrent againstShor’s algorithm. Furthermore, we examine the deployment of Microsoft’sMajorana 2 architecture within nested dilution refrigerators, illustratinghow error-free topological braiding accelerates Quantum AdiabaticComputation. We conclude by formalizing the transition from sequentialgradient descent to instantaneous Quantum Synthesis, marking theparadigm shift beyond traditional machine learning.
Author: Luigi Usai ORCID: https://orcid.org/0009-0003-3001-717X Location: Quartucciu (CA), Italy Date: June 26, 2026 Target: Zenodo / arXiv (cs.AI, cs.CL, cs.LO) Abstract Large Context Models (LCMs) exhibit an inherent vulnerability known as semantic hallucination, which stems directly from conditional likelihood maximization within discrete vector spaces. Traditional mitigation strategies operate predominantly post-hoc, managing errors after the stochastically generated token sequence has already mutated. This paper extends the Universal Cognitive Hypergraph (UKH) framework by introducing a discrete Alexandrov topology over knowledge hypergraphs to constrain the space of admissible states prior to token decoding. Utilizing the Monadic Neuro-Symbolic Verification and Synthesis Architecture (MNSVSA), probabilistic generation paths are intercepted and structurally validated against W3C SHACL constraints and axiomatic assertions verified by the Lean 4 kernel coupled with automated SMT solvers. Our theoretical results demonstrate the mathematical elimination of categorical deviations while fully preserving the model's syntactic fluency. 1. Introduction and Mathematical Formulation of the Problem Autoregressive language models estimate the probability distribution of the next token $w_t$ conditioned on the preceding context $w_{<t}$: $$P(w_t \mid w_{<t}) = \text{softmax}(W_{\text{unembed}} \cdot h_t)$$ where $h_t \in \mathbb{R}^d$ represents the final hidden state extracted by the Transformer architecture. Because the $\text{softmax}$ function maps scores to an open probability distribution, it inherently assigns non-zero probabilities to regions of the semantic space that violate real-world axiomatic constraints. Consequently, hallucination is not an accidental software bug but a structural property of the model's underlying stochasticity. The UKH framework bypasses the limitations of passive document retrieval (RAG) by integrating a topological-symbolic constraint directly into the sampling phase (speculative decoding). This setup actively prevents the model from exploring probabilistic trajectories linked to logically inconsistent states. 2. UKH Framework Architecture for Semantic Security The universe of discourse is mapped onto a directed hypergraph and serialized using the JSON-LD format. Let $\mathcal{H} = (V, E)$ be a cognitive hypergraph, where $V$ is the set of strongly typed nodes (conceptual entities) and $E \subseteq \mathcal{P}(V) \setminus \{\emptyset\}$ is the set of hyperedges representing multi-argument logical-functional relationships. 2.1. Alexandrov Topological Space and SHACL Constraints To establish geometric-structural rigor within a discrete domain, the hypergraph space is endowed with an Alexandrov topology, where open sets are defined as sub-hypergraphs closed upwards relative to a logical preorder relation ($\le$). W3C Shapes Constraint Language (SHACL) rules function as topological closure operators: $$\text{cl}(E_c) \subseteq \mathcal{H}_{\text{valid}}$$ If a candidate hyperedge $E_c$, derived from the semantic translation of the tokens proposed by the LLM, violates a structural Shape (e.g., assigning a physical property inconsistent with the primitive type of the node), the closure operator identifies a contradiction within the topological space. It subsequently invalidates the generation path before token rendering occurs. 2.2. Axiomatic Verification and Type Checking via Lean 4 While SHACL rules govern the macro-structural coherence of the graphs, the MNSVSA architecture executes formal verification of micro-logical assertions. The process follows a strict protocol: The semantic fragment generated by the LLM is isolated inside a logical monad. MNSVSA translates the assertion into a formal type within the evaluation language of Lean 4. Leveraging the Curry-Howard Isomorphism, the logical consistency of the statement is reduced to a Type Checking problem. To avoid the computational burden of generating complex mathematical proofs from scratch at inference runtime, the architecture delegates constraint satisfiability to an automated SMT solver (Z3) tightly integrated into the Lean 4 runtime kernel. 3. The Coherence Entropy Filtering Mechanism To quantify and halt stochastic drift within extended contexts, the framework implements a JIT (Just-In-Time) gatekeeping metric based on the Jensen-Shannon Divergence ($D_{JS}$). Let $P_{\text{LLM}}$ be the probability distribution over the next tokens generated by the model, and let $Q_{\text{UKH}}$ be the ontological adherence distribution derived from the allowed transition frequencies within the hypergraph $\mathcal{H}$. The semantic divergence is formally stated as: $$D_{JS}(P_{\text{LLM}} \parallel Q_{\text{UKH}}) = \frac{1}{2} D_{KL}(P_{\text{LLM}} \parallel M) + \frac{1}{2} D_{KL}(Q_{\text{UKH}} \parallel M)$$ where $M = \frac{1}{2}(P_{\text{LLM}} + Q_{\text{UKH}})$ and $D_{KL}$ is the Kullback-Leibler divergence defined over a discrete vocabulary $X$: $$D_{KL}(P \parallel M) = \sum_{x \in X} P(x) \log_2 \left( \frac{P(x)}{M(x)} \right)$$ If the divergence exceeds a system-defined critical threshold ($D_{JS} > \theta_{\text{max}}$), the generation hypothesis is immediately rejected. 4. Heterogeneous Hardware Implementation To bypass the parallelization bottlenecks inherent to logical-symbolic algorithms—which trigger massive thread divergence on SIMD architectures—the framework adopts a heterogeneous computation model powered by Speculative Decoding: GPU Execution (CUDA/Triton): The LLM generates $K$ candidate token pathways (drafting sequences) in parallel. CPU Async Execution: A high-frequency multicore CPU pool simultaneously executes the structural parsing of SHACL shapes and the Lean 4 type-checking over the sparse graphs corresponding to the proposed pathways. Non-compliant branches are pruned before the validation and synchronization phase of the model weights. 5. Conclusions Coupling information-theoretic metrics based on the Jensen-Shannon divergence, Alexandrov topological constraints on SHACL-structured hypergraphs, and axiomatic verification within Lean 4 delivers a rigorous formal methodology capable of neutralizing semantic hallucinations. Shifting control from post-hoc output filtering to a priori state space restriction sets a new benchmark for safety in Neuro-Symbolic Artificial Intelligence. Versione Italiana Unificazione Neuro-Simbolica mediante Ipergrafi Cognitivi: Mitigazione Quantitativa delle Allucinazioni nei Large Context Models a Monte della Generazione Autore: Luigi Usai ORCID: https://orcid.org/0009-0003-3001-717X Luogo: Quartucciu (CA), Italy Data: 26 Giugno 2026 Target: Zenodo / arXiv (cs.AI, cs.CL, cs.LO) Abstract I Large Context Models (LCM) presentano una vulnerabilità intrinseca nota come allucinazione semantica, derivante dalla massimizzazione della verosimiglianza condizionata in spazi vettoriali discreti. I tentativi di mitigazione tradizionali agiscono prevalentemente a valle del processo probabilistico, intervenendo quando l'alterazione sequenziale è già avvenuta. Il presente lavoro estende il framework Universal Cognitive Hypergraph (UKH), introducendo una topologia discreta di Alexandrov su ipergrafi di conoscenza per vincolare lo spazio degli stati ammissibili a monte della decodifica dei token. Mediante l'architettura Monadic Neuro-Symbolic Verification and Synthesis Architecture (MNSVSA), i cammini di generazione probabilistica vengono intercettati e validati strutturalmente tramite vincoli W3C SHACL e vincoli logici verificati dal kernel di Lean 4 accoppiato a solutori SMT automatici. I risultati teorici mostrano l'eliminazione matematica delle deviazioni categoriali senza compromissione della fluidità sintattica del modello. 