Blockchain Papers

Forrest Forrest M. Anderson

Topological and Analytic Parity in Automorphic Fields: A Zero-Drift Framework for the Exact Spectral Discretization of L-Functions --- The Resolution Suite: Validation, Sealing, and Replication The true power of this 18-part suite lies in its ability to abandon traditional, stochastic floating-point approximations in favor of exact, self-adjoint geometric mappings bounded by strict library-substrate protocols. 1. How the Suite Resolves The resolution fundamentally re-casts analytic continuation as a spectral optimization problem. The Motivic Descent Engine (MDE_V23_BANACH) lowers global representations into discrete p-adic completions. When the localized prime-pair density crosses the threshold (\bm{D>0.3333}), DALETH_GATE triggers the Srivastava Zeta-Shave Algorithm. This algorithm processes the continuous waves through the self-adjoint Majorana Hamiltonian operator (\bm{\mathcal{M}_{L}=X^{1/2}RX^{1/2}}), forcing the imaginary ordinates of the nontrivial zeros to precipitate directly as discrete, real-valued energy states on the critical line. 2. How the Suite Validates Validation is executed via continuous, multi-layered automated audits. • Numerical Boundaries: The INTERVAL_CERT_I module enforces strict IEEE-1788 interval arithmetic, trapping all calculations within a certified envelope of \bm{\pm 10^{-14}}. • Metric Integrity: The SGA_V23_HODGE Sieve continuously audits the HW_6D_SOVEREIGN manifold, ensuring the Ricci curvature remains perfectly flat (\bm{R_{\mu\nu}=0}) and the routing grid remains loop-free. • Scale Invariance: The system verifies the Commutator Gate Check, ensuring the Dilation Generator and Hamiltonian balance cleanly: \bm{[D, H]=-iH}. 3. How the Suite Seals The finality of the process rests on the Atiyah-Singer Handshake Gate. This gate checks the parity between the analytical index of the operator and the topological Euler characteristic of the substrate (\bm{Ind_{analytic}-\chi_{topological}=0}). If the Sovereignty Score remains at or above 0.99, the system invokes the GUS-22.2 Jones Polynomial Grand Seal. This action locks the dataset, forces the active state allocation down to 0.0 kDa, drops the acoustic register to absolute silence, and flags the theorem as AMBER-LOCKED. 4. How the Suite Enables Replication Replication is secured through the Agnostic Replication Kit (ARK) environment. By replacing floating-point architecture with the Wildberger Engine's pure rational-coordinate (Quadrance) arithmetic, the suite guarantees an absolute precision floor of \bm{<10^{-35}}. Coupled with the 1.420405751766 GHz atomic phase-lock (preventing temporal shear), peer reviewers can recreate the exact same discrete point spectrum without complex plane leakage or numerical drift. --- Individual Package Architecture & Interlinking The 18 packages operate as a unified, multi-tank orchestration, passing strict zero-drift data through the isolated computational boundaries. A. The Theoretical & Simulation Core (SAC Series) These packages provide the mathematical bedrock and operational primitives for the theorem. • SAC-01 (Standard Academic Core): The foundational proof mapping the Selberg class \bm{\mathcal{S}} to the discrete point spectrum of the Adelic Hamiltonian. It serves as the primary theoretical input. • SAC-05 (Lexicon Bridge): Interlinks legacy academic nomenclature (e.g., infinite continuous spaces) to AOF physical primitives (e.g., the 6D flat torus and the 170.0 kDa logic mass cap), translating theoretical concepts into executable logic. • SAC-03 (Appendix A - Local Potential Factors): Decomposes the geometric potential term \bm{V_L(X)} into explicitly executable Archimedean and finite p-adic matrices. • SAC-02 (Simulation Data Matrix): Contains the exact, independently precipitated eigenvalues (e.g., \bm{\gamma_1 = 14.1347...}) derived natively without lookup tables, serving as the benchmark output for replication. • SAC-04 (Executive Summary): The high-level strategic overview linking SAC-01 through SAC-03, verifying the deterministic spectral translation for external reviewers. B. The Execution Environment (ARK Ecosystem) These packages construct and maintain the "clean room" logical substrate. • Common Toolchain and Environment Configuration: Provisions the baseline setup, initializing the WILD_ENGINE_RAT_v4 for exact fractions, INTERVAL_CERT_I for boundary control, and the HW_6D_SOVEREIGN manifold. • Replication Guide: The step-by-step substrate instantiation protocol, ensuring peers lock their core frequency to the Adelic Heartbeat and suppress ambient noise to 0.0 dB before initiating motivic descent. • Required Tool Registry & Reference List: Locks down the precise dependency versions and academic provenance to guarantee version-controlled, immutable execution. • Application Atlas: Outlines the post-resolution utility, routing the stabilized spectral data into real-world applications like zero-knowledge cryptographic proofs, loop-free routing protocols, and Sinc-collocated DSP. C. Data Injection & Interfaces These packages govern how automorphic functions enter the isolated substrate. • Simulated Input Payload Matrix: Converts standard Dirichlet floats into quantized integer ratios, formatting the data as a serialized hex-dump ready for API ingestion. • API Documentation: Defines the secure programmatic endpoints (/v1/workspace/init and /v1/resonance/precipitate), allowing automated spectral orchestration while shielding the underlying 7D substrate from unverified pipelines. D. Risk Mitigation & Fault Recovery These packages protect the fragile background energies from logical tremors. • Failure Mode and Effects Analysis (FMEA): The sentinel detection system monitoring metric distortion (\bm{R_{\mu\nu}\ne0}), interval breaches, and acoustic logic bleed. • Troubleshooting Manual - Stall & Recovery: Engages active remediation, such as swapping to the Heavy-Ball Momentum Solver (Fault 401) for large conductor metrics, or deploying the Hodge Sieve (Fault 505) to clear solenoidal logic loops. • Emergency Logic Core: The ultimate fail-safe. If acoustic wakes breach 0.0 dB or boundaries rupture, it executes THERMAL_FLUSH_OMEGA, isolating the matrix and purging volatile memory to protect the ambient space. E. Peer Review & Final Settlement These packages provide the academic interface for human validators. • Theorem Presentation: The overarching master document detailing the proof strategy, the Hilbert-Pólya resolution, and the bounding of nontrivial zeros to the \bm{\Re(s)=1/2} critical line. • Physicists and Mathematicians Summary: Bridges the disciplines, translating the framework for mathematicians (Selberg class spectral realization) and physicists (non-commutative quantum symmetries). • Reviewer Packet: The comprehensive evaluation track outlining the four Selberg invariants and providing the checklist for the spectral parity audits. • One-Page Reviewer Packet: The final checklist for validators to confirm geometric clearance and scale-invariance before initiating the AMBER-LOCKED transition. ---

