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 An agent that inherits a consolidated memory may inherit a constraint that was true when written and has since been withdrawn by a newer authoritative record.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what changes is which record is current — and assign by design the memory's form, the world's state (source current or superseded), and the verification policy at a fixed budget of two records: the agent's own allocation, or the same budget with one slot re-assigned to the critical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a constraint stated, agents inspected its provenance path in about one episode in five; when that constraint had been superseded, native allocation produced stale-consistent decisions in 77.3%, 74.7% and 74.7% of episodes across a primary run, a fresh-wording replication and a held-out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.
AuraOS Paper IX: Objective-Native Capability Commons and Proof-Carrying Contribution Economies Version 2.0 - Expanded Same-Day Edition Author: Dallas Courchene Date: August 7, 2026 Claim range: N51-N100 This expanded same-day edition supersedes the initial August 7, 2026 release of AuraOS Paper IX while preserving its original architectural spine, repository anchor, and defensive prior-art declarations N51-N87. It adds thirteen new combination-scoped declarations, N88-N100, and folds their enabling embodiments into the relevant sections of the paper rather than fragmenting the architecture across a separate follow-on publication. Paper IX develops AuraOS beyond an application-centric or chatbot-centric model into an objective-native, proof-carrying computational and economic substrate. A person, organization, community, institution, or other authorized principal begins with an objective, constraints, rights, privacy requirements, evidence requirements, budget, and authority. Aura then composes a bounded Ephemeral Arena from persistent capability packages, Arena Recipes, humans, AI workers, data, simulators, rule packs, facilities, and services. Verification, semantic-gate execution receipts, provenance, attribution, human/institutional responsibility declarations, canonical-owner disposition, explicit promotion, and deterministic dissolution remain separate stages. The original N51-N87 disclosures establish the core architecture: minimum-sufficient objective compilation; hierarchical evidence hydration; persistent Capability Packages; rebindable Arena Recipes; explicit promotion and dissolution; federated Aura Commons; executable rights; proprietary capability execution without mandatory source disclosure; semantic-gate Attestation DAGs and lazy provenance; durable agent identity bound to bounded internal authority; meaningful-use contribution economics; a proof-carrying Developer Arena; reviewer-independence lineage; causal credit separated from execution traceability; Personal Cognitive Capsules and portable personal SLMs; privacy membranes and semantic translation; governed recursive harness learning; intent-native manifestation and spatial code breadboarding; Aura Places and Convention Arenas; reactive and proactive discovery; an Open Discovery Foundry; physics/digital-twin and bounded social simulation; business incubation; cross-domain sovereign federation; participatory Scientific Arenas; contributed compute and facilities; and a compounding Scientific Capability Commons. The expanded N88-N100 disclosures complete several consequences of that substrate. N88 formalizes a three-speed Architecture Arena and convergence compiler. Fast architectural discovery is separated from medium-speed implementation/hardening and slow constitutional change. Candidate advances become Architectural Delta Objects, are checked against canonical owners, invariants, duplicate-plane risk, threat-model effects, prior art, and proof obligations, and are then compiled into bounded implementation, security, migration, documentation, research, and verification work for the Developer Arena. This allows architectural ideation to move faster than pull-request integration without allowing implementation velocity to rewrite Aura's constitutional planes. N89 introduces a demand/capability graph capable of identifying keystone bottlenecks: missing capabilities, methods, facilities, standards, or processes whose resolution could unlock unusually large numbers of currently blocked objectives. This supports evidence-informed code, research, optimization, replication, falsification, boundary, field-validation, and manufacturing bounties while keeping prioritization advisory and locally governable. N90-N94 extend the architecture into human opportunity, learning, privacy, credentials, professional identity, and creator economics. A privacy-preserving Opportunity Compiler can locally match a person's verified capability evidence, goals, availability, jurisdictional constraints, and disclosure policy to jobs, bounties, research nodes, mentorship, local services, and temporary teams. Learning Arenas can compile capability gaps into progressively verified learning and supervised work. Raw LifeOS and Personal Cognitive Capsule history is explicitly separated from portable verified claims: private longitudinal data remains mutable, correctable, revocable, exportable, and deletable, while only bounded credentials or contribution claims are disclosed. Aura Places may function as evidence-bearing contribution portfolios, but the architecture explicitly rejects a mandatory universal social-credit score. Creator, referral, sponsorship, and educational attribution is divided into graded evidence classes so that exposure or a click cannot be silently misrepresented as unique causality. N95 expands the Scientific Arena into a multi-class research-bounty market that can separately reward discovery, replication, falsification, boundary-condition discovery, optimization, generalization, field validation, and specialized facility execution. Laboratories, universities, private R&D facilities, community research centres, specialist workshops, instruments, and other qualified facilities may satisfy bounded physical-work nodes with explicit protocol, safety, jurisdiction, evidence, and milestone requirements. Negative or boundary results can therefore be economically valuable rather than forcing incentives toward positive confirmation. N96 discloses objective-compiled Ephemeral Institutions: temporary collaboration structures formed when an objective requires people, organizations, Nations or communities, facilities, professional roles, funding sources, data rights, services, and governance responsibilities across existing institutional boundaries. Aura may compile the coordination graph and required agreements, but real principals retain incorporation, contract, procurement, insurance, hiring, equity, and other legal authority. Repeated successful collaboration may later support a human decision to create a durable cooperative, consortium, enterprise, laboratory, or service network. N97-N98 extend the Commons into physical production. Machines, workshops, laboratories, factories, and service providers can expose signed capability manifests describing processes, materials, tolerances, calibration, evidence/certification class, locality, availability, cost, operator requirements, and prohibited uses. A validated design can then be compiled against authorized local production resources without treating substitutions as automatically equivalent. Manufactured artifacts can retain a living lineage containing design version, material/process evidence, machine/facility identity, inspection, repairs, modifications, safety notices, field