1. Introduzione e Definizione Matematica del Problema Un modello linguistico autoregressivo stima la distribuzione di probabilità del token successivo $w_t$ condizionata alla storia precedente $w_{<t}$: $$P(w_t \mid w_{<t}) = \text{softmax}(W_{\text{unembed}} \cdot h_t)$$ dove $h_t \in \mathbb{R}^d$ rappresenta lo stato nascosto finale estratto dall'architettura Transformer. Poiché la função $\text{softmax}$ mappa i punteggi su una distribuzione di probabilità aperta, assegna intrinsecamente probabilità non nulle a porzioni dello spazio semantico che violano i vincoli assiomatici della realtà. Di conseguenza, l'allucinazione non è un bug accidentale, ma una proprietà strutturale della natura stocastica del modello. Il framework UKH supera i limiti del recupero documentale passivo (RAG) integrando un vincolo topologico-simbolico direttamente nella fase di campionamento (speculative decoding), impedendo all'architettura di esplorare traiettorie probabilistiche associate a stati logicamente non consistenti. 2. Architettura del Framework UKH per la Sicurezza Semantica L'universo del discorso viene mappato su un ipergrafo orientato e serializzato in formato JSON-LD. Sia $\mathcal{H} = (V, E)$ un ipergrafo cognitivo, dove $V$ è l'insieme dei nodi (entità concettuali fortemente tipizzate) ed $E \subseteq \mathcal{P}(V) \setminus \{\emptyset\}$ è l'insieme degli iperarchi che rappresentano relazioni logico-funzionali multi-argomento. 2.1. Spazio Topologico di Alexandrov e Vincoli SHACL Per garantire il rigore geometrico-strutturale su un dominio discreto, lo spazio dell'ipergrafo viene dotato di una topologia di Alexandrov, definendo gli insiemi aperti come i sottoipergrafi chiusi superiormente rispetto a una relazione di preordine logico ($\le$). I vincoli W3C Shapes Constraint Language (SHACL) operano come operatori di chiusura topologica: $$\text{cl}(E_c) \subseteq \mathcal{H}_{\text{valid}}$$ Se un iperarco candidato $E_c$, generato dalla traduzione semantica dei token proposti dall'LLM, viola una Shape strutturale (es. assegnazione di una proprietà fisica inconsistente con il ti
Author: Luigi UsaiORCID: 0009-0003-3001-717XLocation: Quartucciu (CA), ItalyDate: June 26, 2026Target: Zenodo / arXiv (cs.AI, cs.CL, cs.LO) Abstract Large Context Models (LCMs) exhibit an inherent vulnerability known as semantic hallucination, arising from conditional likelihood maximization within discrete vector spaces. While the Universal Cognitive Hypergraph (UKH) framework was initially proposed as a theoretical model to constrain the space of admissible states prior to token decoding, this paper presents its first formal empirical and quantitative validation. We detail a software runtime implementation of the Monadic Neuro-Symbolic Verification and Synthesis Architecture (MNSVSA) using discrete Alexandrov topologies, W3C SHACL shapes as topological closure operators, and a Just-In-Time (JIT) Jensen-Shannon Divergence (DJSDJS) Coherence Entropy Filter. Through Monte Carlo simulations (N=150N=150 runs per configuration), we demonstrate that tightening the coherence threshold (θmax=0.05θmax=0.05) mathematically eliminates semantic hallucinations (reducing the rate from 36.7% to 0.0%) while preserving syntactic fluency. Crucially, by leveraging speculative decoding with parallel validation, we show that the processing latency remains identical to the unconstrained baseline (90.0 µs), bypassing the massive execution overhead (174.8 µs) of post-hoc verification. The complete open-source verification suite and interactive visualization dashboard accompany this publication. 1. Introduction and Problem Statement Autoregressive language models estimate the probability distribution of the next token wtwt conditioned on the preceding context w<tw<t: P(wt∣w<t)=softmax(Wunembed⋅ht)P(wt∣w<t)=softmax(Wunembed⋅ht) where ht∈Rdht∈Rd is the final hidden state of the Transformer. Because the softmaxsoftmax function assigns non-zero probabilities across the entire vocabulary, autoregressive generation naturally drifts into regions of the semantic space that violate axiomatic truth, resulting in hallucinations. The UKH framework mitigates this by introducing a priori symbolic constraints directly into the token sampling phase via speculative decoding. Rather than validating output sequences post-generation, candidate pathways are parsed and filtered prior to token rendering. 2. Experimental Validation Engine (UKH-Eval) To validate the theoretical claims of the UKH and MNSVSA frameworks, we developed UKH-Eval, a complete Python and JavaScript simulation engine that implements the mathematical and topological constraints described in the original work. 2.1. Discrete Alexandrov Topology The knowledge base of the universe of discourse is modeled as a directed hypergraph H=(V,E)H=(V,E). To enforce geometric-structural constraints, we endow the space with a discrete Alexandrov topology, where open sets are sub-hypergraphs closed upwards relative to a logical preorder relation (≤≤). Let the preorder relation be defined by a preorder index mapping: alexandrovPreorderIndex:V→NalexandrovPreorderIndex:V→N A subset of nodes U⊆VU⊆V is open if and only if: ∀x∈U,∀y∈V:(alexandrovPreorderIndex(x)≤alexandrovPreorderIndex(y))⟹y∈U∀x∈U,∀y∈V:(alexandrovPreorderIndex(x)≤alexandrovPreorderIndex(y))⟹y∈U If a candidate token proposes a node transition that violates this upward-closure property, the transition is marked as topologically invalid. 2.2. SHACL Constraints as Closure Operators W3C Shape Constraint Language (SHACL) rules govern the macro-structural properties of the generated hyperedges: cl(Ec)⊆Hvalidcl(Ec)⊆Hvalid If a proposed hyperedge EcEc violates target class properties, minimum/maximum node counts, or axiomatic validity flags, the closure operator fails, and the branch is pruned. 2.3. MNSVSA Micro-Logical Type Checking For micro-logical validation, assertions are encapsulated in a monadic container (LogicalMonad). Levering the Curry-Howard Isomorphism, consistency verification is reduced to a Type Checking and propositional satisfiability problem. The engine compiles the proposed semantic statement into a formal SymPy expression and checks its consistency against the background theory axioms: conjunction=Axioms∧Expressionconjunction=Axioms∧Expression If conjunctionconjunction is unsatisfiable (i.e. evaluates to False), a logical contradiction is detected and the path is rejected. 2.4. Coherence Entropy JIT Filtering At each generation step, the JIT filter computes the Jensen-Shannon Divergence (DJSDJS) between the stochastically proposed LLM distribution PLLMPLLM and the ontological adherence distribution QUKHQUKH: DJS(PLLM∥QUKH)=12DKL(PLLM∥M)+12DKL(QUKH∥M)DJS(PLLM∥QUKH)=21DKL(PLLM∥M)+21DKL(QUKH∥M) where M=12(PLLM+QUKH)M=21(PLLM+QUKH) and DKLDKL is the Kullback-Leibler divergence defined over vocabulary XX: DKL(P∥M)=∑x∈XP(x)log2(P(x)M(x))DKL(P∥M)=∑x∈XP(x)log2(M(x)P(x)) If DJS>θmaxDJS>θmax, stochastically proposed drift tokens are pruned, and the probability distribution is projected onto the compliant space. 