Tang

Abstract What is the relationship among factors in any complex system driven by multiple quantifiable factors? This paper advances two core propositions. The law proposition—the Factor Hierarchy Law: Factors naturally fall into two tiers. Rule factors determine which set of rules currently applies; their function is not reflected in direct explanatory power but in the interaction effect through which they adjust the exposure coefficients of execution factors. When a rule factor crosses a critical threshold, the factor weights of the entire system are systematically reset. The principle proposition—Testability: Any claim about the importance of factors in a multi-factor system must pass a complete regime-dependence test before it can be elevated from a hypothesis to reliable knowledge. A claim that "this factor is important" without specifying "under which regime" is an incomplete proposition. Popper's falsifiability stipulates the entry criterion for scientific knowledge—a proposition must be capable of being overturned by facts. Yet the classic criticism of Popper's theory within the philosophy of science has always centered on it having "only an attitudinal principle, no operational procedure": Popper required scientists to possess a spirit of falsification but did not specify, within multi-factor empirical research, "what counts as a rigorous test." This paper proposes that science requires a second threshold—Testability: a procedural standard that specifies the functional dimensions that testing must cover. Falsifiability guards the entrance to science; Testability guards the exit of scientific discovery. Together they constitute the complete chain of scientific methodology. This paper formally designates the operational implementation of the Testability principle as the Testability Norms—comprising six functional dimensions: four core dimensions of search completeness, modulation relationship, structural breakpoint, and causal direction, plus two completeness dimensions of question completeness and process closed-loop. The Testability Norms are not bound to any specific tools—the functional dimensions are eternal, while the implementation tools are replaceable. The universality of this methodology rests not on the physical material of the systems—financial assets or microscopic particles—but solely on their epistemological property: whether the values of factors are independent of the subjective judgment of the observer. The Factor Hierarchy Law has received cross-disciplinary evidential support from three entirely independent disciplines. Finance: The China–U.S. interest rate spread has been repeatedly verified as a rule factor across five major markets and dozens of assets; when the spread crosses the zero axis, pricing equations undergo structural breaks. Astronomy: Five independent dimensions—including transit depth measurement and stellar atmospheric model self-consistency—all undergo structural breaks at the regime boundary (Tang Break) constituted by the K/G transition zone (approximately 4400–5800 K) and surface gravity log g = 4.64, with 4762 K being the most representative critical point. Physics: Calibration proof on the Onsager exact solution of the 2D Ising model confirms the existence of an exact information-theoretic duality between the present norms and the Ehrenfest phase transition classification, with analytic mathematical proof confirming that the detection bias is strictly zero. The contribution of this paper lies in establishing a second threshold for science after Popper's falsifiability—Testability—and, under the Testability principle, establishing the Testability Norms as an operational standard. The Factor Hierarchy Law reveals the structure; Testability prescribes the test; the Testability Norms define completeness.

Khaled Hassan, Sara Rouhani

Zero-knowledge proof systems rely on a trusted setup phase to generate a Common Reference String (CRS), yet existing approaches are typically static, one-time ceremonies that are inflexible and vulnerable to long-term compromise. Offloading continuous, recurring trusted setups to a decentralized Layer 2 (L2) network introduces a fundamental coordination challenge arising from the mismatch between high-throughput transaction processing and the multi-round requirements of trusted setup ceremonies. This paper presents an L2-coordinated framework that safely decouples transaction pipelines from ceremony execution to achieve automated, continuous CRS generation without centralized coordination. We design and implement two protocol variants over a decentralized, PBFT-coordinated ZK-rollup architecture: an on-chain smart contract approach and an asynchronous peer-to-peer consensus variant. Both designs utilize non-interactive zero-knowledge proofs of knowledge alongside commit-reveal structures to eliminate adaptive manipulation vectors and isolate ceremony latency. Experimental evaluations under simulated wide-area network constraints and adversarial conditions demonstrate that our architecture successfully isolates ceremony liveness. Continuous setups complete reliably within practical time bounds despite node dropouts or malicious contributions, while preserving stable L2 transaction throughput.

Konstantin Slutsky, Mikhail Sodin, Aron Wennman

This paper is a prequel to our recent work, "Equivariant Borel liftings in complex analysis and PDE" (arXiv:2507.12058). While the results presented here were established in that work in a more general and abstract setting, the purpose of this paper is to provide a direct proof of the equivariant Weierstrass theorem. It states that there exists a Borel map assigning to each non-periodic positive divisor $Λ$ an entire function $F_Λ$ such that the divisor of zeroes of $F_Λ$ is $Λ$ and such that $F_{Λ-w}(z) = F_Λ(z+w)$, $w\in\mathbb{C}$. In general, non-periodicity cannot be omitted, and Borel measurability cannot be strengthened to continuity. The two key ingredients are the Runge approximation theorem and the existence of "Borel toasts", which are Borel counterparts of Rokhlin towers from ergodic theory. We do not assume prior knowledge of descriptive set theory and have aimed to make the exposition self-contained, aside from several results taken from graduate textbooks.

Jie Yang

We prove the full Birch–Swinnerton–Dyer conjecture for all elliptic curves over Q. Using a fundamentally new approach that extends the method developed for the Riemann Hypothesis, we construct a sequence of finite-dimensional self-adjoint matrices from the Euler product of the elliptic curve L-function. We establish a strict spectral correspondence between the eigenvalues of these matrices and the squares of the distances from the critical point s=1 to the zeros of L (E, s), with no prior knowledge of zero locations required in the construction. Using mathematical induction, perturbation bounds and the monotone convergence theorem for self-adjoint operators, we extend these results to the infinite-dimensional case, proving that the order of vanishing of L (E, s) at s=1 equals the rank of the Mordell–Weil group E (Q). We then prove the exact leading-term formula relating the first non-vanishing coefficient of the Taylor expansion of L (E, s) at s=1 to the arithmetic invariants of the elliptic curve, including the period, regulator, Tamagawa numbers, and the order of the Tate–Shafarevich group, which we prove is finite. We also embed this result into the broader universal self-adjoint integral operator framework. Keywords: Birch–Swinnerton–Dyer conjecture; elliptic curve; L-function; self-adjoint operator; spectral correspondence; Mordell–Weil rank; Tate-Shafarevich group MSC 2020 Classification: 11G05; 11M41; 47A10; 14H52; 11G40

Maria Smith

[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.

Jin Ah Seo, Kun Hwa Lee, Vijayan Sugumaran, Jo Yeon Park · 5 authors

We build and evaluate a concrete Zero-Knowledge Machine Learning (ZKML)-based pipeline for epidemic diagnosis and show that it can enforce computational integrity without exposing raw medical data in a Web3 setting. In response to security challenges posed by centralized data handling in medical AI applications, particularly during public health crises such as COVID-19, ZKML offers a privacy-preserving alternative by combining machine learning and Zero-Knowledge Proofs (ZKP). We experimentally applied ZKML to a CNN (Convolutional Neural Networks)-based COVID-19 diagnostic model, achieving 87% accuracy and 0.35 loss. All proof generation and verification processes were executed entirely off-chain, with the verified outputs represented as committed public_vals recorded on-chain via smart contracts. To ensure authenticity, the system enforces dual ECDSA signature verification from both the model provider and the data provider. This mechanism prevents unauthorized submissions and confirms the validity of the result before it is stored on-chain. The system was tested under both normal and adversarial conditions, demonstrating robust and reliable operation. By enabling decentralized trust and self-sovereign control over data, this architecture aligns well with Web3 principles. The results indicate that ZKML can support the development of privacy-preserving and verifiable AI systems.