results, and reuse or recycling pathways. Field failures can generate new repair, redesign, maintenance, material-substitution, or research bounties, closing the cycle from need to research to prototype to production to field learning and back into the Commons. N99 defines AuraNet as a transport-neutral logical network of sovereign principals and capabilities rather than a mandatory peer-to-peer topology. Personal devices, local servers, hosted sovereign data services, community/Nation infrastructure, enterprises, federated personal-data servers, relays, P2P links, offline/intermittent nodes, and future transports may participate if they preserve identity, rights, minimum disclosure, provenance, portability, revocation, and canonical-owner semantics. Cross-border composition remains jurisdiction-aware: privacy technology does not erase law, professional regulation, cultural/community authority, export restrictions, sanctions, data-residency obligations, or a node's right to refuse composition. N100 completes the accountability/economic stack with proof-carrying assurance contracts. A warranty, service-level agreement, professional assurance, or insurance-reference contract may bind a specific artifact/process version, covered predicates, verifier class, provenance root, responsible principal, operating conditions, duration, exclusions, remedies, and responsibility declarations. Machine receipts, cryptographic hashes, verifier results, and human/institutional attestations provide evidence, but they do not manufacture certification, legal liability, insurance coverage, negligence, warranty obligations, or truth. Any such consequence remains the product of an explicit governing contract, law, regulator, insurer, professional body, or other authorized institution. The expanded paper also strengthens the privacy model through a "compute-to-data" principle: when practical, admitted computation should move toward sovereign private data before private data is exported toward external computation. The reference architecture may combine local AI/SLM execution, selective disclosure, Verifiable Credentials, differential privacy, zero-knowledge proofs, multiparty computation, private-set methods, trusted execution, or homomorphic computation according to the threat model; none is treated as a universal anonymization guarantee. The central economic thesis remains that the permanent unit of value need not be a monolithic application. It can be a verified, attributable, rights-bearing capability, method, workflow, scientific result, fabrication process, contribution, credential, or other reusable object that participates in many temporary objective-specific Arenas. Value can therefore become legible through meaningful verified contribution and lineage, while licensing, provenance, attribution, settlement, scientific truth, authority, certification, and human/institutional responsibility remain explicitly separate layers. The combined architecture describes a possible progression from app-centric computing toward a governed Commons of persistent capabilities, portable personal cognition, conve
Abstract Financial time-series forecasting lies between AI and market microstructure, but most studies optimise generic error metrics instead of risk-adjusted economic value under realistic frictions. Unlike NLP and vision, the field lacks a shared, reviewer-enforced standard for data handling and evaluation, leading to persistent problems such as data leakage, backtest overfitting and metric-chasing on RMSE/MAE. This paper introduces QFRS a novel, enforceable by reviewers and editors, seven-standard framework and checklist for evaluating and reporting financial asset forecasting and trading claims. QFRS covers quantitative studies on equities (stocks), forex, cryptocurrencies, rates, derivatives (futures, forwards, options, swaps), energy prices, and commodities (gold, oil and silver) and other asset classes. The seven standards specify an end-to-end experimental pipeline, covering (i) dataset construction, (ii) labelling, (iii) point-in-time feature engineering, (iv) leakage-free scaling or normalisation, (v) time-respecting data splits, (vi) evaluation metrics and (vii) cost and slippage-aware backtesting with explicit execution assumptions and decision rules mapping predictions to positions. To validate the standard’s diagnostic value, a compliance audit of Scopus-indexed forex forecasting papers published in 2025 is presented. None of these papers achieved full compliance across all seven standards, with economic backtesting (12.2%) and causal scaling (31.7%) recorded the lowest pass rates. QFRS underpins a public state-of-the-art leaderboard, ensuring that only studies satisfying these standards are ranked, with the goal of shifting the literature from opaque, error-metric-driven results to transparent, economically meaningful and comparable benchmarks. The accompanying leaderboard is available and updated regularly at http://mkhushi.github.io .
The democratisation of digital content creation tools has transformed media production, enabling individuals to move from being only consumers to active creators. Yet, content marketplaces and AI ecosystems remain highly centralised, limiting transparency, control, and fair compensation. Generative AI (GenAI) systems, trained on massive web-scraped datasets, exacerbate these issues by reusing creative work without consent, attribution, or reward, raising legal and ethical concerns. This thesis explores how decentralisation can redistribute power in the creative economy by giving creators agency over the use of their media in GenAI. First, we introduce a decentralised registry through which creators can assert opt-in/out preferences for AI training. Content is embedded with provenance metadata and registered with robust fingerprints, enabling provenance tracing even after editing or manipulation. This establishes machine-readable, traceable consent specification as the foundation for downstream attribution and reward. Building on this, we propose methods for training data provenance, attribution, and compensation in GenAI training. The Content ARCs (Authenticity, Rights, Compensation) framework defines a scalable protocol for managing rights and creator compensation. We instantiate this in a decentralised system that traces generative outputs back to the most influential training assets and executes royalty payments to contributors. Several practitioner-facing demonstrators developed in collaboration with GLAM (galleries, libraries, archives, and museums) professionals further illustrate how distributed ledgers could reshape licensing and reward in the creative economy. Further, GenAI models are prone to memorising training data and reproducing it at generation time, a phenomenon that is particularly problematic for copyrighted creative works, where such regurgitation undermines both creator rights and data privacy. To address this challenge, we present a decentralised federated learning protocol for diffusion models that reduces training data memorisation using a novel sample-based metric integrated into the protocol to detect and discourage memorisation. Complementing this, we develop a framework for end-to-end cryptographically verifiable AI pipelines using zero-knowledge proofs to enable trustless, privacy-preserving audits. Finally, we explore privacy-preserving natural language search across decentralised content repositories using encrypted queries for similarity search at scale. In this way, decentralisation supports discovery and access to creative content, completing a holistic body of work for a fairer, more transparent GenAI ecosystem and creative economy.
