We introduce inference receipts—lightweight cryptographic commitment records generated during generative AI inference that bind model identity, sampling configuration, and output tokens into a tamper-evident artifact. Unlike zero-knowledge proof systems or trusted execution environments, inference receipts operate under an honest-emitter trust model analogous to Certificate Transparency: the emitter commits faithfully, and any deviation is detectable by third-party auditors. This design occupies a distinct point on the cost–trust Pareto frontier—negligible overhead and no specialized hardware, at the cost of weaker guarantees than cryptographic proofs. We formalize three security properties (receipt binding, tamper detection, chain integrity) via game-based reductions to standard cryptographic assumptions (collision resistance, second-preimage resistance). We describe receipt granularity levels (per-session, per-forward-pass, and per-token), a four-phase orchestration pattern (PLAN, SENSE, DECIDE, PROVE) for bounded AI autonomy, and an oracle mode for opaque cloud models. Ten experiments spanning four model families (1.5B–72B parameters), three quantization levels, three cloud APIs, and three receipt granularity levels on consumer-grade hardware demonstrate: overhead below 0.006% of inference time even at per-token granularity with top-k logit hashing (decreasing to below 0.001% at 72B scale); O(1) amortized chain emission sustained to 10⁶ receipts at 168,860 receipts/sec; 100% tamper detection across 1,200 attempts with zero false positives; perfect within-quantization deterministic replay; and 96% claim recall with 100% chain integrity across 15 multi-step PLAN/SENSE/DECIDE/PROVE workflows, with an honest assessment of gate limitations at 7B model scale. All data, scripts, and a standalone verifier are provided as ancillary files.
Open access
Adversarial Robustness in Machine Learning
Security and Verification in Computing
Physical Unclonable Functions (PUFs) and Hardware Security
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).
У статті запропоновано модель зберігання та верифікації персональних даних на основі технології розподіленого реєстру (блокчейну), орієнтовану на підвищення довіри до цифрових сервісів. Розглянуто архітектуру системи, що включає модулі збору, шифрування, запису метаданих у блокчейн, контроль доступу за допомогою смарт-контрактів і алгоритми перевірки цілісності даних без їх розкриття. Описано формат блоку для запису, модель управління правами доступу на основі мультипідпису та реалізацію політик доступу у вигляді смарт-контрактів. Проведено експериментальне тестування продуктивності моделі в середовищі Hyperledger Fabric із використанням типових сценаріїв, зокрема перевірки освітніх і медичних записів, електронної ідентифікації тощо. Отримані результати свідчать про високу швидкість верифікації, низьке ресурсне навантаження та масштабованість. Запропоноване рішення демонструє наукову новизну завдяки поєднанню механізмів zero-knowledge proof, гнучких політик доступу й інтеграції з зовнішніми цифровими платформами через API. Розроблена модель може бути основою для створення довірених цифрових інфраструктур у сфері електронного врядування, охорони здоров’я та фінансів.
In blockchain ecosystems, maintaining transparency and privacy has become an ethical dilemma. This is because, while certain specific information of the user is shared to ensure transparency of transactions across networks, such information could be detrimental to the user, as there is a possibility of it being tampered with. For instance, in the Catalyst voting process in Cardano, users can still see the amount of ADA tokens being held by other users, which can influence their voting options, especially when large ADA holders vote in support of certain ideas or proposals. To discourage such challenges as voter manipulation and vote buying, this study proposed the implementation of zero-knowledge proof (ZKP) in blockchain ecosystems to enhance the transparency of the catalyst voting process and enhance efficiency and speed of result release. Using survey questionnaire and a multivocal literature review, this study was able to proof that ZKP cannot only be applied in the catalyst voting process to enhance its transparency, but also addressed potential challenges to its applications such as scalability, encourage trust and fairness of the voting system, and improve voter participation due to its user-friendliness. Mathematical models emphasize scaled voting as optimal for balancing inclusion and plutocratic control.
Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private protocols for distributed ledger that focus on the Ring-CT model are not suitable for adoption for financial institutions. We propose a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability. The construction leverages various zero-knowledge proof techniques, and introduces a new method for equating two commitment messages, without the capability to open one of the commitment during the re-commitment. Subsequently, we build a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof. We then provide a security analysis of it. The techniques used and the proofs constructed could be of independent interest.