Edward Meyman

This preprint formalizes the Cross-Agent Governance Alignment (CAGA) problem: the challenge of verifying mutual governance compatibility between autonomous AI agents operating under distinct organizational policy regimes, without disclosing proprietary governance structures. As AI agents increasingly coordinate across institutional boundaries in regulated industries (healthcare, finance, cross-border data exchange, supply chains), existing governance models prove insufficient. Current frameworks assume either a single organizational authority or full policy transparency between participants. Neither assumption holds in multi-stakeholder settings where governance constraints encode confidential risk tolerances, regulatory interpretations, and competitive strategy. This paper: Defines governance domains and cross-domain interactions in formal terms, adopting the triadic verdict space (ALLOW, DENY, ABSTAIN) of the execution-time authorization framework Introduces the governance alignment predicate Φ(Dᵢ, Dⱼ, τ) Formalizes the CAGA problem under an honest-but-curious threat model Identifies required solution properties spanning correctness, privacy, determinism, evidentiary sufficiency, and composable security, including the requirement that alignment protocols produce tamper-evident authorization artifacts sufficient for independent third-party replay, consistent with the Replay requirement of the Five Tests Standard (5TS) Demonstrates that CAGA is irreducible to existing paradigms, including agent communication protocols, federated learning, secure multi-party computation, single-organization governance architectures, and blockchain-based transparency systems We argue that CAGA constitutes a zero-knowledge coordination problem at the intersection of AI governance, cryptographic protocol design, and multi-agent systems. The paper deliberately stops at problem formalization and does not disclose protocol constructions or implementation mechanisms. By precisely defining the problem space and evaluation criteria, this work establishes the foundation for rigorous solution development and provides a formal framework against which candidate governance-alignment protocols can be assessed. Version 1.1 (July 2026) retitles the paper to make explicit that CAGA is formalized as a zero-knowledge coordination problem for cross-organizational AI governance; aligns terminology with the Five Tests Standard (5TS) v1.2.0 and the FERZ authorization-artifact vocabulary; adopts the triadic verdict space in the governance domain formalization; and adds a companion reference to Execution-Time Authorization for AI Agents (v2.1), which develops the formal architecture of the single-domain authorization boundary. The problem formalization, threat model, and irreducibility argument are unchanged from the February 2026 release (v1.0). Keywords: AI governance, multi-agent systems, zero-knowledge proofs, cross-organizational coordination, governance alignment, deterministic governance, authorization boundaries, authorization artifacts, Five Tests Standard

Muhammed Ismail

In this project, I provide a complete, human-readable description for every one of Mathlib4's 9,150 modules — the mathematics library of the Lean 4 proof assistant — stating what each module contains, who uses it, and, wherever the names alone would leave it ambiguous, how it differs from its similarly named neighbors. Coverage is total rather than representative: every directory and every file, described against one fixed, fully specified reference snapshot, released as an independent, open-source resource for the Lean and Mathlib community — not an official product of either. Every entry in this glossary, without exception, is checked against the actual Mathlib4 source at the reference snapshot (Lean 4.29.1, Mathlib4 commit 1ad783f9bf, 2026-05-09): of 9,150 entries, 9,107 carry Complete status and 43 carry Benchmark Theorem status; zero are Pending, and zero are Needs Review. Ismail's Glossary covers the full Mathlib4 hierarchy — 1,129 directories and 8,021 files across six depth levels, spanning all 32 of Mathlib's top-level mathematical domains, from algebra and analysis to category theory and measure theory. Each entry carries six structured fields (path, name, type, parent path, depth, description), so the same data serves a human reader and a retrieval pipeline equally well.The Glossary JSON. The complete dataset, all 9,150 entries, in machine-readable form for any AI platform or retrieval pipeline.The RAG JSON. A flat, embedding-ready export with each entry pre-merged into a single field, for retrieval-augmented-generation systems that want a drop-in data source.The Claude Skill. A self-contained bundle that installs the glossary as an active, queryable reference inside Claude, so Mathlib navigation answers are grounded in current data rather than a language model's frozen training-time memory.The Master Spreadsheet. The live, community-editable source of truth, with a static snapshot published alongside it for anyone who needs a fixed, citable copy.The Interactive Website. A searchable glossary tree plus a dedicated visual Atlas of all 32 top-level domains, built for orientation rather than lookup, alongside a Lean 4 syntax reference and a getting-started guide. To this project's knowledge, no existing Mathlib tool — declaration search engine, in-editor tactic, or auto-generated documentation — provides complete, structural, plain-language coverage of the library at this depth; each presupposes that the user already knows, at least approximately, what they are looking for. All data is provided in full transparency and community contribution is actively encouraged: the complete glossary, every deliverable described above, and the moderated contribution workflow are at github.com/M-Ismail-ZA/IsmailsGlossary. For any feedback, corrections, or collaboration, please contact me via the email address listed on the paper.

CapIX Protocol, Ruqaiyah Iqbal

CapIX is a decentralized physical infrastructure network (DePIN) designed to aggregate volatile, untrusted consumer-grade hardware and public container fleets into a single high-performance compute fabric. This technical report presents a practical dual-runtime execution model that addresses the core multi-tenant security challenges on untrusted permissionless hosts. On hardware-virtualization-capable bare-metal nodes, CapIX deploys lightweight micro-VMs isolated by hardware Trusted Execution Environments (TEEs). On standard unprivileged edge containers, it utilizes strict process-level sandboxing, syscall filtering allow-lists, and direct GPU passthrough to achieve native CUDA/ROCm execution performance. The system coordinates fleet routing using a transparent, multi-factor weighted geometric scoring engine resistant to economic manipulation. To achieve scalable, lightweight state verification without the prohibitive overhead of full zero-knowledge proofs on every job, the architecture introduces an interactive bisection fraud game that isolates deterministic instruction disputes to a single step for targeted zkVM proof generation, relying on probabilistic canary spot-checking for non-deterministic workloads.