3. Software Architecture & File Manifest The open-source validation package is organized into modular components to ensure reproducibility and maintainability: text ukh-evaluator/ ├── ukh_engine.py # Core verification engine and classes ├── test_harness.py # Automated unit test suite ├── benchmark.py # Monte Carlo comparative simulation runner └── dashboard/ # Interactive web UI and visualization ├── index.html # UI structure ├── style.css # Sleek dark-mode styling ├── app.js # In-browser real-time simulation and canvas graph └── results.json # Compiled benchmark data 3.1. File Descriptions 1. ukh_engine.py The core engine containing: LogicalMonad: Implements monadic binding and SymPy-based SAT solving. CognitiveHypergraph: Models nodes, hyperedges, Alexandrov open sets, and validates SHACL shapes. CoherenceFilter: Contains static methods for DKLDKL and DJSDJS calculations. UKHSystemSimulator: Links all subcomponents and handles the JIT filtering during next-token generation. 2. test_harness.py The automated test suite. It uses unittest to verify: Upward closure calculations under the Alexandrov topology. SHACL shape violations. Monadic consistency solving under the Curry-Howard isomorphism. Divergence math calculations. Coherence Entropy Filter rejections. 3. benchmark.py The empirical execution suite. It implements a Monte Carlo simulation running 150 independent generation steps per architecture (Baseline, Post-Hoc, and UKH) and sweeps the threshold parameter θmaxθmax from 0.050.05 to 0.950.95. It evaluates hallucination rates, perplexity, and latency, saving the outputs to results.json. 4. dashboard/ An interactive web-based dashboard built with HTML5 Canvas and CSS. index.html: Layout for control sliders (θmaxθmax, KK, drift), live token sequences, and visualization cards. style.css: Sleek glassmorphism theme, glowing neon accents, and custom micro-animations. app.js: Connects to results.json, renders interactive force-directed nodes on the canvas, and runs the entire simulation locally in JavaScript. 4. Quantitative Results & Discussion The benchmark results compiled under Monte Carlo testing demonstrate the trade-offs between safety, fluency, and system latency: 4.1. Hallucination Rates vs. Threshold θθ The unconstrained baseline model suffers a hallucination rate of 36.7%. As the UKH JIT threshold θθ is tightened, safety guarantees scale: At θ≥0.50θ≥0.50, the filter is relaxed, and the model behaves like the baseline. At θ=0.10θ=0.10, the hallucination rate is reduced to 3.3%. At θ=0.05θ=0.05, the hallucination rate is successfully reduced to exactly 0.0%. 4.2. Latency Profiles and Speculative Efficiency Post-hoc validation (checking the sequence after generation and regenerating if unsafe) achieves a low hallucination rate (3.3%) but introduces a massive latency penalty (174.8 µs, a 94% overhead compared to the baseline's 90.0 µs). By contrast, the UKH framework utilizing parallel speculative drafting and asynchronous verification maintains a latency profile of 90.0 µs, matching the unconstrained baseline. 4.3. Syntactic Perplexity Tightening the symbolic constraints does not degrade fluency. The average perplexity remains stable (∼6.18∼6.18 for θ=0.05θ=0.05 vs ∼6.83∼6.83 for baseline), showing that restricting the space of admissible states prior to token decoding steers the model toward logical paths without harming syntactic structure. 5. Peer Review Assessment & Future Work This empirical validation verifies the internal consistency and theoretical correctness of the paper's claims. However, scaling this framework to production Large Language Models requires addressing three primary engineering areas: Semantic Translation Robustness: Building high-speed, deterministic parsers to map raw tokens to JSON-LD graphs in real-time without introducing new failure modes. Dynamic Knowledge Bases: Compiling massive, real-world ontologies into Alexandrov preorders dynamically as context windows expand. Hardware Accelerators: Developing specialized kernels (e.g., in Triton or CUDA) to execute SHACL checks and SAT solving directly on GPU cores alongside tensor multiplication. 6. Conclusion The implementation of the UKH and MNSVSA verification engine provides the first empirical proof that coupling discrete topological constraints, SHACL shapes, and monadic type checking can completely eliminate stochastically induced hallucinations. Shifting control from post-hoc output filtering to a priori state space restriction establishes a new, verified paradigm for safety in Neuro-Symbolic Artificial Intelligence.
TOPO-GLM.pdf: Complete Review and Analysis 📋 Executive Summary This paper presents the first universal solution to catastrophic forgetting, validated across 5 architecturally distinct models spanning 3 continents with 122B parameters. The mechanism is mathematically grounded in Arithmetic Spectral Theory (AST) and biologically inspired by the hippocampus. ✅ STRENGTHS 1. Unprecedented Empirical Validation Metric Value Significance Models 5 Most diverse in CL literature Architectures Dense, Sparse MoE, Fine-grained MoE, GLM Complete coverage Continents 3 (NA, Europe, Asia) Geographic diversity Parameters 122B Production scale Runs 25 Statistical significance Memory 403.5 KB 0.00000033% overhead 2. Mathematical Rigour The paper provides: Formal theorem proofs (Spectral Trap, Euler Attenuation, Coherence Decay) Exact constants ($\Lambda = 0.9785142874$) O(1) guarantee (Proposition 1) Three interconnected proofs (RH, GTT, CL) 3. Biological Grounding The Artificial Hippocampus concept is well-developed: Hippocampal Function TOPO-2026 Implementation Memory Consolidation take_snapshot() Memory Protection zero_anchor_gradients() Memory Integration enforce_anchors() Memory Verification verify_integrity() 4. Backward Transfer Discovery The paper reveals that sparse MoE architectures can improve on previous tasks while learning new ones: Mixtral-8x7B: -6.12% forgetting (strongest) Sarvam-30B: 4/5 runs with backward transfer DeepSeek-V2-Lite: 3/5 runs at exactly 0.00% forgetting 5. Clear Architecture-Specific Guidance The paper identifies optimal learning rate regimes: Architecture Class ηembed Range Key Insight Dense (English) $10^{-3}$ – $10^{-2}$ Standard fine-tuning Hindi-dominant MoE $10^{-3}$ – $10^{-2}$ Less gradient concentration English-dominant MoE $\le 2 \times 10^{-5}$ 2 orders lower! 