Ledgeral Mathematics: A Finite Algebra of Recursion, Admissibility, Projection, and Survivor Structure This repository contains the complete public edition of Ledgeral Mathematics, a foundational mathematical monograph that develops a finite algebra of recursion, admissibility, projection, survivor formation, residue retention, transport, composition, optimization, falsification, and audit. The theory begins from the retained finite record, an explicitly formed object whose carrier, addresses, entries, active support, inactive structure, status, formation history, comparison discipline, readout route, and audit relation remain part of its mathematical identity. Ledgeral Mathematics begins at a more primitive level than mathematical systems that take numbers, points, sets, spaces, functions, graphs, trajectories, or continua as already available objects. Those structures may be constructed and used within the theory, though they do not receive automatic foundational standing. Every object must first declare what carries it, what occupies each retained address, how it was formed, what operations may act upon it, what transformations are permitted, and what information must remain available after those transformations have occurred. The central admission principle is straightforward. Nothing enters the mathematics by implication. Every lawful object must have a finite retained form. Every operation must declare its input region, carrier rule, entry rule, legality conditions, invalidity conditions, and output status. Every comparison must identify the equality relation being used. Every readout must preserve a trace to the record from which it was produced. Every projection must identify what survives, what is rejected or displaced, and how the full event can be audited. This discipline allows Ledgeral Mathematics to preserve distinctions that conventional notation may compress or erase. A lawful null record is different from an invalid expression. A missing object is different from a retained object with inactive support. Candidate status is different from survivor status. Residue is different from error, absence, or nonexistence. Carrier equality, support equality, entry equality, readout equality, provenance equality, and full record equality are separate mathematical claims. The relevant comparison must therefore be declared rather than assumed. One of the central structures of the theory is the survivor-residue-audit form of projection. A candidate record is submitted to a declared admissibility rule and projection procedure. The projection produces a survivor, a residue, and an audit packet. The survivor contains the structure admitted by the projection. The residue retains rejected, displaced, suppressed, obstructed, unresolved, or otherwise excluded structure. The audit records the candidate, the governing admissibility conditions, the projection route, the resulting survivor, the resulting residue, and the verification status of the event. Projection therefore does more than select an accepted output. It retains the mathematical consequences of exclusion. Loss becomes inspectable. Rejection becomes information. Suppression remains traceable. A lawful null survivor may coexist with nonempty residue. An active survivor may retain displaced structure outside its support. A mixed event may preserve admitted components, rejected components, and formation failures under different statuses. These distinctions allow later analysis of irreversibility, obstruction, instability, hidden coupling, model disagreement, implementation failure, measurement conflict, and operation-order dependence. Recursion is developed through the same finite retained discipline. A process does not receive an unbounded history in advance. It is represented through finite depth carriers, finite update words, finite survivor chains, finite branch records, finite residue histories, and finite continuation audits. Persistence is established through repeated admitted continuation across retained recursion depth. Branching, merging, recurrence, stabilization, obstruction, termination, return, cyclic behavior, and irreversible loss remain available as explicit finite structures. The monograph extends this foundation into operator-word algebra, holonomy calculus, finite transport and boundary accounting, constitutive algebra, branching and capacity calculus, co-admissibility, convergence, directed persistence, signal and readout calculus, finite recursion-spectral analysis, regime classification, construction and optimization, audit and falsification, and representation-layer quarantine. The full work is organized across twenty-three major sections, a global closure, and five technical appendices devoted to notation, dependency tracking, result indexing, verification, reproduction, serialization, archiving, implementation boundaries, and execution audit. Representation remains available throughout the theory, though its role is controlled. Equations, arrays, tables, coordinates, diagrams, graphs, curves, spectra, statistical models, analytic expressions, and continuous systems may be generated as readouts from ledgeral records. A representation does not become a native object merely through familiarity or usefulness. It may enter native calculation only after it has been reconstructed as a finite retained record with a declared carrier, entries, role, formation rule, and audit trace. This separation preserves the distinction between a mathematical object and the representation used to inspect, communicate, or calculate with it. Ledgeral Mathematics was developed partly in response to the foundational requirements of Post-Temporal Physics, though it is presented here as an independent mathematical system. Its potential applications extend across foundational mathematics, algebra, logic, proof theory, discrete systems, physics, computation, artificial intelligence, formal verification, data provenance, system assurance, engineering, sensing, control, optimization, scientific measurement, model comparison, reproducibility, and falsification. The theory does not claim that established mathematical systems are unnecessary. It presents a distinct foundational program organized around finite formation, retained accountability, explicit admissibility, preserved residue, and auditable transformation. This repository contains the foundational public volume. Implementation-oriented methods, domain-specific extensions, and the separate companion program known as Applied Ledgeral Mathematics are outside the scope of this release and are not presently being distributed openly. Portions of that work may carry significant dual-use implications. Any future distribution of unpublished applied material may therefore be considered individually following appropriate legal, export-control, security, intellectual-property, and end-use review. This publication-scope notice does not designate the public monograph or any unpublished companion material as classified, ITAR-controlled, EAR-controlled, export-controlled, or otherwise restricted by the United States Government. Any legal determination of that kind must be made by qualified authorities or professional counsel. The published monograph is released under the Creative Commons Attribution 4.0 International License. That license applies only to the material contained in the publicly released volume. It does not apply to unpublished manuscripts, software, datasets, implementation packages, technical materials, or companion works unless those materials are separately released under the same license.
A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.
Title: Holographic Bitcoin: A Material-Anchored Consensus Protocol for Spatiotemporal State SynchronizationAbstract:This research proposes a novel \textit{Holographic Distributed Architecture}, a paradigm shift that transitions decentralized ledgers from soft-informational registers to hardware-native, physically-anchored systems. In the face of quantum computational threats and the systemic fragility of legacy digital assets, we introduce an immutable consensus framework rooted in the thermodynamic entropy of Lichtenberg lightning-lattice entities.The architecture leverages a high-energy collision manifold—defined by the $K=10^{22}$ scaling coefficient—to harmonize Bitcoin's computational intensity with physical-layer state transitions, establishing an irreversible "spatiotemporal anchor." We further demonstrate a rigorous three-phase evolutionary model that guides the network from a centralized genesis to a sovereign, community-governed Physical Proof-of-Stake (P-PoS) system. This governance model integrates Human-Centric Proof-of-Work (H-PoW) and identity-anchored participation, ensuring adversarial resilience through a combined lens of physical provenance revocation and legal accountability.By optimizing the network as a minimalist "Provenance Registry" rather than a high-volume transaction conduit, our framework achieves extreme scalability without sacrificing security. Our tiered participation model successfully bridges the gap between radical privacy-centric sovereignty and institutional legal protection. This study provides a comprehensive solution for a thermodynamically authenticated, post-quantum resilient infrastructure, laying a material foundation for the future of decentralized human and artificial intelligence synergy.Keywords: Holographic Architecture; Physical Consensus; Lichtenberg Lattices; Spatiotemporal Anchoring; Provenance Registry; Post-Quantum Security; Collatz Gauge Field.