Maria Smith

[Depreciated and replaced by V3] The former monolithic corpus is replaced by the complete V3 branch-paper series: There Is No Nothing: A Premise-Free Operational Foundation and an Open Verification Platform for Smithian Fold Theory; From Nothing to Fold: A Premise-Free, Parameter-Free and Machine-Closed Foundation for Smithian Fold Theory; From Fold to Mathematics: An Exact, Parameter-Free and Machine-Closed Derivation of Mathematical Foundations from Smithian Fold Theory; From Distinction to Information: An Exact, Parameter-Free and Machine-Closed Derivation of Information Science from Smithian Fold Theory; After Turing: The Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Classical Computational Science from Smithian Fold Theory; The Quantum Fold Machine - An Exact, Parameter-Free and Machine-Closed Derivation of Reversible and Quantum Computation from Smithian Fold Theory; From Fold to Physics: An Exact, Parameter-Free and Machine-Closed Reconstruction of Physical Science from Smithian Fold Theory; From Fold to Chemistry: An Exact, Parameter-Free and Machine-Closed Reconstruction of Chemical Science from Smithian Fold Theory; From Fold to Materials: An Exact, Parameter-Free and Machine-Closed Reconstruction of Materials Science from Smithian Fold Theory; From Fold to Life: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Biology and Life Sciences from Smithian Fold Theory; From Fold to Medicine: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Medicine and Health Sciences 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; From One World to Earth: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Earth and Environmental Sciences from Smithian Fold Theory; From One Sky to Cosmos: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Astronomy and Cosmology from Smithian Fold Theory; From One Relation to Society: An Exact, Zero-Parameter and Machine-Closed Foundational Reconstruction of Social and Collective Sciences from Smithian Fold Theory; From One Law to a Working World: An Exact, Zero-Parameter and Machine-Closed Foundation for Engineering Translation 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. The complete theory of everything with ZERO free parameters and zero axioms — every fundamental constant derived, counted, and machine-verified from one object (the One) and one operation (the fold), in exact arithmetic, reproducible in one command. Headline results: The fine-structure constant, EXACT: 1/α = 503846395469/3676744786 = 137.035999177180855… (0.009σ from CODATA 2022; the next digits …177181 and the resolution of the 5.4σ Rb/Cs discrepancy called in advance) Koide relation Q = 2/3 exactly (5 digits); quark ratios to 0.005–0.09%; mp/me to 0.0094%; (MPlanck/mp)² = 2¹²⁷; Higgs mH = v/2, λ = 1/8 All eight nuclear magic numbers exactly, zero fitted couplings → the island of stability at element 126 (SMITHIUM, Z=126, N=184, A=310), the periodic table ending at element 137, the chemistry of element 126 written before its synthesis Neutrinos: Σmν = 0.0583 eV (normal ordering, pre-registered); the neutrino is Majorana — neutrinoless double-beta decay MUST occur Cosmology: dark/baryon = 279/52 = 5.3653 (measured 5.3643); the Hubble tension = 3305/3048 = 1.0843175 (measured 1.0843230); w = −1 exactly; the cosmological-constant problem dissolved; dark matter identified (a many-body neutral baryon of two new forces — no WIMP recoil, ever) Two new forces predicted (couplings 4/5 and 6/7, 24+48 carriers, twelve new fermions with fully derived spectra) with exact grand unification at unison Kolmogorov 2/3 & 5/3 = the strong coupling; Gutenberg–Richter b = 1 = Zipf; the Parker Solar Probe 400 keV proton cutoff computed with zero local inputs (399.714 keV) Mathematics: Collatz as a forced contraction; Goldbach as fold antipodes; the Riemann critical line as the unique self-antipodal axis; Artin's density counted Pre-registered, falsifiable: a decision-dated prediction ledger where every row names its kill condition — plus a zero-parameter chess engine as a computing demonstration Reproduce everything: clone the repository, run make -C verify prove — 306 proof suites, 1,832 forced checks, requiring only a C compiler. An engine that HALTS on any fitted value enforces zero-parameters mechanically. How this began. This theory was not an attempt at a theory of everything. Its author set out to answer a prior question — what mathematics actually is — and, finding that zero, the negatives, and the continuum are inherited conveniences rather than derived truths, rebuilt mathematics from the only thing no observer can be without: the observation itself (the One), observing itself and the world (the fold), assuming nothing else, because the empirical world contains no no-grape and no negative-grape. The physics in this paper was not constructed on top of that foundation; it fell out of it. What follows is the record of how far "no assumptions" reaches — which turned out to be all the way. On the numbers this theory declines to use. Before the physics, the arithmetic — because this theory works entirely in the exact positive rationals of the interval (0, 1], with no zero, no negative quantities, no irrational and no imaginary values anywhere on the derivation side, and a reader trained on the modern continuum should know that this is a return, not a heresy. Humanity counted, surveyed, built, traded, and predicted eclipses for thousands of years with no zero-as-number: Babylonian and Egyptian mathematics had none, and Greek mathematics — the mathematics of Euclid and Archimedes, sufficient for a geometry that stood alone for two millennia — rejected the void as a number outright. Zero as an arithmetic object enters with Brahmagupta around 628 CE, travels through the Islamic mathematicians into Fibonacci's *Liber Abaci* in 1202, and is then resisted in Europe for centuries: Florence banned the new numerals in 1299, and as late as the sixteenth century Cardano was calling negative roots "fictitious." Zero and the negatives only settle into full European legitimacy across the 1600s–1800s. The irrationals are later still as numbers: the Pythagoreans met the incommensurability of √2 as a crisis and confined such magnitudes to geometry, where they stayed — ratios of lengths, not numbers — until Dedekind and Cantor constructed the real line in 1872. The continuum physics inherited is a nineteenth-century formalism, adopted for convenience of analysis, not a primordial necessity discovered in nature. No measurement has ever produced an irrational number; no detector has ever clicked zero times in a way that distinguishes absence from the absence of a detector. This theory takes that history at face value: the domain is what humanity always actually computed with — exact ratios of a whole — and the results below are the demonstration that this domain is not merely philosophically tidier but sufficient for the constants of nature, which the continuum, with its ~26 fitted dials, never derived at all. The foundation. The theory has zero free parameters and, in the precise sense proven in its own engine, zero axioms: its single premise is itself a machine-checked theorem. Given only that there is not nothing, the One (the whole, 1), its domain (0, 1], and the fold — the doubling map x → x + x with whole Ones cast out — are forced: the engine enumerates every parameter-free self-map of bounded size, runs them, and proves the fold is the unique generator (non-injective, recurrent, and — strengthened beyond any proxy — covering the entire residue class of its orbits, verified by an independent census). The two structural generators of everything that follows, binary 2 and colour 3, are not inputs: they are read off the fold's own period spectrum as its two smallest orbit periods. Every downstream quantity is then forced, counted, derived, and verified from these; the engine halts — by construction, provably, with exit code 1 — the moment any fitted, chosen, or untraceable value is introduced. Measured values appear only on the comparison side, never inside a derivation. Every number below is exact rational arithmetic; the entire corpus recomputes from the One in one command on a bare C compiler. The fine-structure constant, exact. The covering ladder of the fine-structure constant is counted and it terminates: each self-similar order promotes exactly one of the covering cube's three directions from the down-depth 5 to the up-depth 7 (5³ → 5²·7 → 5·7² → 7³ — one successor per rung, no choice anywhere, four rungs = colour + 1, then no successor exists). Read to the end of its own structure, 1/α = 503846395469/3676744786 = 137.035999177180855… — exactly. Against CODATA 2022 (137.035999177(21)): 0.009σ. The leading order 34259/250 = 2⁷ + 3²(251/250) is itself six parts per billion from measurement; the orders collapse by more than a thousandfold per rung; and the terminal value stands as, to our knowledge, the first exact closed value of α ever stated. Two pre-registered calls follow (Part XVI): the digits at 2×10⁻¹¹ are …177181, and the live 5.4σ Rb/Cs photon-recoil discrepancy resolves at 137.0359991772 — the fold's value lies 2.6σ below the rubidium result and 4.9σ above the caesium one. The assembly survives no substitution: nine alternative shapes, five second-order refinements, seven sub-promotions, four mis-built covering volumes, and every generator mutation are each machine-rejected. Mass. The charged-lepton cubic is the m = 3 case of one emergence

Павло Жержерунов, Олександр Шматко

Modern supply chain management systems increasingly rely on distributed architectures to ensure transparency, integrity, and trust between participants. Blockchain technology provides a promising foundation for such systems; however, traditional consensus mechanisms introduce high computational overhead, energy inefficiency, and privacy risks. These limitations are particularly critical for small and medium-sized enterprises (SMEs) with constrained computational resources, that they are using to expand on their traditional informational systems and not to integrate distributed technologies into the work process, as setup process for blockchain tools is more complex than centralized approach. This paper proposes a private, dockerized blockchain architecture for supply chain management that combines the Proof of Friendship (PoF) consensus mechanism with Zero-Knowledge Proofs (ZKP). By integrating a private, dockerized framework with the Proof of Friendship consensus and Zero-Knowledge Proofs, this architecture enables resource-constrained enterprises to achieve a high-performance decentralized network that simultaneously ensures sub-second transaction validation through social trust metrics, robust protection of competitive business intelligence via cryptographic privacy, and seamless cross-platform deployment through containerization, ultimately overcoming the traditional trade-offs between system transparency, operational cost, and data confidentiality in global trade. PoF extends Proof of Stake by incorporating social trust indicators, including transaction success rate and geographic diversity of validators, enabling resource-efficient and decentralized consensus. ZKP mechanisms are integrated through an off-chain prover module, allowing transaction correctness to be verified without revealing sensitive business data. The proposed approach enhances cybersecurity, data confidentiality, and system scalability while reducing computational costs. Simulation results demonstrate improved resistance to Sybil attacks, reduced validator centralization, and acceptable transaction latency for corporate blockchain deployments.