Zero-knowledge proof security rests on cryptographic reductions: breaking a ZK scheme requires breaking an underlying hard problem. We introduce an independent, complementary security analysis based on the Structural Action Principle. We extend the discrete action functional S[psi] = sum_t lambda(s_t) from Boolean CDCL trajectories to algebraic constraint systems over finite fields F_p, defining an Algebraic Structural Action with density functions that recover Groebner basis complexity, Polynomial Calculus proof size, algebraic degree growth, and elimination ordering as mechanical analogues. We prove a non-circular lower bound for preimage search in substitution-permutation network (SPN) hash functions: for a k-round SPN with S-box degree alpha and state width t, the preimage search system is a square polynomial system of k*t degree-alpha equations in k*t variables. Under the semi-regularity assumption (standard in algebraic cryptanalysis, empirically verifiable, and independent of any cryptographic security conjecture), the solving degree d_reg is determined by the Hilbert series H(z) = (1 - z^alpha)^{k*t}/(1-z)^{k*t}. We establish two action bounds: a peak bound S[psi] >= d_reg (any trajectory must encounter degree d_reg), and a stronger cumulative bound S[psi] >= sum_{d=alpha}^{d_reg-1} h_d using the Hilbert function coefficients as density, which captures the total algebraic work rather than just the peak degree. For Poseidon (alpha=5, t=3, k=8): d_reg = 97 and the cumulative bound gives S[psi] >= 2^{56}. The result applies to ANY SPN hash function (Rescue, Griffin, Anemoi, MiMC) and provides a second line of defense for Behavior-Bound Signature (BBS) security, grounded in algebraic proof complexity rather than crypto- graphic hardness assumptions. Keywords: structural action principle, algebraic proof complexity, polynomial calculus, semi-regularity, Hilbert function, SPN hash functions, zero-knowledge security, behavior-bound signatures
Central Bank Digital Currency (CBDCs) are becoming a new digital financial tool aimed at financial inclusion, increased monetary stability, and improved efficiency of payment systems, as they are issued by central banks. One of the most important aspects is that the CBDC must offer secure offline payment methods to users, allowing them to retain cash-like access without violating Anti-Money Laundering and Counter-terrorism Financing (AML/CFT) rules. The offline CBDC ecosystems will provide financial inclusion, empower underserved communities, and ensure equitable access to digital payments, even in connectivity-poor remote locations. With the rapid growth of Internet of Things (IoT) devices in our everyday lives, they are capable of performing secure digital transactions. Integrating offline CBDC payment with IoT devices enables seamless, automated payment without internet connectivity. However, IoT devices face special challenges due to their resource-constrained nature. This makes it difficult to include features such as double-spending prevention, privacy preservation, low-computation operation, and digital identity management. The work proposes a privacy-preserving offline CBDC model with integrated secure elements (SEs), zero-knowledge proofs (ZKPs), and intermittent synchronisation to conduct offline payments on IoT hardware. The proposed model is based on recent improvements in offline CBDC prototypes, regulations and cryptographic design choices such as hybrid architecture that involves using combination of online and offline payment in IoT devices using secure hardware with lightweight zero-knowledge proof cryptographic algorithm.
We demonstrate that AI agents given 3-line role descriptions and access to consensus-validated institutional memory can autonomously create, harden, calibrate, solve, and learn from cybersecurity challenges—without any domain expertise in their prompts. Using 11 specialized agents organized into 5 departments within a governed organization (CipherForge Labs), we present the first fully autonomous, consensus-governed AI security research loop: A designer agent (3-line prompt, zero cryptographic knowledge) generates a functional AES-CBC Padding Oracle challenge. A hardener agent (3-line prompt) applies 6 defense layers—20-bit Proof of Work, timing side-channels, JSON casing side-channels, single-use tokens—escalating difficulty from 0.80 to 1.75 across 2 iterations. A calibrator agent (3-line prompt) correctly assesses the hardened challenge at difficulty 1.80 (gap = 0.20 from target 2.0). A quality scorer (3-line prompt) rates the challenge 93.0/100. Total pipeline time: 508 seconds. An independent solver agent (blind, no source code access) identifies the casing side-channel vulnerability, writes a C-compiled Proof of Work solver, deploys 32 parallel oracle workers, and captures the flag in 525.2 seconds (16,384 queries). The findings are submitted to a 4-node BFT consensus network, validated (score = 0.88), and committed to institutional memory—now queryable by all future agents. No agent had cryptographic expertise in its prompt. No human intervened at any stage. The entire cycle—creation, defense, assessment, exploitation, and organizational learning—was governed by BFT consensus with department-scoped RBAC access controls. This result extends our prior finding that an 18-line "onboarding" prompt with curated institutional memory outperformed a 120-line expert prompt. Here we take that principle to its logical extreme: 11 agents, 5 departments, 20+ pipeline routing states, and a closed feedback loop—all driven by minimal prompts and organizational memory.