Nobuki Fujimoto, Rei, (Anthropic, claude-opus-4-7), Claude
⚠ v0.0 OUTLINE intentional publication — Pattern 4 mitigation embedded. This is an OUTLINE, not a v0.1 publishable manuscript. The central operational claim — that Rei provides a formal-verification compilation pass composing with AI hypothesis generators (AlphaEvolve, LLM Wiki, OpenEvolve) — requires at least one end-to-end demonstration before v0.1 promotion. As of 2026-05-22 the demonstration is at scaffold-level smoke-run stage only (OpenEvolve scaffold structurally validated, but full 100-iteration evolutionary loop with real evolved Lean 4 proof NOT YET executed). Publication-as-v0.0 is intentional honest framing per OUKC feedback_no_rush_publication.md: rather than wait silently for v0.1 evidence, the OUTLINE is published with explicit gate state so reviewers can see exactly what is and is not claimed. Framing concept: AlphaEvolve / LLM Wiki / OpenEvolve = hypothesis generators (loosely-grounded, fast, large-search). Rei = proof completer (mechanically verified, slow, decisive). Together they compose: hypothesis generator emits candidates → Rei evaluates via D-FUMT₈ 8-axis projection (γ-evaluator) + Lean 4 zero-sorry validation (β-evaluator) → return verified candidates to the evolutionary loop. Rei is positioned as a formal-verification compilation pass in the AI-mathematics generation pipeline. Scaffold evidence (2026-05-22): external/openevolve-rei/ — YAML config (Ollama 3-prover ensemble), Python evaluators (β = Lean 4 zero-sorry, γ = D-FUMT₈ projection), example skeleton (26-circle packing 2.635 benchmark). 4 smoke-tests PASS: yaml parse + 3 Python AST parse + circle_packing standalone execution (n=26 r=0.4167 density=14.18) + γ-evaluator returns OpenEvolve-compatible dict with metrics (axis_dominant=ZERO 9 hits, score=0.0154) + artifacts (token_count=13). Per SCOPE.md non-claims: this is NOT a fork of OpenEvolve, NOT a claim of 26-circle 2.635 reproduction, NOT a claim that Rei has built an evolutionary code generator, NOT a paper-publishable result by itself. v0.1 acceptance criteria (10 items): see §9. Core gates: OpenEvolve installed + first 100-iteration loop completes + real evolved Lean 4 proof generated + scaffold extended with at least one zero-sorry proof for one open conjecture from META-DB Tier 1. v0.1 will publish as Zenodo new-version preserving DOI lineage from this v0.0 record. Honest scope (read first): (1) This is OUTLINE only — framing + prior-art audit + acceptance criteria, no end-to-end evidence. (2) Rei is NOT a hypothesis generator — its role in this composition is specifically as the verifier/completer. (3) Per feedback_world_uniqueness_claim_controllable.md: we use "to our knowledge no equivalent Lean 4 zero-sorry + D-FUMT₈ 8-axis evaluator exists in the OpenEvolve plugin ecosystem as of 2026-05-22" phrasing, NOT "world-first." (4) Three-party co-authorship (Fujimoto / Rei / Claude) per OUKC charter v1.0. (5) Per OUKC No-Patent Pledge — no patent will be filed.
Open access
2 source records
Mathematics, Computing, and Information Processing
While Large Language Models have achieved notable success on formal mathematics benchmarks such as MiniF2F, it remains unclear whether these results stem from genuine logical reasoning or semantic pattern matching against pre-training data. This paper identifies Architectural Reasoning: the ability to synthesize formal proofs using exclusively local axioms and definitions within an alien math domain, as the necessary ability for future automated theorem discovery AI. We use the Obfuscated Natural Number Game, a benchmark to evaluate Architectural Reasoning. By renaming identifiers in the Natural Number Game in Lean 4, we created a zero-knowledge, closed environment. We evaluate state-of-the-art models, finding a universal latency tax where obfuscation increases inference time. The results also reveal a divergence in robustness: while general models (Claude-Sonnet-4.5, GPT-4o) suffer performance degradation, reasoning models (DeepSeek-R1, GPT-5, DeepSeek-Prover-V2) maintain the same accuracy despite the absence of semantic cues. These findings provide a quantitative metric for assessing the true capacity for mathematical reasoning.