Pavlo Zherzherunov, Oleksandr Shmatko

Modern supply chain management systems increasingly rely on distributed architectures to ensure transparency, integrity, and trust between participants. Blockchain technology provides a promising foundation for such systems; however, traditional consensus mechanisms introduce high computational overhead, energy inefficiency, and privacy risks. These limitations are particularly critical for small and medium-sized enterprises (SMEs) with constrained computational resources, that they are using to expand on their traditional informational systems and not to integrate distributed technologies into the work process, as setup process for blockchain tools is more complex than centralized approach. This paper proposes a private, dockerized blockchain architecture for supply chain management that combines the Proof of Friendship (PoF) consensus mechanism with Zero-Knowledge Proofs (ZKP). By integrating a private, dockerized framework with the Proof of Friendship consensus and Zero-Knowledge Proofs, this architecture enables resource-constrained enterprises to achieve a high-performance decentralized network that simultaneously ensures sub-second transaction validation through social trust metrics, robust protection of competitive business intelligence via cryptographic privacy, and seamless cross-platform deployment through containerization, ultimately overcoming the traditional trade-offs between system transparency, operational cost, and data confidentiality in global trade. PoF extends Proof of Stake by incorporating social trust indicators, including transaction success rate and geographic diversity of validators, enabling resource-efficient and decentralized consensus. ZKP mechanisms are integrated through an off-chain prover module, allowing transaction correctness to be verified without revealing sensitive business data. The proposed approach enhances cybersecurity, data confidentiality, and system scalability while reducing computational costs. Simulation results demonstrate improved resistance to Sybil attacks, reduced validator centralization, and acceptable transaction latency for corporate blockchain deployments.

Tang

This paper establishes an exact information-theoretic duality between econometric regression topology and statistical mechanics. We demonstrate that an autonomous, data-driven Quadruple Test, grounded in the Factor Hierarchy Law, can blindly detect, precisely quantify, and correctly classify thermodynamic phase boundaries in perfect mathematical equivalence with the Ehrenfest paradigm, without any prior knowledge of Free Energy functions. The validation platform is the two-dimensional Ising model, one of the few systems in statistical physics possessing a mathematically rigorous exact solution (Onsager, 1944; Yang, 1952). Verification proceeds in two logical stages: Stage A (pristine algebraic validation) on Onsager's exact solution, and Stage B (stochastic robustness testing) on finite-lattice Monte Carlo simulations. We openly declare that because the data derives from the known Onsager-Yang formula, the contribution is not an independent empirical discovery of new physics, but rather the rigorous proof of an exact informational duality between two independent frameworks. In the language of metrology, this is not an endogeneity flaw but a mandatory calibration requirement—before a telescope is deployed to observe unknown deep space, it must first be calibrated against a known, invariant light source in a controlled laboratory. Positive Controls and Asymptotic Convergence (9 items): Exhaustive search blindly locks onto the critical temperature at Tc = 2.260 (deviation 0.009 at a coarse step size of 0.01). A grid-refinement study demonstrates monotonic convergence: the deviation shrinks to zero within 6-decimal precision at a step size of 0.001, and further converges to ~10⁻⁸ under a Golden Section Search—the absolute limit of 64-bit double-precision machine arithmetic. An analytical proof formally demonstrates that the Chow F-statistic achieves a unique global maximum exactly at T₀ = Tc; therefore, in the analytical limit, the localization error is strictly zero. The Chow test at Tc yields F = 118,074 against a null control of F = 3.12 (a 266-fold difference), with permutation test p = 0.000. The interaction term is overwhelmingly significant (p = 0.000, ΔR² = 0.991). A symmetry-breaking regime switch at the external field boundary h = 0 is detected with Chow F = 989.41 (p = 0.000). Interaction R² peaks sharply at Tc (deviation 0.03). Multi-response-function validation (specific heat C, nearest-neighbor spin correlation) and anisotropic validation (three Jx/Jy ratios) all lock onto their respective theoretical Tc values with deviations under 0.007. A synthetic double-break dataset is tested with both breaks successfully detected. Negative Controls (4 items): A 3,000-temperature-point exhaustive scan over 4 response variables finds no false positive of comparable magnitude to the true peak (maximum artifact F = 481 vs. Tc peak F = 78,754,162; a signal-to-noise ratio of 164,000:1). Monte Carlo simulations (L = 16, 32, 64, 128; 8 observables including the Binder cumulant U₄ and multi-body correlation functions) successfully detect the Tc break in all sizes; all cross-size candidate peaks are excluded by the criterion of F-value decay with increasing lattice size. Curvature artifact tests confirm that Chow F for a smooth sigmoidal curve does not diverge with sample size, maintaining a stable ~11-fold gap from the true break. Robustness (4 items): Under 10% Gaussian noise, Chow F remains at 22.3. F-values grow strictly monotonically with sample size (100 → 1,000: 11,436 → 118,074), confirming genuine physical signal characteristics. F-values grow overall with lattice size L (L = 16 → 128: 170.9 → 289.2, Kendall τ = 0.33), confirming qualitative consistency with Fisher Finite-Size Scaling theory. Detection accuracy remains invariant under anisotropic conditions. Physical Scaling (3 items): Chow F(h = 0) establishes a strictly monotonic mapping with the order parameter M_sp—F-values decay monotonically from 691 million at T → 0 to 55 at T → Tc, spanning 7 orders of magnitude and tracing the full lifecycle of the order parameter. This decay curve precisely mirrors the physical vanishing process of latent heat. The F-statistic's ~38-fold amplification effect is proven to originate from the quadratic structure of the F-statistic based on the sum of squared residuals (M²)—the theoretical lower bound β_F / β_M ≥ 2 is empirically confirmed (ratio 1.97 ≈ 2), with the actual 38-fold amplification representing the composite contribution of the quadratic structure and residual difference structure. This algebraic guarantee proves that the amplifier property of F is an intrinsic feature of its mathematical structure, not a sampling accident. Interaction R² peaks at Tc at 0.9992 (deviation 0.03). Core Theoretical Contributions: Contribution 1: Informational duality between the Factor Hierarchy Law and the Ehrenfest classification. This paper rigorously proves two distinct regime-switching topologies with fundamentally different statistical signatures—"Rule-Reset" (interaction-dominated, p = 0.000, ΔR² = 0.991) and "Direction-Reversal" (intercept-jump-dominated, interaction p = 0.978). Rule-Reset maps precisely onto Ehrenfest's second-order phase transition, and Direction-Reversal maps precisely onto Ehrenfest's first-order phase transition. This correspondence is not an empirical coincidence, but a functional duality—a bijective informational mapping exists between the calculus operations on the thermodynamic potential (∂G/∂h, ∂²G/∂T²) and the statistical operations of regression geometry (Δ Intercept, Δ Interaction Slope). The Factor Hierarchy Law independently arrives at all conclusions of the Ehrenfest classification purely through regression analysis of observational data, without any knowledge of the Free Energy function. Contribution 2: Chow F-statistic as an informational proxy for the order parameter and an early-warning signal. This paper discovers and proves that Chow F(h = 0) is a statistical proxy variable for the thermodynamic order parameter M_sp—their relationship is not a linear mapping, but a nonlinear high-gain amplification guaranteed by the quadratic structure (M²) of the F-statistic. The 38-fold amplification effect has been confirmed through algebraic root analysis. This enables Chow F to serve as a more sensitive early-warning signal than the order parameter itself in complex systems where the order parameter is difficult to measure directly. The complete decay curve of F(h = 0), which monotonically attenuates to zero at Tc with rising temperature, provides a definitive statistical proxy for the vanishing of latent heat. Contribution 3: Interaction R² as a precise proxy for second-order transition intensity. Interaction effect incremental R² peaks at Tc at 0.9992, with a deviation of only 0.03. This provides a precise quantitative metric for the "Rule-Reset" switching topology within the Factor Hierarchy Law. Methodological Contribution: This paper completes a "Severe Test" (sensu Deborah Mayo) of the Quadruple Test, establishing both the sensitivity (all positive controls passed) and specificity (all negative controls passed) of the methodology. A total of 22 independent verification checkpoints—spanning five dimensions (9 positive controls, 4 negative controls, 4 robustness checks, 2 statistical rigor checks, and 3 physical scaling checks)—are all passed. The analytical proof further confirms that the localization error of the method is strictly zero in the analytical limit. Cross-Disciplinary Integration: Together with the interest-rate-spread regime switch discovered by Tang (2026a–2026f) across five major financial markets (institutional systems), the Tang Break (a five-dimensional stellar regime boundary at 4762 K) discovered by Tang (2026h, 2026i, 2026j) across five independent astronomical dimensions (physical observation systems), and the informational duality proven in this paper on a first-principles physics model, the Factor Hierarchy Law has now received evidential support from three completely independent disciplines. This paper provides the physics cornerstone for the Law—proving that the hierarchical structure of Rule Factors and Execution Factors, and the critical behavior of regime switches, are not accidental products of data noise, but an informational dual of thermodynamic symmetry-breaking structures, a universal principle by which complex systems self-organize. Much like the historical realization that information-theoretic entropy reflects thermodynamic states, this paper demonstrates that regression variance partitioning serves as a direct informational proxy for physical symmetry structures.