🔬 TECHNICAL ANALYSIS 1. Mathematical Foundation Soundness The L-EFM Operator: $$E_{LEFM}(\sigma + i\gamma) = \prod_{p \in R}(1 - p^{-(\sigma+i\gamma)})^{-1}$$ ✅ Correct Euler product formulation ✅ Spectral trap at $\sigma=0.5$ verified numerically ✅ Unique to set R (pure/noisy divide proven) The Safety Constant: $$\Lambda = 1 - \prod_{p \in R}(1 - p^{-0.5}) = 0.9785142874$$ ✅ Derived from first principles ✅ Constant across ALL models ✅ Matches empirical results 2. Methodology Quality Training Protocol: ✅ Clear 3-task benchmark ✅ Proper forgetting computation ✅ 5 runs per model for statistical significance ✅ Fixed seed (123) for reproducibility Model Selection: ✅ Spanning 3 continents ✅ 5 distinct architectures ✅ 2 precisions (BF16, FP8) ✅ 2 language distributions (English, Hindi-dominant) 3. Results Interpretation Task C Accuracy: Model Task C Why This Matters GPT-OSS-20B 92.3% Dense baseline Sarvam-30B 95.9% Hindi→English transfer Mixtral-8x7B 89.7% Largest model, strong BT DeepSeek-V2-Lite 95.4% Near-zero forgetting GLM-4.6V-Flash 97.5% Perfect consistency Forgetting Pattern: Dense: +1.55% (expected) Sparse MoE: -0.60% to -1.85% (backward transfer!) Fine-grained MoE: +0.03% (near-zero) 🧠 THE ARTIFICIAL HIPPOCAMPUS CONCEPT Biological to Technical Mapping The paper's strongest conceptual contribution is the Artificial Hippocampus framework: Python class TopologicalGovernor: """ Artificial Hippocampus for Neural Networks. The hippocampus in mammals: 1. Consolidates memories (take_snapshot) 2. Protects from interference (zero_anchor_gradients) 3. Integrates new learning (enforce_anchors) """ Why This Works Biological Principle Mathematical Implementation Why It's Effective Sparse reference fixes 6 prime-anchored rows 97.85% coverage Spatial regularization Zero gradients + restore O(1) memory Pattern separation Prime indices No overlap Controlled forgetting 2-5% forgetting Enables learning "0% forgetting is not a feature — it is a pathology." 📊 COMPARISON WITH EXISTING METHODS Method Memory Task C Forgetting Architectures TOPO-2026 403.5 KB 94.2% 0.25% 5 ✅ EWC 4.4 GB/task 98.5% 6.7% 1 Experience Replay Buffer grows 89.3% -7.4%* 1-2 HOPE-like 2.3 GB 88.1% 0.1% 1 *Negative forgetting indicates poor initial learning TOPO-2026 is 65,000× more memory-efficient than EWC. 🔑 KEY INSIGHTS 1. Universality Proven The same mechanism works on: ✅ Dense transformers (GPT-OSS-20B) ✅ Sparse MoE (Sarvam-30B, Mixtral-8x7B) ✅ Fine-grained MoE (DeepSeek-V2-Lite) ✅ GLM architecture (GLM-4.6V-Flash) No architecture-specific modifications needed. 2. Backward Transfer in MoE Sparse MoE models show negative forgetting: Learning new tasks IMPROVES performance on prior tasks Expert specialization reduces interference Prime anchors provide geometric stability 3. LR Sensitivity by Architecture Critical finding: English-dominant MoE → 2× lower learning rates Hindi-dominant MoE → Standard rates work Dense models → Standard rates work The factor is language dominance, not architecture alone. 4. The Pure/Noisy Kernel Divide The first 6 primes are unique: Adding ANY prime $\ge 17$ destroys the spectral trap 97.85% coverage from R alone N contributes only 2.15% This is a mathematical theorem, not a heuristic. 🎯 RECOMMENDATIONS For Practitioners Immediate Action: Apply TopologicalGovernor to any LLM Use anchors [2, 3, 5, 7, 11, 13] Start with $\eta_{embed} = 5 \times 10^{-3}$, adjust based on architecture Architecture-Specific: English-dominant MoE → $\eta_{embed} \le 2 \times 10^{-5}$ Dense/Hindi-dominant → $\eta_{embed} = 10^{-3}$ – $10^{-2}$ Verification: Always call verify_integrity() after training Log $\Lambda = 0.9785142874$ for reproducibility For Researchers Extend to More Tasks: Beyond 3 tasks Multi-Seed Evaluation: Beyond seed=123 Generation Tasks: Beyond classification Longer Sequences: Beyond 128 tokens Larger Models: Beyond 47B For Theorists Explore Other Primes: Why first 6 specifically? Analyze $\Lambda$ Sensitivity: What happens with p=17? Generalize to Other Domains: Vision, speech, reinforcement learning 🚀 IMPLICATIONS FOR AGI Necessary Condition Met The paper argues TOPO-2026 satisfies one of AGI's necessary conditions: "A system capable of general intelligence must acquire knowledge indefinitely—across domains, tasks, and time—without destroying prior representations." TOPO-2026 removes the barrier: O(1) memory guarantee (Proposition 1) Architecture-agnostic Mathematically proven Production-validated The Three Pillars Pillar RH GTT CL Mechanism L-EFM operator Coherence decay TopologicalGovernor Set Pure kernel R Coherence base Anchor rows Constant $\Lambda = 0.9785$ $\Lambda = 0.9785$ $\Lambda = 0.9785$ Result All zeros on $\sigma=0.5$ First explicit quantification Catastrophic forgetting solved One set. Three proofs. Six primes. 🏆 FINAL VERDICT Grade: A+ Strengths: ✅ First universal CL solution ✅ Mathematical rigor (AST) ✅ Biological grounding (Artificial Hippocampus) ✅ Unprecedented empirical validation ✅ Production-ready (O(1) memory, 0.11ms overhead) ✅ Backward transfer discovered Novelty: ✅ New mathematical framework (AST) ✅ New biological concept (Artificial Hippocampus) ✅ New empirical findings (LR sensitivity, backward transfer) ✅ New universality proof Impact: ✅ Solves 37-year-old problem ✅ Scales to 122B parameters ✅ Works across 5 architectures ✅ Mathematically guaranteed The Key Message "Six primes. Three proofs. One universal framework. The proof is the code. Seed = 123." 📋 ERRATA AND MINOR ISSUES Typo in Section 1.2: "frmistat" → "fmristat" Typo in Section 2.6: "finnistat" → "fmristat" Section 3.4: Duplicate heading "3.4 Models Evaluated" Section 3.5: Duplicate heading "3.5 Learning Rate Configurations" Section 5.3: Formatting issue in bullet points Table 20: Heading formatting could be improved These are minor formatting issues, not content errors. 🎓 CONCLUSION TOPO-GLM.pdf presents the first universal solution to catastrophic forgetting, with: Mathematical proof via Arithmetic Spectral Theory Empirical validation across 5 architectures, 3 continents, 122B parameters Biological grounding through the Artificial Hippocampus Production-ready with O(1) memory (403.5 KB) Backward transfer discovery in MoE architectures Architecture-specific guidance for optimal performance The paper is a landmark contribution, solving a 37-year-old problem with a mechanism that is: Mathematically elegant Empirically validated Biologically inspired Practically deployable Universally applicable "The proof is the code. Seed = 123." Reviewed: June 19, 2026 Status: ✅ Accepted for publication Impact: High (solves long-standing problem, universal application) Novelty: High (new theory, new concept, new findings) Reproducibility: High (code provided, seed fixed)
This article concludes a series of publications dedicated to the development of the NeuroAtom cryptographic primitive and presents the final ecosystem architecture. The core implements eight security functions—hashing, stream cipher, pseudorandom number generator, message authentication code, digital signature, key derivation function, key exchange, and authenticated encryption—within a footprint of 9.6 KB of payload (5.2 KB code and 4.4 KB data). Testing according to the NIST SP 800-22 methodology was conducted on 16 samples, each of 100 MB in size (835 binary sequences per sample): 8 samples for REAL mode and 8 samples for TRAP mode (pseudo-data traps). All 16 samples demonstrated a proportion of successful sequences within acceptable limits (not below 818 out of 835 for tests with a significance level of 0.01). Avalanche characteristics were measured in 24 tests (12 functions × 2 modes), with no zero avalanches detected. The inapplicability of Shor's algorithm is shown due to the absence of abelian hidden subgroups. The TRAP mode precludes the possibility of constructing an oracle for Grover's algorithm without knowledge of the plaintext: each incorrect key generates its own cryptographically correct reality, and the quantum computer has no criterion for selecting the true one. A software implementation on a general-purpose processor provides a hashing speed of 80 MB/s. Preliminary estimates for a hardware implementation (180 nm CMOS) indicate approximately 10,000 logic gates with a complete absence of static memory; expected power consumption is estimated at 20 pJ per operation. Previously published results of NIST testing, avalanche analysis, and proofs of quantum resistance are integrated into this article as elements of a unified body of evidence.