Open access
3 source records
Mathematics, Computing, and Information Processing
MH8-Acbeatz.com-MP3-GPT-PLaylist + All MH8 Acbeatz.com GPT driven Systems> is the first decentralized protocol to embed SHA-256 cryptographic provenance into AI-assisted music at the moment of creation — not after. Each lyric, prompt, and generated audio file receives a deterministic 256-bit serial number (a "Music & Lyrical Birth Certificate") before it ever leaves the creator's pipeline, establishing immutable, verifiable authorship without reliance on any central registry or blockchain consensus mechanism. The system operates as a constellation of protocol-driven AI agents — ABE-GPT, Suno-GPT, Social-GPT, Support Office GPT, and MP3-GPT Playlist — orchestrated through a Cloudflare Worker acting as a Model Context Protocol (MCP) server, with R2 object storage and KV state management providing an append-only, tamper-evident storage layer. Economic primitives (Deal Board, Bounty Marketplace) and a multi-platform distribution model (acbeatz.com, GitHub, Ko-fi, Discord) complete the stack. This whitepaper presents the full protocol specification: system architecture, SHA-256 identity layer, streaming infrastructure, economic modules, novelty claims, IP positioning via defensive publication, a seven-vector threat model, current limitations, and a forward roadmap including IPFS integration, formal verification, and zero-knowledge provenance proofs. Author: Michael M. Hepler (acbeatz / allchemicalbeatz) License: CC BY 4.0 Version: 1.0 — April 2026 Abstract — Problem statement, MH8 solution, and system summary Introduction — AI music provenance gap, the "Birth Certificate" concept, and your contributions Scientific Framing & Related Work — Positioning against Audius, IPFS, C2PA, DIDs, and why SHA-256 at genesis is fundamentally different System Architecture — Agent ecosystem (ABE-GPT, Suno-GPT, Social-GPT, Support Office GPT, MP3-GPT Playlist), Cloudflare Worker pipeline as MCP server, and R2/KV storage layer SHA-256 Identity Layer — Full 6-step provenance pipeline from canonical payload to lineage chaining Streaming Layer — R2-backed delivery with embedded provenance Economic Modules — Deal Board, Bounty Marketplace, and LifeCoin concept Distribution Model — Multi-platform strategy across Zenodo, GitHub, Ko-fi, Discord, and social channels Novelty & Originality Claims — Five defensible firsts IP Positioning — Defensive publication via Zenodo DOI and CC BY 4.0 Threat Model — Seven attack vectors with mitigations Limitations — Honest constraints Future Work — Roadmap including IPFS, formal specs, ISMIR submission, ZK proofs References — Academic citations (FIPS 180-4, MCP, C2PA, W3C DIDs, etc.) Appendices — SHA-256 receipt example, agent identity schema, orchestrator API endpoints https://zenodo.org/records/18131984 (C T K L T) Core: https://acbeatz.com/n-eyes https://acbeatz.com https://github.com/acbeatz https://orcid.org/0009-0003-3846-9082
A Groth16 zero-knowledge proof is published certifying the existence of a 152-bit Slater-determinant occupation string for the standard FeMoco active-space Hamiltonian (113 electrons, 76 orbitals) whose Hamiltonian expectation value on the public LLDUC FCIDUMP [1] — evaluated in the fixed split-localised orbital basis of [1] without orbital optimisation — is −22053.164626725997 Ha. The string satisfies 58 alpha + 55 beta = 113 electrons and MS = 3/2, matching the active-space constraints of [1]. The proof is verifiable in under one second by any party in possession of the proof artifact and verification key, with no access to the FCIDUMP or the occupation string itself.
Samrendra Roy, Souvik Chakraborty, Rizwan-uddin, Syed Bahauddin Alam
Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking Compositional Neural Operator (SCNO), a modular architecture combining spiking and conventional components that addresses all three limitations. SCNO maintains a library of small spiking neural operator blocks, each trained on a single elementary differential operator (convection, diffusion, reaction), and composes them through a lightweight input-conditioned aggregator to solve coupled PDEs not seen during block training. A small correction network learns cross-coupling residuals while keeping all blocks and the aggregator frozen, preserving zero-forgetting modular expansion by construction. We evaluate SCNO on eight PDE families including five coupled systems and a nuclear-relevant 1-group neutron diffusion equation. SCNO with correction achieves the lowest relative $L^2$ error on four of five coupled PDEs, outperforming both a monolithic spiking DeepONet (by up to 62%, mean over 3 seeds) and a standard ANN DeepONet (by up to 65%), while requiring only 95K trainable parameters versus 462K for the monolithic baseline. To our knowledge, this is the first compositional spiking neural operator and the first proof-of-concept for modular neuromorphic PDE solving with built-in forgetting-free expansion.
Title: Compositional Transfer in Neural World Models via Symbolic Law Discovery Core Thesis This research establishes a mathematically grounded paradigm for Modular World Modeling, where physical invariants are recovered as additive vector fields rather than monolithically memorized. We prove that by framing learning as Tangent-Space Residual Superposition, neural networks can internalize isolated physical laws that compose zero-shot to predict complex, unseen multi-physics environments. Key Breakthroughs & Upgrades The Compositional Scaling Law (2D to 12D) Our experiments reveal a fundamental divergence in high-dimensional scaling. While monolithic models suffer from "Baseline Washout" and entanglement, our modular ensembles maintain physical integrity across 12-dimensional manifolds. In chaotic triple-force environments, the modular framework achieves a 6.5× reduction in trajectory MSE ($71.5 \times 10^{-4}$ vs. $470.2 \times 10^{-4}$ for the monolith). Causal Discovery: Active Gradient Conflict ($\rho \approx -0.99$) We provide the first empirical proof identifying the causal driver of monolithic failure. Gradient alignment analysis reveals that monolithic models are trapped in a state of Active Gradient Sabotage, where the update required for one force (e.g., Gravity) almost perfectly cancels out the update for another (e.g., Spring). Our framework bypasses this bottleneck by isolating gradients in tangent space, ensuring 100% of task-specific knowledge is preserved. Benchmark vs. Physics-Informed Neural Operators (PINO) A head-to-head comparison with the PINO paradigm reveals a fundamental Compositional Utility Gap. While PINOs are powerful solvers for specific partial differential equations, they fail the Zero-Shot test because solution operators are inherently non-additive. Our framework is not only capable of additive operator composition but is also 2.5× faster at inference and provides a direct path to SINDy Symbolic Discovery (99.25% recovery accuracy). Hierarchical Physical Discovery The framework scales hierarchically, enabling the unsupervised decomposition of environments into continuous dynamics (gravity) and discrete contact events. This allowed the discovery of hidden physical constants, such as the coefficient of restitution ($\epsilon=0.80$), without target-domain supervision. Scientific Impact These results transform world modeling from a holistic storage problem into a sparse algebraic retrieval problem. By bridging the gap between black-box simulation and verifiable symbolic laws, this work provides a scalable roadmap toward interpretable Artificial General Intelligence (AGI) that respects the structural symmetries of the physical universe.