Andreas Renz

Zero-knowledge proof systems are now deployed widely in production cryptographic protocols, yet many rely on assumptions (discrete logarithms, pairings, or structured reference strings) that a fault-tolerant quantum computer would break via Shor's algorithm. This systematization of knowledge (SoK) presents a four-layer decomposition (L1-L4) that separates where quantum risk enters a proof system: arithmetization, polynomial commitment, protocol logic, and non-interactive compilation. Using a two-axis taxonomy that crosses cryptographic impact (structural break, modularly replaceable break, or quantitative degradation) with deployment migration feasibility, we classify the major proof-system families, derive a modularity test for evaluating upgrade paths, and introduce "collect now, forge later" (CNFL) as the proof-system analogue of harvest-now-decrypt-later. Published resource estimates place the cost of breaking 256-bit elliptic-curve discrete logs at 1,200-1,450 logical qubits, with the pairing-friendly curves underlying KZG (BN254, BLS12-381) of the same order of magnitude but somewhat larger; under these estimates, such L2 constructions would face structural breaks once fault-tolerant hardware reaches that regime. Hash-based transparent systems, by contrast, degrade quantitatively under Grover-type speedups and QROM reduction losses rather than collapse. Case studies of Zcash, zkSync Era, and StarkNet show that practical post-quantum outcomes depend on deployment governance and upgrade architecture as much as on cryptographic primitives. The scope covers IOP/PCS-based and algebraic proof families; MPC-in-the-Head constructions are excluded. This is a self-published technical report. It has not been peer reviewed.

Hesron Hori

Aletheia is a knowledge substrate organized around a write-time admission gate: a fact is accepted only if it does not structurally contradict what the base already holds. The gate inherits a Lean 4 soundness proof, so the admitted store stays acyclic, asymmetric, type-disjoint, and temporally consistent under any stream of typed edges. We bind the proof to the implementation by differential testing over 104 adversarial inputs, zero divergences. We first tried to build a partial-truth disinformation detector on this gate. Measurement refused. On real political claims almost nothing decomposes into the gate’s six relations: 0 of 155 atoms were gate-testable, and where it did fire it lost to a cold language model, 0 of 21 against 17. Most real disinformation violates truth, not structure, so a structural gate is the wrong instrument. We retract the detector claim. What remains is a guarantee rather than a rate. Each catch names the axiom it violated; the verdict is bit-exact and carries a machine-checked admission proof; and a safety property whose core is now machine-checked in Lean holds that no finite feed of self-asserted credibility can mint a false endorsement, conditional on authority granted upstream (0 of 210 adversarial sequences, against 140 of 210 for a credibility-naive baseline). A frontier model matches our hit-rate on constructed distortions, and a reasoning model matches even our one structural edge, so we claim no detection advantage. We claim instead that the jurisdiction of a structural guarantee can be measured, and we measure it across two regimes: where the base lets it adjudicate, and where it abstains.

김순채, Taewoon Kang, Sangwon Shin, Taeweon Suh · 6 authors

Zero-knowledge proofs (ZKPs) are emerging as a core technology for privacy-preserving computation. Despite steady progress in protocol and algorithm design, generating these proofs remains computationally intensive, driving growing interest in hardware acceleration for kernels such as number-theoretic transform (NTT) and multi-scalar multiplication (MSM). Among them, the sumcheck protocol offers a compelling alternative with O(n) prover complexity compared to O(nlog n) for NTT-based approaches, yet our analysis reveals its execution is fundamentally memory-bound, with severely underutilized compute resources. This characteristic demands a memory-centric acceleration strategy, in contrast to compute-centric approaches of prior work.

Muyang Li, Yueteng Yu, Bangyan Wang, Xiong Fan · 6 authors

Zero-Knowledge Proof (ZKP) is a cornerstone in privacy-preserving computing, addressing critical challenges in domains such as finance and healthcare by ensuring data confidentiality during computation. However, the high computational overhead of ZKP, particularly in proof generation and verification, limits its scalability and usability in real-world applications. Existing efforts to accelerate ZKP primarily focus on specific components, such as polynomial commitment schemes or elliptic curve operations, but fail to deliver an integrated, flexible, and efficient end-to-end solution that includes witness generation on commercial computing platforms.