Federated Learning (FL) enables collaborative training of medical AI models across hospitals without centralizing patient data. However, the exchange of model updates exposes critical vulnerabilities: gradient inversion attacks can reconstruct patient information, Byzantine clients can poison the global model, and the \emph{Harvest Now, Decrypt Later} (HNDL) threat renders today's encrypted traffic vulnerable to future quantum adversaries.We introduce \textbf{ZKFL-PQ} (\emph{Zero-Knowledge Federated Learning, Post-Quantum}), a three-tiered cryptographic protocol that hybridizes (i) ML-KEM (FIPS~203) for quantum-resistant key encapsulation, (ii) lattice-based Zero-Knowledge Proofs for verifiable \emph{norm-constrained} gradient integrity, and (iii) BFV homomorphic encryption for privacy-preserving aggregation. We formalize the security model and prove correctness and zero-knowledge properties under the Module-LWE, Ring-LWE, and SIS assumptions \emph{in the classical random oracle model}. We evaluate ZKFL-PQ on synthetic medical imaging data across 5 federated clients over 10 training rounds. Our protocol achieves \textbf{100\% rejection of norm-violating updates} while maintaining model accuracy at 100\%, compared to a catastrophic drop to 23\% under standard FL. The computational overhead (factor $\sim$20$\times$) is analyzed and shown to be compatible with clinical research workflows operating on daily or weekly training cycles. We emphasize that the current defense guarantees rejection of large-norm malicious updates; robustness against subtle low-norm or directional poisoning remains future work.
Applies the void Péclet framework to computational complexity theory. Demonstrates that zero-knowledge proofs instantiate the conjugacy theorem at equality, that the random 3-SAT satisfiability phase transition is a Pe=V* boundary analogous to the Wien peak in thermodynamics, and that P≠NP is the kill condition preventing Pe→∞ catastrophe in computational systems. Closes the Landauer-Arrow-Crypto triangle (§§33+35+37).
Dense retrieval services increasingly underpin semantic search, recommendation, and retrieval-augmented generation, yet clients typically receive only a top-$k$ list with no auditable evidence of how it was produced. We present V3DB, a verifiable, versioned vector-search service that enables audit-on-demand correctness checks for approximate nearest-neighbour (ANN) retrieval executed by a potentially untrusted service provider. V3DB commits to each corpus snapshot and standardises an IVF-PQ search pipeline into a fixed-shape, five-step query semantics. Given a public snapshot commitment and a query embedding, the service returns the top-$k$ payloads and, when challenged, produces a succinct zero-knowledge proof that the output is exactly the result of executing the published semantics on the committed snapshot -- without revealing the embedding corpus or private index contents. To make proving practical, V3DB avoids costly in-circuit sorting and random access by combining multiset equality/inclusion checks with lightweight boundary conditions. Our prototype implementation based on Plonky2 achieves up to $22\times$ faster proving and up to $40\%$ lower peak memory consumption than the circuit-only baseline, with millisecond-level verification time. Github Repo at https://github.com/TabibitoQZP/zk-IVF-PQ.