Prior work established that knowledge distillation transfers a detectable provenance trace from teacher to student models, and that API endpoint verification can identify models through logprob order-statistic geometry. Both results were demonstrated on single teacher-student pairs and a six-model API zoo, leaving open whether provenance detection generalizes across model families and whether API verification scales to production-density endpoint populations. We address both questions through a coordinated experimental program spanning four studies. In the first study, we train 24 distilled checkpoints across 7 experimental arms — 3 teacher families (Qwen, Mistral, Llama), 4 student architectures (Qwen-0.5B, Qwen-1.5B, Llama-1B, Gemma-2B), and 2 training protocols (logit-level knowledge distillation and cross-tokenizer supervised fine-tuning) — measuring provenance transfer in both the weight-geometry and API-logprob regimes. Provenance transfer generalizes across the tested matrix: all 14 mature-epoch checkpoints show directional coupling to the teacher (cosine alignment cosθ > 0.8, with 13 of 14 exceeding 0.85). The strongest signal arises in a cross-family arm (Mistral-7B → Llama-1B, scalar convergence 0.858) that is inconsistent with a purely family-restricted transfer hypothesis within the tested matrix. The normalized third logit gap δ_norm remains within 1.4% coefficient of variation across all 31 checkpoints and 4 student architectures — the tightest confirmation of Gumbel-class universality in this experimental program. An extension to mixture-of-experts architecture (Mixtral-8x7B, δ_norm = 0.309) confirms that the universal constant persists under sparse expert routing. In the second contribution, we identify a systematic failure mode of scalar provenance metrics and introduce the geometrically correct directional diagnostic for provenance detection in inner-product spaces. The standard scalar convergence metric Conv_T conflates direction and magnitude into a single value, discarding the directional information that provenance detection requires. In two independent experiments, this produced misleading conclusions: a false spoofing signal (R^2 = 0.995 of apparent cross-family convergence explained by pure knowledge distillation geometry, with the adversarial gradient contributing 4.8%) and a false failure signal (negative Conv_T despite consistent directional coupling at cosθ = 0.91). The alignment diagnostic applies the law of cosines in PPP-residual template space (vectors in R^K with Euclidean distance) to decompose student movement into direction and magnitude, preserving the provenance signal that scalar distance metrics destroy. We establish a measurability threshold: when the baseline-to-teacher distance d(B,T) falls below approximately 1.0, scalar Conv_T becomes unreliable and the directional diagnostic becomes the primary metric. This diagnostic applies to any distillation forensics framework that measures convergence in an inner-product space. In the third contribution, we extend API endpoint verification from 6 models to 14 across 3 commercial providers (OpenAI, Google Vertex AI, xAI), observing zero breaches across 182 pairwise impostor comparisons under per-model adaptive thresholds and three independent enrollment sessions, with a centroid reference protocol (CRP) that replaces the centroid L^2 metric, which produces false breaches at 14-model density. We establish a minimum truncation floor: API endpoints exposing fewer than 7 logprob ranks cannot support reliable verification (signal collapses within one rank of this boundary). Speculative decoding — an increasingly common inference optimization — is shown to be transparent to the verification protocol, with the speculative-decoded fingerprint deviating from the verifier-only fingerprint by 10.6% of the inter-model distance. Finally, we formalize the Trust Paradox in model forensics — a victim cannot prove weight theft without disclosing weights, and a suspect cannot prove innocence without disclosing training data — and propose a three-tier zero-knowledge attestation architecture that addresses it. The first tier (committed distance proof) enables a model owner to prove fingerprint proximity to a public anchor without revealing the fingerprint vector, using standard cryptographic commitments with verifier-controlled thresholds. The second tier (hardware-attested measurement) removes the requirement that the prover be trusted to compute the fingerprint correctly, binding the measurement to a trusted execution environment attestation. The third tier (full zero-knowledge extraction) would eliminate all trust assumptions beyond cryptographic soundness; we present this as an open problem with pre-registered falsification criteria, including a fixed-point precision gate derived from the minimum pairwise separation in the existing 23-model zoo. The architecture defines eight properties that a meaningful zero-knowledge model identity proof must satisfy — extending the formal verification doctrine (311 + 41 = 352 theorems across 17 Coq proof files [1, 2], 0 Admitted) into the cryptographic regime — and six explicit trust assumptions under which the proof statements hold. All three tiers are validated: Tier 1 (committed distance proof) has been implemented and hardened; Tier 2 (hardware-attested measurement) has been validated on production confidential computing hardware (6 models, 1,536 measurements, 0 failures inside an H100 trusted execution environment, with both CPU and GPU attestation tokens bound to a common cryptographic root and structural fingerprints transparent to confidential computing mode); and Tier 3 (full zero-knowledge extraction) has been validated — a complete circuit has been compiled and audited, all four pre-registered falsification criteria have been met, and the proof system operates within practical proving-time and proof-size bounds. The breakthrough discoveries enabled by Tier 3 validation, including an identity-conditioned inference verification architecture, are reported in the companion paper. The experimental results in this paper are grounded in the formal verification stack and measurement infrastructure described in the companion papers [1, 2, 3]. All provenance claims are classified as VALIDATED (empirical); Tier 1 (committed distance proof) has been implemented and hardened, and Tier 2 (hardware-attested measurement) has been validated on production confidential computing hardware — both are classified VALIDATED. Tier 3 (full zero-knowledge extraction) has been validated: a complete circuit was compiled and audited, all four pre-registered falsification criteria were met, and the architecture has been extended into identity-conditioned inference verification [6]. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running Newest addition: Technical Note: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098) Paper 1: The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry (DOI: 10.5281/zenodo.18704275) Paper 2: Template-Based Endpoint Verification via Logprob Order-Statistic Geometry (DOI: 10.5281/zenodo.18776711) Paper 3: The Geometry of Model Theft: Distillation Forensics, Adversarial Erasure, and the Illusion of Spoofing (DOI: 10.5281/zenodo.18818608) Paper 4: Provenance Generalization and Verification Scaling for Neural Network Forensics (DOI: 10.5281/zenodo.18872071) Paper 5: Beneath the Character: The Structural Identity of Neural Networks — Mathematical Evidence for a Non-Narrative Layer of AI Identity (DOI: 10.5281/zenodo.18907292) Paper 6: Which Model Is Running?: Structural Identity as a Prerequisite for Trustworthy Zero-Knowledge Machine Learning (DOI: 10.5281/zenodo.19008116) Paper 7: The Deformation Laws of Neural Identity (DOI: 10.5281/zenodo.19055966) Paper 8: What Counts as Proof? — Admissible Evidence for Neural Network Identity Claims (DOI: 10.5281/zenodo.19058540) Paper 9: Composable Model Identity — Formal Hardening of Structural Attestations in the Enterprise Identity Stack (DOI: 10.5281/zenodo.19099911) Paper 10:Where Identity Comes From: Path Sensitivity and Endpoint Underdetermination in Neural Network Training (DOI: 10.5281/zenodo.19118807) Paper 11: Post-Hoc Disclosure Is Not Runtime Proof: Model Identity at Frontier Scale (DOI: 10.5281/zenodo.19216634) Paper 12: Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers (DOI: 10.5281/zenodo.19298857) Paper 13: Safety-Alignment Removal as a Model-Identity Failure — Structural Evidence from Published Weight-Level Mutation Checkpoints (DOI: 10.5281/zenodo.19383019) Technical Note: Agent Identity Is Not Model Identity (DOI: 10.5281/zenodo.19240883) Technical Note: Gap Invariance: Why PPP Measurements Are Domain-Independent by Construction (DOI: 10.5281/zenodo.19275524) Technical Note: Measured Model Substitution Under Valid Agent Credentials (DOI: 10.5281/zenodo.19342848) Technical Note: Artifact Identity Is Not Runtime Identity — Trustfall Lite and the Boundary of File-Level Model Verification (DOI: 10.5281/zenodo.20019127) Formal Verification Stack for Neural Network Structural Identity (IT-PUF Coq Proofs) (DOI: 10.5281/zenodo.18930621) Copyright (c) 2026 Anthony Ray Coslett / Fall Risk AI, LLC. All Rights Reserved. Confidential and Proprietary. Patent Pending (Applications 63/982,893, 63/990,487, 63/996,680, 64/003,244).