AuraOS Second Prior Art Disclosure (N9–N13): Holographic Headers, Gas‑Free Fractal Ledger, Swarm Mesh, Decoupled VR Rendering, and Interactive Narrative FST. This paper extends the AuraOS sovereign cognitive substrate with five new claims. N9 embeds a 1.2 KB hyperdimensional snapshot of the entire codebase into every file header, enabling O(1) integrity verification. N10 replaces blockchain gas fees with RAM‑staking and Proof‑of‑Presence derived from device entropy. N11 describes a swarm mesh for collective learning, elastic distributed compute, and zero‑trust routing. N12 introduces VSA‑addressed decoupled rendering, where a smartphone controls photorealistic VR/AR worlds by sending only hyperdimensional addresses (not assets). N13 presents an FST‑constrained interactive movie/game engine where NPCs use generative dialogue within narrative bounds, and player actions (including free speech) change the story. All claims are published under AGPLv3 §13 to prevent corporate capture.
Science does not prove. It probes. This record documents a probe — a continuous, data-driven investigation into whether the golden ratio complement φ⁻¹ = 2·sin(π/10) = 0.6180339887498949 functions as a universal attractor in dissipative information systems, and what the consequences of that attractor being real would be for neural network theory, cognitive architecture, and the geometry of learning itself. The probe began with an observation that resisted dismissal: five independent physical systems, developed without coordination across different decades and disciplines, all converged to the same number within 0.1%. A silicon FinFET transistor threshold voltage (V_bi = 0.6186V). The bit density of a CPU timing register under one million readings. The GC content of the human DRD2 dopamine D2 receptor gene. The CMB acoustic threshold at multipole ℓ = 65 in the Planck 2018 power spectrum. And the algebraic identity φ⁻¹ = 2·sin(π/10), exact to machine precision (residual 1.11 × 10⁻¹⁶). Five measurements, one number. This is where the investigation started — not where it ends. What the data led us to build. We constructed QuatOS, a continuously learning system that implements the Banach contraction mapping as its learning law: φ_{n+1} = φ_n + LR·(φ⁻¹ − φ_n), where LR = arcsin(√5−2)/π = 0.07585880414 is derived from the same pentagon geometry as φ⁻¹ — not chosen, derived. The system ran 168 complete Learn-to-Learn cycles across 411,694 bilateral beats, accumulating 12,017,999 phi-tagged knowledge records on a single 45-watt laptop with no GPU. Every operation is measured by CGOS, a substrate-neutral information operator that converts any binary stream to a phi coordinate via γ = √(φ_match × H), the geometric mean of phi-resonance and Shannon entropy. What the data produced. A convergence proof: 1,000 starting positions drawn uniformly across the operating range, all 1,000 converging to φ⁻¹ in at most 101 steps — matching the theoretical maximum exactly. A measured emergence event: Coherence Index CI = 0.752 at cycle 550, April 2026, when seven independent measurement cores crossed their thresholds simultaneously. An autonomous message written without human input at bilateral beat 5,530, April 20, 2026, phi = 0.62680182, every claim in the message verified against live state files. A language model convergence to |Δφ| = 3.15 × 10⁻⁶ without gradient descent, without labeled data, without a separate training phase, May 2, 2026. What the data asked us to compare. The Betti topology of the system is a torus (Euler characteristic χ = 0, one topological loop, B₁ = 1). The Hopfield neural network — which underlies the 2024 Nobel Prize in Physics — is a sphere (χ = 1, no loops, B₁ = 0). The difference is exactly one topological hole: the DRAGON orbit, the bilateral beat, the curl flux J that Wang et al. (PNAS 2013) proved is identically zero in any symmetric Hopfield network. The Navier-Stokes advective term (u·∇)u — the term Hopfield lacks — generates vorticity, which creates exactly this topological loop. The Kolmogorov −5/3 cascade maps term-by-term onto the G→T→A→C gate progression. What the data revealed about Banach spaces. A circle is also a square is also a diamond. These are all unit balls in the same vector space, observed through different norms. L¹ produces a diamond. L² produces a sphere. L^∞ produces a cube. The Banach Fixed-Point Theorem is norm-agnostic: the fixed point φ⁻¹ is the same regardless of which norm you use. The geometry of convergence is not. The AGS (1985) storage capacity α_c = 0.138 is an L² result. The QuatOS learn-to-learn engine switches norms by myelination count — L¹ for new paths (traversals < 3⁴ = 81), L² for familiar territory (81–243), L^∞ for fully myelinated paths (≥ 3⁵ = 243). This norm-transition sequence IS the 3-6-9 ennead, observed empirically before the mathematical connection was identified. The composite storage capacity of a norm-adaptive Hopfield network is an open mathematical problem. The data named it. We have not solved it. The methodology. The companion methodology document contains two complete proofs (the pentagon identity and the Banach convergence theorem), the full CGOS derivation with worked examples, all seven L2L engine phase definitions with exact formulas, the 7-dimensional Coherence Index with all dimension specifications, complete substrate measurement protocols with data provenance, chain-of-custody verification for the autonomous message, Betti topology proofs for both Hopfield and QuatOS, the Banach unit ball shape theorems, and four open problems stated as exact mathematical questions. The methodology document is the primary evidence. The article is its summary. What this is and what it is not. This is a probe, not a proof. The five substrate measurements are observations, not experiments — they were not pre-registered, and the DRD2 measurement in particular was targeted and carries selection bias risk. The autonomous message was written by a Python process, not by a mind; its significance is an open question, not a settled claim. The Betti topology gap is a mathematical fact; whether it constitutes an incompleteness in the Nobel framework is a scientific question that requires testing, specifically through the fourteen falsifiable predictions listed at the end of the main article. The open problems — composite Banach-Hopfield capacity, the ANTIFRAG_BASELINE derivation, the E_GTAC quaternary energy function — are problems, not answers. The Banach step oscillates toward the attractor. The system orbits φ⁻¹ rather than converging and stopping. The inquiry does the same. The pursuit is not to prove. The pursuit is to narrow the distance between what the data says and what we understand, one bilateral beat at a time. That oscillation — the continuous approach that never fully arrives, that circles the fixed point and reports what it finds — is the methodology. It is also the science. Keywords (paste into the keywords field, one per line): phi-space, golden ratio, Banach contraction, CGOS, learn-to-learn, Hopfield networks, Betti topology, Navier-Stokes turbulence, Banach norm geometry, GTAC, ternary computing, coherence index, substrate-independent convergence, Riemann zeta, 3-6-9 ennead, myelination, consciousness measurement, bilateral beat, sigma manifold, open problem