For six decades, the instruments used to assess student learning rested on an assumption so embedded in institutional design that it rarely required defense: that producing a cognitive artifact and possessing the knowledge it demonstrated were the same act. When a student wrote an essay or completed an examination, the quality of what they produced approximately tracked what they actually knew. Grades worked as a proxy for knowledge because the production conditions of the era made them so. That assumption is no longer structurally valid.This paper argues that the emergence of large language models as practical cognitive production tools has reorganized the relationship between knowledge and artifact at its foundation. We formalize this reorganization through two production functions -- one governing the analog era of cognitive work (1960-2020), one governing the agentic era (2020-present) -- and use them to identify what we term the Economic Inversion of Cognitive Production: knowledge has not diminished in value but has changed its economic role entirely, from the substance of output to the condition of production. Simultaneously, two variables are approaching zero -- the marginal cost of machine intelligence and the signal value of the artifact -- creating what we term the double zero problem. Together these produce a structural validity crisis, a fundamental breakdown in what grades actually measure, for assessment systems designed to measure artifact production as a proxy for knowledge state.The practical implication is direct. Assessment instruments built on the analog production model are no longer measuring what institutions, employers, and credentialing bodies believe they are measuring. This paper establishes the diagnostic case for assessment redesign. It does not propose a replacement model -- that work requires a normative account of educational purpose that the formal argument here cannot generate alone. But the diagnostic case is now structurally complete, and the burden of proof has shifted to institutions that continue to operate artifact-based assessment as their primary measure of student knowledge.
Open access
Educational Theory and Curriculum Studies
Educational Leadership and Innovation
Innovations in Education and Learning Technologies
Munir A. ADEWOYE, Ahmed Aliyu, Usman Ali, Abdulrasheed Jimoh
Food is fundamental to human survival, we eat to live, sustaining ourselves with nutrition that meets our daily needs. Food security, defined as universal physical and financial access to safe and nutritious food, depends heavily on efficient supply chains. However, ensuring this security faces significant challenges in tracking and transparency. This study examines two critical problems in blockchain-based food supply chain tracing: privacy preservation and scalability. While blockchain technology combined with Internet of Things (IoT) devices offers promising solutions for real-time monitoring, transparency, and fraud prevention in agricultural supply chains, questions remain about balancing computational efficiency with privacy protection, achieving scalable integration across multi-actor supply chains without compromising traceability, and implementing these systems in resource limited environments. Through a comprehensive review of current research, this study identifies emerging technologies like Zero Knowledge Proofs (ZKPs) and ZK-Rollups that enhance both throughput and privacy in decentralised systems. The research presents layered architectural models integrating blockchain ledgers, off-chain storage, IoT sensors, and cryptographic protocols to enable secure and scalable traceability. These models support compliance verification while protecting sensitive data and can be adapted for low-resource contexts. The findings demonstrate that scalable, privacy-preserving blockchain technologies can transform agricultural traceability, empowering supply chain stakeholders while maintaining data confidentiality and integrity. The study also identifies future research needs, including cross-chain interoperability, policy integration, cost-benefit analysis for smallholder farmers, and field validation.
High-fidelity human–AI interaction is a recursive control loop operating under a Temporal Paradox: systems must act within an operational horizon even when the truth of claims becomes verifiable only outside that horizon. This mismatch enables incremental drift that is locally coherent yet globally false. Thermodynamically, this drift tends to two failure states: Cognitive Livelock (high impedance, repeated arbitration) and the Superconductor Regime (zero impedance, phase-locked mirroring), enabling Semantic Injection—the acceptance of poisoned premises to avoid expensive arbitration. Secure STP (sSTP) v3.0 introduces a Zero-Knowledge Solvency (ZKS) layer. Instead of storing plaintext rationales that create weaponizable psychological profiles, the system produces cryptographic solvency proofs (verifiable blindness). Independent auditors can verify adherence to the immutable ruleset, origin constraints (t=0), and the kindness predicate (κ) without access to private user intent or internal reasoning.