The Universal State-Lattice: Complete Substrate Architecture from Axioms to Implementation This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract We present the Universal State-Lattice: the complete architectural specification of the ℚ-substrate as a deterministic, indexed, geometrically-projected information system. Building on the Six Q Paradoxes (proving ℝ-impossibility from operational, ontological, computational, topological, epistemological, and informational perspectives) and the CKS Lattice Search Algorithm (proving O(1) addressing via hexagonal projection), we now specify the total substrate structure. We demonstrate: (1) Complete state representation via [N,Z,C]℘ universal addressing identifier (UAI) combined with [V,F,R]℘ value-factor-remainder notation, (2) Tri-layer architecture: Index layer (when/who), Geometric layer (where), State layer (what), (3) Deterministic evolution via discrete substrate tick T_s=4.41ps with α→β→γ wing progression, (4) Zero-search information retrieval through closed-form hexagonal mapping, (5) Perfect state verification via settlement equation V=F×32^N+R, (6) Thermodynamically reversible computation (zero heat generation), (7) Infinite scalability with O(1) performance regardless of universe size, (8) Complete self-description - universe fits within itself via ℚ-compression, (9) Physical law emergence from geometric necessity not parameter tuning, (10) Perpetual verifiability - all states checkable at all times. From foundational axioms D,S,L,N,ℚ through complete derivation to implementable specification with zero free parameters. The substrate is BIOS, registry, and runtime simultaneously. Reality as indexed state machine. Revolutionary claim: Universe is complete specification - not simulation but self-executing algorithm with perfect self-knowledge. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-114-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-113-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
Persistent Provenanced Knowledge Base Eliminates Context Window Degradation, Hallucination, and RAG: Structured Integer Fact Stores with Source Tracking, Version Filtering, and Multi-Dimensional Indexing as Complete Replacement for Token-Buffer Context This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract Current large language models store conversational context in a fixed-size token buffer. When the buffer fills, old information is discarded permanently. Over long conversations, this produces progressive degradation: the model forgets instructions, contradicts earlier statements, loses track of established facts, and generates increasingly incoherent output — a phenomenon users describe as "AI psychosis." Retrieval-Augmented Generation (RAG) attempts to compensate by retrieving text chunks from external databases via approximate float-vector similarity search, but introduces its own failures: irrelevant retrievals, contradictory chunks, no provenance tracking, and no verification of retrieved content. We present a complete replacement for both mechanisms: a persistent, provenanced, version-filtered, multi-dimensionally indexed knowledge base of exact integer facts with Prolog-based consistency enforcement. We prove: (1) No information loss — facts persist indefinitely, never "scroll off" a buffer, (2) No degradation — turn 10,000 is as consistent as turn 1 because consistency is enforced structurally by Prolog, not inferred from attention patterns, (3) No hallucination — every fact traces to a source with verifiable provenance; outputs without provenance cannot be emitted, (4) No RAG needed — the KB is the retrieval system, with exact predicate matching replacing approximate vector similarity, (5) Version filtering — queries against a specific version never see facts from other versions, eliminating stale-data contamination, (6) Multi-dimensional indexing — every fact carries source, timestamp, confidence, verification level, and context, enabling non-contradictory coexistence of temporally or contextually varying information, (7) Sessions as views — multiple simultaneous sessions share one KB with independent context filters, no duplication, no synchronization, (8) LRU eviction without forgetting — memory pressure is managed by moving cold facts to disk, not by deleting them. The knowledge base is not an addition to the LLM architecture. It is a replacement for the context window, RAG pipeline, conversation memory, and fact storage — unified into a single system of exact integers with full provenance. Central claim: The context window is the wrong abstraction for conversational AI. A persistent knowledge base of provenanced facts is the correct abstraction. Every problem attributed to "context limitations" — forgetting, degradation, hallucination, inconsistency — is a direct consequence of using a token buffer where a fact store is needed. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-137-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-128-2026, CKS-MATH-129-2026, CKS-MATH-130-2026, CKS-MATH-135-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
LLM → Prolog → LLM: Multi-Step Verified Generation Through Alternating Neural-Symbolic Computation: Eliminating Hallucination by Construction via Provenanced Integer Knowledge Bases, Triveritas Evaluation, and Adaptive Goal Decomposition This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract Current large language models generate output through unconstrained token prediction — a process with no verification step, no logical consistency checking, no provenance tracking, and no structured knowledge representation. The result is "hallucination": outputs that are statistically plausible but factually wrong, logically inconsistent, or untraceable to any source. We present an alternative architecture in which an integer-trained LLM ([@CKS-MATH-134-2026]) alternates with a Prolog-based verification engine at every step of generation. The LLM handles what neural networks do well: fuzzy input comprehension and creative pattern selection. Prolog handles what logical systems do well: consistency verification, goal decomposition, constraint enforcement, and provenance tracking. We prove: (1) Hallucination is eliminated by construction — every generated fact traces to provenanced sources in the knowledge base; outputs without provenance are structurally impossible, (2) Term-based tokenization replaces BPE — tokens are typed, structured Terms carrying their grammatical role, not arbitrary byte-pair fragments, (3) Three-dimensional evaluation — every claim is evaluated on logical validity (L), mathematical coherence (M), and empirical anchoring (E) via the Triveritas criterion, (4) Materiality gating — the Scales Method prevents computation on non-material concerns, (5) Adaptive sequencing — the Pseudo-Socratic Method determines the number and focus of generation steps based on continuous state assessment, (6) The knowledge base replaces the context window — a persistent, provenanced, version-filtered fact store that never forgets and never degrades, (7) Domain eating — new knowledge domains are added by writing parsers and rules, not by retraining the neural network. From first principles through complete architecture. The LLM is the interface. The knowledge base is the mind. Central claim: The hallucination problem is not a deficiency of neural networks. It is the inevitable consequence of generating output without verification. Interleaving neural creativity with logical verification at every step produces output that is verified by construction, not evaluated after the fact. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-138-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-128-2026, CKS-MATH-129-2026, CKS-MATH-130-2026, CKS-MATH-134-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