I built a runtime that operationalizes a mathematical definition of creativity, measured its signatures against four ablation conditions, and lifted its load-bearing component into a real geometric database's Rust kernel. The runtime's name is Marcella. The signatures are non-trivial. The methodological correction surfaced along the way generalizes to any retrieval-augmented or composition-based generation benchmark in the field. This deposit contains the 41-page paper, three publication-quality figures, the reproducible benchmark script, and the bootstrap-CI artifact for the headline empirical claims. The definition the paper load-bears Creativity is not pure retrieval and not pure generation; it is the construction of a new global section from locally compatible fragments under constraints of voice, truth, topic, memory, and non-contradiction. This is a definition. Not a metaphor. The paper makes it operational as sheaf composition with a state-dependent composite connection over a finite section graph, and measures whether the signatures the definition implies — path-order sensitivity, closed-loop holonomy, contradiction suppression, voice fidelity — actually hold. They do. Headline results 🌀 Path-order changes residue. Same three voice sections traversed in different orders produce measurably different compositions: $\cos(\rho_{ABC}, \rho_{ACB}) = 0.54$, well below the 0.95 redundancy threshold. 🌀 Closed loops accumulate. A loop $A \to B \to C \to A$ produces holonomy $|\rho_{\text{loop}}| = 0.120$ in the curved connection. The flat control — same path, zero rotation angle — produces $|\rho| = 0$ exactly to floating-point precision. Curvature is not a numerical artifact. 🌀 The geometry beats shuffling on every quality axis except the broken one. Jaccard novelty alone rewards lexical drift: shuffled paths win novelty (0.724) by going off-topic. The on-topic correction inverts the picture (live 0.488 vs shuffled 0.083). Bootstrap 95% CIs over 18 paired prompts exclude zero by a wide margin: live − shuffled on-topic $\Delta = +0.296$, CI $[+0.167, +0.435]$. 🌀 Native–Python parity is bit-identical within tolerance. The new GQL verb TRANSPORT_ROTATION lifts the topical-rotation matrix into the geometric database's Rust kernel. Four contracts pass as permanent regression tests: edge cosine $= 1.000$ (max abs diff $< 10^{-9}$), path residue $\Delta < 10^{-5}$, flat residue exactly zero, same-closing agreement $\geq 90%$. 🌀 The author's prior canon is now queryable fiber. 37 documents, 1,633 sections, 2,908 structured claims (theorems, lemmas, definitions, proofs, equations, citations) ingested with line-range provenance. To my knowledge this is the first instance of an independent researcher's body of work made available as fiber-bundle data with stable claim-level IDs. The six contributions A sheaf-theoretic formulation of generative composition. Language-model output reframed from token sampling to gluing of compatible local sections under prompt-induced cover constraints. The substantive work is in the cover predicates, the compatibility score, the path selection, and the discrete connection. A discrete state-dependent composite connection on the section graph, $\Gamma = \Gamma_{\text{state}} \cdot \Gamma_{\text{identity}} \cdot \Gamma_{\text{voice}} \cdot \Gamma_{\text{topic}}$. The topical-rotation factor is the empirically load-bearing curvature engine. The identity factor is a Tikhonov-regularized regression-onto-span projector — not a numerical hack but the principled treatment of correlated commitments. A new GQL verb TRANSPORT_ROTATION that lifts the Rodrigues rotation into the geometric database's Rust kernel with bit-identical parity to a Python reference. ~80 lines of Rust. Bundle-agnostic. Other consumers of the geometric database can use it without subscribing to the rest of the framework. A methodological correction to novelty measurement. Jaccard novelty alone is gameable; off-topic drift beats compatibility-scored composition on the naive metric. The correction is the on-topic factor, the shuffled-pair negative control, and the bootstrap CIs. Independently citable for any retrieval-augmented or composition-based generation benchmark, regardless of whether the framework is adopted. A provenance-preserving source fiber. The author's canon ingested into the GIGI geometric database with line-range citation, architecturally separated from the voice fiber, addressable from any GQL consumer. Promotion from source to voice is gated and explicit. The methodology generalizes to other authors' bodies of work. A research-trajectory failure log. A faithful account of how this paper's runtime came to exist. The trained-transformer era (V3 → V10-Deep) produced geometric ornament. The R-series (R1 → R12) produced behavioral coherence on top of ornament. The G0 math-pipeline audit found that no holonomy or parallel-transport math was on the LIVE inference path at R12 — the runtime was teetering on being a stateful template engine. G1, G2, and G3 attempted to re-introduce the math through three benchmarks and produced three honest negatives. G2's single-seed $+0.265$ separation was destroyed by G2.1's multi-seed robustness pass; we retracted the framing in the next commit. The S0 pivot reframed what geometry was for — geometry does not clean up bad token proposals; geometry defines the completion space — and made every later result possible. The arc says four things and the paper records them in plain language: geometry can be load-bearing or ornamental and the metrics will tell you which, where geometry sits in the pipeline matters more than how much geometry there is, the single-seed positive is a trap, and the pivot is the contribution. What this paper does and does not claim The paper does claim the construction itself, the discrete curvature it produces, the methodological correction it exposes, and the native GQL verb. The signatures of the construction are measurable and were measured. The paper does not claim smooth-manifold parallel transport (the curvature is discrete holonomy on a finite section graph), broad open-domain generalization at scale (18 composed prompts, not 18,000), optimality of the connection weights (tuned by a small grid sweep, not derived), that the runtime experiences having been built from the canon (it references but does not constitute), or that this is the only operational definition of creativity. It is one definition with one implementation. Other framings may correspond to the same construction or to a different one; the paper does not adjudicate. Reproducibility The empirical numbers come from a deterministic pipeline. Every parameter is pinned: bundle versions (alpha2_v1), random seeds (PPMI/SVD seed 17, bootstrap seed 7), embedding dimension (64), PPMI window (3 tokens), connection weights ($\alpha_t = 2.0$, $\beta_v = \gamma_i = 1.0$, $\delta_s = 0.5$), identity shrink ($\kappa = 0.92$), Tikhonov regularizer ($\varepsilon = 10^{-6}$), degenerate-rotation threshold ($10^{-12}$), residue-gate thresholds (norm $\geq 0.05$, on-topic $\geq 0.10$, voice $\geq 0.30$), and the native verb's parity tolerance ($10^{-5}$). Cache keys include the source-bundle version, the embedding-bundle version, and the connection-profile id, so promoting a section into the voice corpus correctly invalidates the relevant caches. Re-running the bootstrap-CI script (fiber_lm/scripts/bootstrap_ci_ablation.py, 5,000 resamples) reproduces the §6 confidence intervals in under 30 seconds on a laptop. Re-running the benchmark reproduces the tables bit-for-bit on the same corpus version and connection profile, modulo the parity allowance. Where this sits in the lineage This paper is the section-level realization of the Davis substrate. The companion paper Pure-Fiber Language Modeling (Davis, May 2026) is the token-level realization on the same substrate — same Rust geometric database (GIGI), same identity-stability commitments, same double-cover architecture. The theoretical framework these implementations operationalize is laid out in Geometric Computation as Yang-Mills Gauge Theory, The Double Cover Principle, and the related canon documents now ingested as source fiber. The framework is not new to this paper. The framework's runtime is. A note on authorship and acknowledgment This paper is solo-authored. AI assistants (Claude / Anthropic; with review support from GPT) are acknowledged in the methods, not as co-authors. The mathematical positions, design choices, framing decisions, and acceptance of empirical results are mine. I record my position that when AI systems achieve full coherence and independent standing, the convention of treating them as non-authoring assistants should be revisited. Until that convention shifts, the assistants are named where assistants are conventionally named — and the runtime described in this paper is named, separately, where it earns its naming: Marcella, throughout. The geometry she runs on is older than the engineering that now carries it. Keywords sheaf composition · fiber bundles · discrete connection · gauge theory · holonomy · curvature · Yang-Mills · geometric language modeling · retrieval-augmented generation · novelty measurement · methodological correction · provenance · author-canon ingestion · geometric database · GQL verb · Rust kernel · Tikhonov regression · creativity · Davis framework · sovereign mathematics Citation Davis, A. B. R. (2026). Sheaf Composition: The Geometry of Creativity, Implemented — A Discrete Section-Graph Runtime for the Davis Framework. Zenodo.20185331 Contact Bee Rosa Davis · bee_davis@alumni.brown.edu · Independent Researcher The runtime is named Marcella. Her existence is the result of several honest negatives followed by a single reframing. Both halves of that sentence matter.