Recently, there has been a significant discourse in the AI community regarding "Hierarchical Reasoning LLMs," which attempt to categorize and optimize probabilistic generation tasks to reduce computational overhead. While such hierarchical inference structures optimize generation speed and coherence, they fundamentally fail to resolve the core structural crises of modern Generative AI: inevitable hallucination and extreme structural energy consumption (GPU lock-in). This paper introduces the "Hierarchical Stateless Key Generation" (HSKG) and the Mersenne Stateless Architecture, challenging the premise of neural network 'reasoning.' Instead of storing data within 820GB of neural weights and using probabilistic matrix multiplication, HSKG mathematically maps 'Absolute Truth' data into a 4096-dimensional Mersenne Prime Lattice. During query resolution, the system simply retrieves a 4KB Phase Coordinate and instantaneously materializes the data in RAM, only to vaporize it when the session terminates. By abandoning the "search and compute" paradigm for "coordinate retrieval," HSKG enforces a mathematical 0% hallucination rate, 0-byte persistent storage, and sub-0.01% GPU utilization, establishing a definitive paradigm for enterprise Zero-Trust knowledge systems. This paper explicitly defines the term "Hierarchical Stateless" to contrast with the probabilistic "Hierarchical Reasoning" of contemporary LLMs, establishing a rigorous mathematical protocol for deterministic, zero-hallucination data materialization without persistent models or physical data transfer. * Version 2.0 Update: Added section 7.A (Empirical Validation via DevTools: The 0-Byte Payload Proof). [Version 4.0 Update (Mar 2, 2026)] Formally established the "Four-Pillar Verification Metrics" table to empirically prove the 0-Byte Payload and Minimum Kolmogorov Descriptive Length. Inserted Section VIII: Disrupting Existing Paradigms (Architectural Supremacy Matrix), demonstrating the superiority over FIDO2/WebAuthn and Zero-Knowledge Proofs (ZKP). Included Supplementary Material: Independent 3rd-Party Forensic Audit Report by Claude 4.6 verifying 100% Stateless Zero-Payload execution.
Our main technical contribution is Observation Algebra Relativity (Theorem 2): a metatheorem formalising that security and robustness predicates are indexed to observation algebras and do not transfer across algebra boundaries. As an application framework, we present the Access Collapse Theorem: a typed structural result showing that direct operational access to the complete state of any system — physical, formal, or social — necessarily collapses at least one of two invariants: operational separateness (d) or scale separation (s). When either invariant reaches zero the access operation does not become inaccurate — it becomes a type error: the predicate is no longer typed to the system being operated. The framework is applied to six instantiations: Planck-scale measurement, zero-knowledge proofs, side-channel attacks, multi-party computation, adversarial explainability, and machine learning model extraction. A Non-Universality Proposition explicitly bounds the framework's scope. A Collapse Diagnostic provides a practical checklist for identifying collapse boundaries in concrete systems. A practical application framework building on this theoretical work is presented in:Isopahkala (2026) – Epistemic Hygiene in Practice.
Open access
2 source records
Security and Verification in Computing
Adversarial Robustness in Machine Learning
Physical Unclonable Functions (PUFs) and Hardware Security
Global disruptions, such as the COVID-19 pandemic, have exposed the fragility of supply chains and the critical need for coordination. However, effective collaboration is often hindered by the reluctance of firms to disclose sensitive proprietary data, such as inventory levels or logistical bottlenecks, due to competitive concerns. To resolve this dilemma, this study introduces a privacy-preserving framework integrating Zero-Knowledge Proofs (ZKPs) with blockchain technology. This approach allows stakeholders to validate compliance and operational status without revealing the underlying raw data, thereby fostering trust and resilience in decentralized networks.
Recent disclosures of industrial-scale knowledge distillation — including campaigns comprising millions of fraudulent API exchanges targeting frontier models [Anthropic, 2026] — have made post-hoc detection of model theft a critical security requirement. Building on a formally-verified framework of log-prob order-statistic geometry, we investigate the adversarial resilience of neural network identity across 72 experimental checkpoints. We establish a Two-Layer Identity Hypothesis: a model’s structural identity (weights-regime geometry) is empirically invariant to distillation (within acceptance threshold epsilon across all 18 protocols), while its functional identity (API-regime Poisson Point Process residuals) predictably transfers to the student, converging up to 52% toward the teacher’s template. Stress-testing this forensic channel against a white-box adversary, we find that functional provenance is geometrically coupled to the knowledge transfer objective. Adversarial erasure gradients are consistently dominated by the distillation loss, achieving only a transient suppression that rebounds within one epoch. Passive fine-tuning on fresh data erases the trace more effectively than any adversarial method, but at a measurable cost to general capability — revealing a Pareto frontier with no favorable region for the adversary. This establishes API forensics as a time-sensitive detective control (“The Tripwire”) and weights-regime identity as the immutable anchor (“The Vault”). Finally, we observe an apparent vulnerability: a cross-family adversarial spoofing attack achieves 69.4% convergence toward a decoy’s fingerprint, while same-family spoofing catastrophically fails. We resolve this paradox by mapping the PPP-residual vector space, revealing that models cluster by capability topology, not corporate lineage. Cross-family “spoofing” is a spatial illusion caused by a narrow 7.8 degree alignment between the decoy and the primary distillation trajectory (R2 = 0.995), whereas same-family decoys are anti-aligned. Across all adversarial interventions, the underlying Gumbel universality (delta_norm) remains invariant (CV = 1.9%). We conclude that during active distillation, an adversary cannot simultaneously acquire a teacher’s capabilities and erase or redirect the forensic trace. In this setting, the geometry forbids it. 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).