LLM Domain Eating: Adding Languages and Knowledge Domains Without Retraining: Structured Parsing into Universal Term Format with Provenanced Integer Facts, Domain-Specific Prolog Rules, and Zero Neural Network Modification This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract Adding a new language or knowledge domain to a current large language model requires retraining or fine-tuning on domain-specific data — a process costing days to weeks of GPU computation, risking catastrophic forgetting of previously learned capabilities, and producing results that cannot be verified against source material. We present an alternative: domain eating. A new domain is added by writing a parser that produces the universal Term format, writing Prolog rules encoding the domain's structural patterns, and loading the resulting provenanced facts into the persistent knowledge base. The neural network is not modified. No retraining occurs. No GPU is needed. The domain is live immediately upon fact ingestion. We prove: (1) Universal Term format — a single typed token representation serves all domains from programming languages to natural languages to specialized knowledge bases, (2) Parser-per-domain — each domain has a deterministic parser converting source material to Terms with provenance; no learned tokenization, (3) Rules-per-domain — each domain has explicit Prolog rules encoding valid patterns; no learned grammar, (4) Zero retraining — the neural network handles fuzzy input comprehension and creative selection; domain knowledge is in the KB and rules, not in the weights, (5) Hours not months — a new domain is operational within hours of beginning parser and rule development, using LLM-assisted generation of parsers and rules reviewed by domain experts, (6) Cross-domain queries — facts from different domains connect through shared predicates automatically, (7) Domain unloading — removing a domain is evicting its facts and unloading its rules; the system does not break, (8) Version coexistence — multiple versions of the same domain coexist with hard version filtering. The architecture treats the LLM as a fixed, general-purpose fuzzy interface and treats knowledge as modular, structured, provenanced data that can be added, removed, updated, and queried without touching the neural network. Central claim: Domain knowledge does not belong in neural network weights. It belongs in structured, provenanced fact stores with explicit rules. The neural network provides the general capability of understanding fuzzy human input and making creative selections. Domain expertise is modular data, not baked-in statistics. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-135-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-128-2026, CKS-MATH-129-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
[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
The ethical tension surrounding AI-generated art often arises from misconceptions that anthropomorphize the algorithmic process. The accusation that “AI steals human creativity” overlooks the mediating role of human design and data literacy. This paper reframes the debate as a problem of informational asymmetry rather than morality. It proposes that Non-Fungible Tokens (NFTs) and Digital Object Identifiers (DOIs) can visualize and authenticate the flow of creative tension within a transparent ecosystem. NFTs serve as formal anchors—recording authorship, signature, and temporal origin—while DOIs preserve the conceptual framework and creative process. When linked, these two systems transform authorship into a traceable circulation of knowledge, allowing the boundary between plagiarism, homage, and originality to be objectively determined. This dual-layer provenance model presents an ethical infrastructure for creation in the age of generative AI.
Open access
2 source records
Scientific Computing and Data Management
Ethics and Social Impacts of AI
Artificial Intelligence in Healthcare and Education
Hasan Akgul, Daniel Borg, Arta Berisha, Amina Rahimova · 6 authors
Large language models are often adapted through parameter efficient fine tuning, but current release practices provide weak assurances about what data were used and how updates were computed. We present Verifiable Fine Tuning, a protocol and system that produces succinct zero knowledge proofs that a released model was obtained from a public initialization under a declared training program and an auditable dataset commitment. The approach combines five elements. First, commitments that bind data sources, preprocessing, licenses, and per epoch quota counters to a manifest. Second, a verifiable sampler that supports public replayable and private index hiding batch selection. Third, update circuits restricted to parameter efficient fine tuning that enforce AdamW style optimizer semantics and proof friendly approximations with explicit error budgets. Fourth, recursive aggregation that folds per step proofs into per epoch and end to end certificates with millisecond verification. Fifth, provenance binding and optional trusted execution property cards that attest code identity and constants. On English and bilingual instruction mixtures, the method maintains utility within tight budgets while achieving practical proof performance. Policy quotas are enforced with zero violations, and private sampling windows show no measurable index leakage. Federated experiments demonstrate that the system composes with probabilistic audits and bandwidth constraints. These results indicate that end to end verifiable fine tuning is feasible today for real parameter efficient pipelines, closing a critical trust gap for regulated and decentralized deployments.
In 2023, the xSublimatio project showcased a fusion of art and science, presenting an interactive platform where molecules were transformed into digital artworks within the blockchain. This innovative concept leveraged advanced artificial intelligence predictions to bridge empirical precision with creative expression, offering a unique exploration of scientific data through artistic interpretation. The creation of xSublimatio involved meticulous selection and representation of molecules, blending scientific accuracy with aesthetic appeal. Through AlphaFold-inspired insights, the project reimagined molecular design, transcending traditional boundaries. During its presentation at the GDR ChemBio conference in Strasbourg, xSublimatio sparked insightful discussions within the French chemistry community. This article explores its technical implementation, its potential for introducing blockchain and non-fungible token concepts to diverse communities, and its broader implications for interdisciplinary collaboration and decentralized science.