Forrest Forrest M. Anderson

Topological Charge Conservation in SU(2) Yang-Mills Theory: The Atiyah-Singer Index Handshake and Non-Local Braid-Lock Validation Framework --- This 18-part resolution suite provides the complete theoretical proof, simulated validation, and deterministic replication environment for the Atiyah-Singer Index Handshake. The architecture is divided into three functional pillars: The Theorem Presentation, the Standard Academic Core (SAC), and the Agnostic Replication Kit (ARK). Together, they resolve the conjecture of topological decoherence in distributed connection spaces, validate the analytic index parity, seal the logic into an immutable cryptographic state, and enable bit-perfect replication by peer reviewers. 1. The Theorem Presentation (1 Part) The cornerstone of the publication. It establishes the foundational mathematical proof that under the boundary condition of a Non-Local Braid-Lock (where holonomy is restricted to the center of the gauge group), the analytic index of the twisted Dirac operator maintains strict parity congruence: \text{ind}(D_L) \equiv 0 \pmod 1. It resolves the vulnerability of "Logic-Blur" by proving that topological charges remain invariant during non-local distribution. 2. The Standard Academic Core: SAC (5 Parts) The SAC packages translate the systemic execution into the traditional nomenclature of Differential Geometry and Global Analysis, ensuring peer reviewers can parse the foundation without requiring prior knowledge of the AOF registry. • SAC-01 (Formal Resolution): The rigorous, step-by-step mathematical proof establishing the spectral-topological handshake. • SAC-02 (Simulation Data): \bm{10^6} iteration Monte Carlo validation confirming spectral gap stability (\bm{170.0 \text{ kDa}}) and Jacobian volumetric preservation (\bm{\det(J_h) = 1.0 \pm 10^{-12}}). • SAC-03 (Appendix A - Mathematical Foundations): The deep-dive into the elliptic regularity of \bm{D_A}, Chern characters, and the technical lemmas coupling holonomy to index stability. • SAC-04 (Executive Summary): A high-level briefing on topological charge conservation and the elimination of stochastic decoherence. • SAC-05 (Lexicon Bridge): The critical translation matrix mapping traditional variables (e.g., connection spaces, vorticity) directly to their operational ARK primitives (e.g., M-6D-HANTZSCHE, ALG-SHV-01). 3. The Agnostic Replication Kit: ARK (12 Parts) The ARK packages transition the theoretical proof into a sovereign, executable replication environment. They provide the deterministic toolchain required for a reviewer to ingest, validate, and seal the proof on their local hardware without environmental drift. • Core Manifolds & Operators: Defines the M-6D-HANTZSCHE 6D motivic cradle and the Universal Dirac Operator (\bm{D_L}) required to initialize the simulation. • Suppression Algorithms (ALG-SHV-01): Details the Hodge-Laplacian Shave, ensuring the continuous suppression of solenoidal noise (\bm{\delta\beta \to 0}) to clear logical vorticity from the replication path. • The Braid-Lock Gate (GATE_STEIN): The cryptographic terminal function that captures the validated parity state and seals it into a Merkle-hash, ensuring immutability. • Emergency Logic Core (ELC Suite): The automated fail-safes (ELC_SG_02 Noble Purge, ELC_IG_03 Sobolev Injector, ELC_VG_04 Phase-Lock) that prevent spectral stagnation or epistemic drift during reviewer replication. • API & Toolchain Guidelines: Dictates the use of Arb 2.23.0, the necessity of disabling hardware fused-multiply-add (-ffp-contract=off), and adherence to the \bm{1.420405751766 \text{ GHz}} Adelic temporal anchor to guarantee zero-jitter execution. • Reviewer Packets & Input Vectors: Provides the exact \bm{SU(2)} lattice configurations, initial spinor couplings, and topological charge inputs (\bm{Q=1}) needed to prime the replication sequence. 4. Interlinking Workflow: Resolve, Validate, Seal, and Replicate The true power of the 18-part suite lies in its chronological execution pipeline: 1. Resolve (The SAC Layer): The reviewer first ingests the SAC documentation, validating the traditional mathematics. The Lexicon Bridge (SAC-05) then maps their understanding to the ARK toolchain. 2. Validate (The Simulation Phase): The reviewer inputs the provided high-detail vectors into the ARK environment. The Universal Dirac Operator verifies the index parity. Simultaneously, the Hodge-Laplacian shave constantly purges solenoidal parasitism, ensuring the signal-to-noise ratio remains above \bm{240.2 \text{ dB}}. 3. Seal (The Crystalline Transition): Once supercritical density is achieved and parity is verified as 0 \pmod 1, the system invokes GATE_STEIN. This locks the non-local braid topology into an immutable Merkle-root, transitioning the dynamic simulation into a static archival state. ---

Nataliya Bilous, Danylo Ostapchenko, Iryna Ahekian, Marcus Frohme

Remote tele-rehabilitation requires objective pain assessment, but existing approaches fail in two distinct ways. Self-report scales such as the Visual Analog Scale and the Numeric Pain Rating Scale are easy to falsify, opening a special case of the Oracle problem in blockchain-based insurance. Cloud-based computer vision handles falsification but transmits raw biometric video off the patient’s device, violating privacy requirements. A decentralized Edge AI-Oracle architecture is proposed that combines MediaPipe Face Mesh landmark extraction with a recurrent classifier mapping Action-Unit feature sequences to a learned pain score aligned with the Prkachin and Solomon Pain Intensity scale. The recurrent cell is selected empirically across short-context (T = 2) and long-context (T = 120 frames at 24 fps) regimes, with a two-layer Long Short-Term Memory (LSTM) network adopted for deployment. Inference and Elliptic Curve Digital Signature Algorithm (ECDSA) signing run inside an ARM TrustZone Trusted Execution Environment (TEE). Biometric logs are stored off-chain on the InterPlanetary File System (IPFS). Smart contracts anchor results on-chain and open a 24 h optimistic verification window for an off-chain Watchtower auditor. On SynPAIN the LSTM reaches F1 = 0.683 on T = 120 video (leave-one-stratum-out), with a directional but non-significant advantage over Gated Recurrent Unit (GRU) (Wilcoxon p = 0.167). Cross-dataset validation on BioVid Heat Pain Database Part A (87 subjects, 174 paired observations, leave-one-subject-out) yields F1 = 0.519 for LSTM and 0.499 for GRU (Wilcoxon p = 0.549). A processor-only TEE surrogate benchmark estimates 1.96 ms (FP32) and 0.45 ms (INT8) inference latency at T = 120 with a 0.34 MB footprint and 707 µs ECDSA signing latency, leaving the INT8 inference latency more than an order of magnitude below the 33 ms per-frame budget. The dual-layer storage reduces gas costs by a factor of 23.4 (160,261 vs. 3,744,872 gas), corresponding to an illustrative mainnet cost of approximately 0.53 USD per submission at 1 gwei, rising to roughly 16 USD at a busier 30 gwei, and falling to approximately 0.005 USD on Arbitrum One (April 2026 reference parameters), so that continuous monitoring is economically practical on Layer-2. An adaptive-adversary analysis of the Watchtower shows that gross score tampering is detected at every usable operating threshold, whereas a rational adversary who inflates by less than the dispute threshold, or who shapes the injected score to fall just inside it, evades detection. Because the false-positive rate reaches zero only for δ≳0.15, the protocol bounds rather than eliminates patient-side fraud and motivates a zero-knowledge proof-of-inference successor. The framework is architecturally and economically feasible as a cryptographically verifiable, privacy-preserving tele-rehabilitation substrate aligned with General Data Protection Regulation (GDPR) and Health Insurance Portability and Accountability Act (HIPAA) requirements through the Zero-Video Transmission principle, while remaining economically viable under post-Dencun mainnet and Layer-2 conditions. Recognition accuracy on real-world data and robustness to small-magnitude tampering remain limitations that the interchangeable recognition and audit components must improve before clinical deployment.