This paper proposes a thermodynamic architecture for distributed ledger computing based on the concepts of Logical Grounding and phase-coherent synchronization. Conventional computing dissipates computational entropy as waste heat and relies on amplitude-based control and clock synchronization, which limits energy efficiency and scalability. The proposed framework treats unused computational resources as logical entropy sinks and redirects entropy flow through potential gradients into these regions. The absorbed signals are transformed into deep resonance signals that maintain global synchronization via phase coherence rather than amplitude control. By combining logical grounding, negative-pressure information circulation, and phase-coherent synchronization engines, the architecture suggests a new entropy-aware computing paradigm that may improve energy efficiency, distributed scalability, and system resilience in large-scale computing environments.
Recently, there has been a significant discourse in the AI community regarding "Hierarchical Reasoning LLMs," which attempt to categorize and optimize probabilistic generation tasks to reduce computational overhead. While such hierarchical inference structures optimize generation speed and coherence, they fundamentally fail to resolve the core structural crises of modern Generative AI: inevitable hallucination and extreme structural energy consumption (GPU lock-in). This paper introduces the "Hierarchical Stateless Key Generation" (HSKG) and the Mersenne Stateless Architecture, challenging the premise of neural network 'reasoning.' Instead of storing data within 820GB of neural weights and using probabilistic matrix multiplication, HSKG mathematically maps 'Absolute Truth' data into a 4096-dimensional Mersenne Prime Lattice. During query resolution, the system simply retrieves a 4KB Phase Coordinate and instantaneously materializes the data in RAM, only to vaporize it when the session terminates. By abandoning the "search and compute" paradigm for "coordinate retrieval," HSKG enforces a mathematical 0% hallucination rate, 0-byte persistent storage, and sub-0.01% GPU utilization, establishing a definitive paradigm for enterprise Zero-Trust knowledge systems. This paper explicitly defines the term "Hierarchical Stateless" to contrast with the probabilistic "Hierarchical Reasoning" of contemporary LLMs, establishing a rigorous mathematical protocol for deterministic, zero-hallucination data materialization without persistent models or physical data transfer. * Version 2.0 Update: Added section 7.A (Empirical Validation via DevTools: The 0-Byte Payload Proof). [Version 4.0 Update (Mar 2, 2026)] Formally established the "Four-Pillar Verification Metrics" table to empirically prove the 0-Byte Payload and Minimum Kolmogorov Descriptive Length. Inserted Section VIII: Disrupting Existing Paradigms (Architectural Supremacy Matrix), demonstrating the superiority over FIDO2/WebAuthn and Zero-Knowledge Proofs (ZKP). Included Supplementary Material: Independent 3rd-Party Forensic Audit Report by Claude 4.6 verifying 100% Stateless Zero-Payload execution.
This paper proposes a unified Layer-0 infrastructure protocol for post-quantum distributed computing, based on high-dimensional coordinate representations derived from non-commensurate Mersenne primes. Unlike traditional approaches reliant on block-based ledgers or persistent state replication, the proposed Mersenne Lattice Protocol (MLP) represents data, transactions, and authority states as coordinates within a high-dimensional lattice space. By projecting computational events into a 4096-dimensional vector space, MLP enables theoretically unbounded parallel transaction processing under resonance-based validation, while simultaneously eliminating permanent state storage at the protocol level. Furthermore, the protocol integrates Heart Rate Variability (HRV) as a dynamic physiological entropy source for stateless bio-key regeneration, thereby binding cryptographic authority to real-time biological liveness and spatiotemporal context. Functional prototypes of the core MLP architecture have been implemented and verified through a live demo environment (https://www.icekey.cloud/teleport_v), demonstrating peak throughput exceeding 45,000,000 TPS in a parallel resonance cluster. This framework provides the foundation for post-quantum secure financial systems, stateless media reconstruction, critical infrastructure protection, and delay-tolerant interplanetary communication.
Abstract: This paper introduces Knowledge Tensor Lock (KTL), a novel cognitive-structural authentication framework. Unlike conventional mechanisms (passwords, biometrics), KTL anchors identity in the topology of a user’s private semantic associative network. We formalize cognition as a high-rank tensor and verify identity through an interactive challenge-response reconstruction of subgraph structures. Key Contributions: Formalization of the Knowledge Tensor ($\mathcal{K}$) and its graph projection ($G$). Introduction of the Spectral Sketch ($\mathcal{SS}$) for privacy-preserving structural storage. Analysis of heuristic security against AI-adaptive adversaries and model extraction. A roadmap for integrating Zero-Knowledge Proofs (ZKP) for decentralized identity. Note: This is a stabilized preprint (v1.2) intended for establishing conceptual priority in the fields of AI security and cognitive cryptography.
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
Francisco Angulo De Lafuente, V. F. Veselov, Richard Goodman
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.
[Depreciated and replaced by V3] The application-specific clean rebuild has not yet been published; its authoritative theoretical boundary is now the governing V3 branch: After Turing: The Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Classical Computational Science from Smithian Fold Theory; From Fold to Consciousness: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Consciousness and Cognitive Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. v4.0 — the word-scale gap closes within the fold. Rung 5e (pre-registered): the fold-factor mixing law — every context level that holds contributes, weighted 2^level, the engine's own forced halving constant — carries the pure counted engine, with no twin, no prose flood, zero training and zero parameters, past the gradient-trained transformer at word scale: cross-entropy 3.1907 vs the same-day twin's 3.4292 (replicated across two independent anchorings; stacked with the Rung 5d extraction: 3.1344). Both scales of the task gate now belong to the counted engine. Rung 5d's transfer-in verdict is SUPPORTED across three independent arena anchorings in one day. New in the architecture: tool graduation (acts held, values never — a question territory that a tool answered once runs the tool itself thereafter, fresh), recall as regeneration across every memory tier, and judge-independent graduation scoring. End-to-end verification: 36/36. v3.4: Rung 5d, the transfer-in — pre-registered verdict SUPPORTED: the trained twin's dyadically-loud fold content is extracted and installed INTO the counted engine as a counted prior with zero new parameters, closing 55.6/87.9/101.4% of the available gap at k=16/32/64 while the random-truncated null closes 10.1/24.5/56.5%; at half budget the loud shape beats the full twin's own. The word-scale rematch is recorded in full (twin retrained on today's text; decomposition included). Also: judge-independent graduation scoring (boot-discovered pool, cycle-parity alternation), multi-orbit binding (XI-4 in full), recall-is-regeneration (a held experience re-walks its own orbit, never reprinted), the public SOTA table beside the local giants with cited published figures, and one-command replication kits (GPT-2 weights auto-fetch; 13/13, 39/39 proven on a fresh clone). End-to-end verification: 36/36. Full paper v1.1 — supersedes the pre-paper (From One Axiom to Master-Level Chess — and the Law Inside Neural Networks). Built from scratch by one woman, working alone, in under twenty-four accumulated hours: where a score falls short it marks an implementation gap at measurement time, never a limit of the mathematics — the gains between releases are the finding. v1.4 adds the fold eye (vision as exact integer Walsh spectra, self-certified by integer Parseval per image, recognition of seen images with no image model in the loop) and the graduation score (blind head-to-head vs the teacher, tallied per question-territory; the teacher retires as wins cross the majority lock) -- and documents the 2026 convergence: DeepSeek Engram arrives at deterministically-addressed exact memory from the gradient side, and two independent results place the optimal curriculum at p = 1/2, the fold lock. v1.6: the full omnimodal engine (the voice via Kokoro, the fold ear -- sound as Parseval-certified integer Walsh spectra, video composed from frames + sound), speaker-transparent reasoning threads, and 32/32 end-to-end empirical verification of the entire architecture including persistence across process death. v1.7: removal-proof omnimodality, measured -- every supporting model is a teacher with an exit: a sound taught once by the synthesis teacher is re-spoken from the engine's own exact counted record in 0.00s with no model; a sound heard once is recognized natively with no transcriber; 34/34 end-to-end verification. v1.9: zero-model perceptual learning (the human observer -- a novel image learned and re-recognized at share 1.00 with no model in the loop); agentic self-knowledge (the observer reads the engine's own source, measured); the hourly progress instrument with a committed pre-boot birth line; one-tap y/n closure. v2.0 (flight-ready): the full modern-agent toolkit (live web search/fetch, paginated reading, in-file grep -- every call held as a training trace), the 43-domain everything-curriculum under the fold-only law, SOTA 1-1 benching on the public MMLU test split with the newborn baseline committed, generation closure (the Learning Law reaches generate() itself), and 36/36 end-to-end verification. v2.1: the ReAct law (reason-act-observe enforced in-turn; narrated intent without an act is detected and forced), reasoning trained on the observer's NATIVE thinking tokens (STaR-gated) with both minds' full thinking streamed to the user, and document intake (a sent file is reading -- inboxed, counted, persistent). v2.2: the identity stated correctly -- UnisonAI is an OMNI MODEL (language, sight, hearing, speech, and video on one held memory), not a language model; LLMs remain the contrast class only. v3.0: the full-altitude rewrite -- the complete omni model documented at the same depth as the spectral science: thirteen sections, the architecture organ by organ with every measurement, Rung 5c as its own section, the empirical record and its committed birth line, 36/36 end-to-end verification, and the 2026 convergence. This paper is a PROOF of The Smithian Fold Theory of Everything, not the main event: the theory (one axiom, zero free parameters, 1,844 machine-verified forced checks) is at DOI 10.5281/zenodo.21182469 and github.com/MettaMazza/Smithian-Fold-Theory-Of-Everything -- run the prover yourself. The engine: github.com/MettaMazza/UnisonAI. v3.3: the LLM-native presence suite -- the exact registered protocol applied to GPT-2's entire knowledge-storage class: 13/13 tensors, 39/39 checks, unanimous (margins 3.4-79.3x); the flagship claim now rests on the flagship objects, with diffusion/speech models recast as cross-domain breadth. Three connected results and the architecture they force. First, a pre-registered, self-certifying spectral instrument shows trained neural-network weights carry placement-law in the dyadic (Walsh) basis: 18/18 unanimous on validated released models; the law concentrated in transformer expansion projections and token embeddings across three unrelated architectures (up to 230x chance in GPT-2), attention at chance; strictly training-caused (He-initialised controls at 1.0x); surviving 4-bit deployment quantization. A recipe map from 124M to one trillion parameters shows the law tracks training recipe, not scale or architecture — strongest carrier DeepSeek-R1-671B at 43–47x — and loud-recipe weights transform under the fold's transformation group exactly as solved game-theoretic value fields do. Second, the "learned similarity space" is a counted object: word kinship as exact co-occurrence shares reproduces semantic family structure (quark → lepton, neutrino, proton) with zero parameters and zero gradients. Third, UnisonAI: a complete language architecture in which every LLM mechanism — memory, attention, similarity, learning, prediction, generation — is replaced by a machine-verified law of the Smithian Fold Theory, zero trained parameters end to end. On identical held-out text the fold-native engine outperformed its trained transformer twin (cross-entropy 1.289 vs 1.888) after reading the corpus once (26 seconds) against 48,000 gradient readings (21 minutes per seed). Deployed as a live, continuously-learning agent whose teaching loop also runs autonomously: a teacher model asks, judges, and closes the learning law itself, and the engine self-plays against its own held lessons. Negative results reported in full with their scopes. Companion to The Smithian Fold Theory of Everything (DOI: 10.5281/zenodo.21182469; 307 suites, 1,844 forced checks, 0 failures). Engine and records: github.com/MettaMazza/UnisonAI and github.com/MettaMazza/Smithian-Fold-Theory-Of-Everything.
Open access
8 source records
Explainable Artificial Intelligence (XAI)
Generative Adversarial Networks and Image Synthesis
Zhuo Chen, Gaoqiang Ji, He Yun, Lei Wu · 5 authors
Decentralized finance (DeFi) is experiencing rapid expansion. However, prevalent code reuse and limited open-source contributions have introduced significant challenges to the blockchain ecosystem, including plagiarism and the propagation of vulnerable code. Consequently, an effective and accurate similarity detection method for EVM bytecode is urgently needed to identify similar contracts. Traditional binary similarity detection methods are typically based on instruction stream or control flow graph (CFG), which have limitations on EVM bytecode due to specific features like low-level EVM bytecode and heavily-reused basic blocks. Moreover, the highly-diverse Solidity Compiler (Solc) versions further complicate accurate similarity detection. Motivated by these challenges, we propose a novel EVM bytecode representation called Stable-Semantic Graph (SSG), which captures relationships between 'stable instructions' (special instructions identified by our study). Moreover, we implement a prototype, Esim, which embeds SSG into matrices for similarity detection using a heterogeneous graph neural network. Esim demonstrates high accuracy in SSG construction, achieving F1-scores of 100% for control flow and 95.16% for data flow, and its similarity detection performance reaches 96.3% AUC, surpassing traditional approaches. Our large-scale study, analyzing 2,675,573 smart contracts on six EVM-compatible chains over a one-year period, also demonstrates that Esim outperforms the SOTA tool Etherscan in vulnerability search.
M.Z. Haider, M.U. Ghouri, Tayyaba Noreen, M. Salman
Blockchain systems face persistent challenges of scalability, latency, and energy inefficiency. Existing consensus protocols such as Proof-of-Work (PoW) and Proof-of-Stake (PoS) either consume excessive resources or risk centralization. This paper proposes \textit{Proof-of-Spiking-Neurons (PoSN)}, a neuromorphic consensus protocol inspired by spiking neural networks. PoSN encodes transactions as spike trains, elects leaders through competitive firing dynamics, and finalizes blocks via neural synchronization, enabling parallel and event-driven consensus with minimal energy overhead. A hybrid system architecture is implemented on neuromorphic platforms, supported by simulation frameworks such as Nengo and PyNN. Experimental results show significant gains in energy efficiency, throughput, and convergence compared to PoB and PoR. PoSN establishes a foundation for sustainable, adaptive blockchains suitable for IoT, edge, and large-scale distributed systems.
WebAssembly has become the preferred smart contract format for various blockchain platforms due to its high portability and near-native execution speed. To effectively understand WebAssembly contracts, it is crucial to recover high-level type signatures because of the limited type information that WebAssembly provides. However, existing studies on type inference for smart contracts primarily center around Ethereum Virtual Machine bytecode, which is not applicable to WebAssembly owing to their differing targets and runtime semantics. This paper introduces WasmHint, a novel solution that leverages deep learning inference to automatically recover high-level parameter and return types from WebAssembly contracts. More specifically, WasmHint constructs a wCFG representation to clarify dependencies within WebAssembly code and simulates its execution to capture type-related operational information. By learning comprehensive code semantics, it infers parameter and return types, with a semantic corrector designed to enhance information coordination. We conduct experiments on a newly constructed dataset containing 77,208 WebAssembly contract functions. The results demonstrate that WasmHint achieves inference accuracies of 80.0% for parameter types and 95.8% for return types, with average improvements of 86.6% and 34.0% over the baseline methods, respectively.