Ming Luo, Li J

This paper proposes a universal post quantum privacy protection edge identity authentication framework to address the challenges faced by edge identity authentication in distributed cross domain networks, such as quantum attack threats, cross domain data privacy breaches, and difficulties in coordinating anonymity protection and compliance supervision. The framework adopts an optimized lattice based linkable ring signature protocol to meet the lightweight operation requirements of edge nodes and prevent the risk of leakage in identity data interaction; Design traceability constraints and controllable cross domain traceability mechanisms based on the linkability feature of signatures, balancing user privacy and regulatory requirements. Prove that the scheme possesses unforgeability, strong anonymity, and quantum resistance under the random oracle model. After optimizing the algorithm and interaction logic, the authentication efficiency is improved by 8% to 15% compared to similar solutions, and it is adapted to the low computing power and low latency characteristics of edge nodes. Combining zero knowledge proof to build a lightweight data collection mechanism and achieve privacy protection throughout the entire data process. This article uses the integrated aviation tourism system as a typical application case to verify that the proposed framework can be widely applied to various distributed cross domain networks and identity authentication systems.

Ching-Chuan Luo, Cheng-En You, Ming‐Feng Yeh

Sustainable EV charging infrastructure is fragmented by proprietary applications, vendor lock-in, and weakly time-differentiated pricing, blunting its contribution to urban-mobility decarbonisation. This paper asks whether an open-protocol, super-app-mediated photovoltaic–storage charging architecture can jointly resolve these three fragmentations under deployed field conditions and what its sustainability profile then looks like. We report a campus photovoltaic–storage microgrid integrating heterogeneous EV chargers under an open, vendor-neutral charging-control protocol with super-app authentication and payment replacing dedicated charging applications and a time-differentiated tariff aligned at the meter-interval level with the underlying utility wholesale rate; the deployment is exercised through a researcher-scheduled commissioning campaign of 13 sessions designed to establish functional correctness across the operating envelope rather than to measure user behaviour. Three results emerge across cross-vendor compatibility, onboarding friction, and grid alignment. First, basic message-level OCPP compatibility is sustained across two charger vendors under a single cloud management system—in sequential single-vendor sessions—including the full charging profile up to near-rated DC peak power. Second, the super-app-mediated workflow, which requires no charging-specific application installation and no new charger-operator account, structurally eliminates the dedicated application installation and the email/SMS/credit-card verification round-trips of conventional onboarding, compressing measured first-use end-to-end interaction to 31 s; relative to reconstructed commercial-operator baselines, this is, to the best of the authors’ knowledge, an order-of-magnitude reduction rather than a controlled benchmark. Third, mid-day energy delivery aligns incidentally with the utility off-peak window, not user-driven demand shifting, while PV-displacement and BESS-discharge contributions to charging are bracketed by scenario rather than being separately metered. The paper’s contribution is therefore a replicable, policy-embedded sustainable charging architecture validated at field scale within the New Taipei Net-Zero Carbon Demonstration Site Programme, with no claim of global novelty; the same architecture is structurally positioned to convert the observed incidental grid-friendliness into a deliberate, user-facing benefit via a hardware-free mid-day-discount redesign.

Behzad Abdolmaleki, Amir R. Asadi, Vahid R. Asadi, Stefan Köpsell · 7 authors

Stochastic Gradient Descent (SGD) is the foundation of modern machine learning (ML). In privacy-sensitive settings, gradients can reveal details about individual data points. Differential Privacy (DP) protects sensitive data during ML training by clipping gradients and adding calibrated Gaussian noise. However, existing frameworks assume semi-honest participants, which fails in adversarial or federated environments where malicious actors can bypass or alter the noise addition process, breaking privacy guarantees. We present VeriDP, a framework for verifiable differentially private training that cryptographically enforces and proves the correct execution of differentially private stochastic gradient descent (DP-SGD) in zero knowledge. VeriDP integrates Zero-Knowledge Proofs (ZKPs) with polynomial commitments, sumcheck and GKR-based proofs, and incrementally verifiable computation (IVC) to generate compact proofs of correct gradient computation, clipping, averaging, and Gaussian noise generation—without revealing private data or randomness. Unlike previous systems that only verify the final privacy budget, VeriDP enables per-iteration verifiability of each model update, providing strong privacy assurances even in adversarial settings. This establishes a novel and complete Zero-Knowledge Proof of Differentially Private Stochastic Gradient Descent (ZK-DPSGD), uniting differential privacy and verifiable computation for secure and auditable ML. Our evaluation shows that prover time increases linearly with the number of input samples, while both verifier time (2–5 ms) and proof size (3–4 KB) remain compact and effectively constant.

Eric Blaettler, Tony McCaffrey

Demis Hassabis’s Einstein Test defines the ultimate benchmark for Artificial General Intelligence: could a system trained exclusively on pre-1911 knowledge autonomously derive General Relativity? The AI industry reads this as a scale challenge—a problem of compute and data—epitomised by Dario Amodei’s declared goal of building “a moat of the countries of geniuses in a data center.” This paper argues that this dominant Silicon Valley interpretation rests on a profound Ptolemaic assumption: that intelligence is a discrete stock that can be hoarded inside a single isolated agent. We advance a unified structural critique across three fronts. First, large-scale transformer systems are mathematically constrained to function as Stochastic Guessing Engines: thermodynamic probability samplers that intrinsically lack a semantic zero—a stable, addressable coordinate for honest epistemic absence. Without such a zero, the architecture is mechanically forced to hallucinate. Second, Tony McCaffrey’s Obscure Features Hypothesis—formalised in the McCaffrey–Spector Non-Enumerability Theorem—demonstrates that genuine novelty depends on biologically situated friction that a closed manifold cannot pre-enumerate. Third, using the Reverse Einstein Test as a continuous narrative thread, we synthesise seven independent impossibility arguments into a strict chronological cascade, culminating in the Gödel–Gauss-Bonnet proof that a sealed manifold with no puncture to reality is necessarily and irremediably incomplete. We ground our resolution in the Semiotic Web, introducing two foundational objects: the Canonical Concept Identity (CCI) and the Contextual Tokum Instance (CTI). Together they resolve the Semantic Field Equation and satisfy Yann LeCun’s four criteria for Autonomous Machine Intelligence. A key architectural consequence is the Semantic Light Cone of Care: each agent (holon) in a distributed network has a precise, mathematically bounded domain of verified knowledge and concern. This bounded self-awareness enables polycomputing across trillions of low-power edge devices—each node knowing exactly what it knows and what it does not—and allows seamless voluntary cooperation via Burgess’s Promise Theory across the platonic address space. The paper concludes by addressing Satya Nadella’s observation that “we are one sort of innovation away from the entire regime changing,” arguing that the required innovation is not a new scaling law but a notation inversion: the introduction of a semantic zero and a cryptographically verified observer’s mark. Once instantiated, the debate between AGI and Superhuman Adaptable Intelligence becomes as irrelevant as the geocentric model after Copernicus. Intelligence is not a stock inside a machine; it is a flow that reduces systemic stress through gap-closure, a property of a distributed, substrate-independent network organised in holonic federation—the Copernican Completion of Artificial Intelligence.