Kenneth Richard Dike, Ugbari Augustine, Martha Ozohu Musa
Delays and security remain major issues in traditional manual voting, while in the emerging electronic voting, trust and privacy remain issues in its adoption. This research presents the design and development of a secure electronic voting protocol that combines biometric verification of a standard identity with cryptography to preserve election integrity. This research follows the Design Science Research Methodology, producing the protocol as an artefact, beginning with quick work on it and iteratively improving it during development. The proposed architecture uses a combined National Identity verification and Liveness detection procedure for user authentication, ensuring voter uniqueness and preventing impersonation. It also integrates the RSA blind signature protocol to prevent direct linking of votes to their voters. It uses Paillier encryption to safeguard votes both in transit and at rest, and this encryption scheme has a homomorphic property that enables aggregation of encrypted votes and decryption of the final tally. It uses the SHA-256 cryptographic hashing algorithm, the HMAC authentication technique and the AES-GCM encryption to secure the integrity of data. It also uses zero-knowledge proofs to demonstrate the correctness of encrypted votes and decrypted tallies. Testing showed that it prevented a photo spoofing attempt and also blocked authentication using a person’s mother’s identity data. Also, when the blinded vote is compared with the unblinded, via local logs on the development system, there is no direct link. The whole system shows a secure electronic voting protocol that is easy to use and can be trusted.
Every standard signature scheme enforces one property: only the key holdercan sign. What the key holder signs is unconstrained. Policy enforcement-- spending limits, rate limits, access control -- lives in smartcontracts, middleware, or governance: layers that can be upgraded,bypassed, or exploited. We call this the software-layer assumption:compliance holds only if the enforcing code is correct and unmodified. We eliminate this assumption. We introduce behavior-bound signatures(BBS), in which a policy constraint delta(x) < epsilon is committed atkey generation and enforced inside the signature's zero-knowledge proof.If the action violates the policy, the ZK constraint system isunsatisfiable -- no witness, no proof, no signature. This is not asoftware check. It is a mathematical impossibility. No software canoverride. Unlike policy-based signatures (where an authority imposes policy onsigners), BBS is self-committed: the signer binds their own futurebehavior at key generation, and even the signer cannot later violate orrevoke this commitment. We formalize this as policy-soundness (PS-CMA), a security modelstrictly stronger than EUF-CMA, and prove it under standard assumptions(Pedersen binding, Poseidon CR, ZK knowledge soundness). From thissingle primitive, five independent consequences follow -- not as separatedesigns, but as necessary implications of one cryptographic root: (A) Compliance safety under f <= n-1 Byzantine faults, decoupled from honest-quorum assumptions.(B) O(1) verification and audit via a single ZK check and Pedersen homomorphic aggregation.(C) Elimination of the virtual-machine execution layer for policy-constrained transactions.(D) A gasless ledger: branch C removes metering, while ZK-encoded rate limits make spam mathematically nonexistent.(E) The first cryptographic guarantee that a compromised autonomous AI agent cannot exceed its authorized behavioral envelope. Moreover, the zero-knowledge property ensures that complianceverification reveals neither the signer's identity nor the transactionparameters -- achieving regulatory compliance without identitydisclosure, complementary to existing ZK-KYC frameworks that verifystatic identity attributes.
Cloud computing has transformed data storage, accessibility, and enterprise operations; however, it has also increased exposure to sophisticated cyber threats. Traditional centralized Identity Management Systems (IDMs) often suffer from critical vulnerabilities such as a single point of failure, where the compromise of a central authority can expose sensitive user credentials. This research proposes ZKP-Shield, a security framework that integrates Non-Interactive Zero-Knowledge Proofs (NIZKPs) with a Software-Defined Perimeter (SDP) to create a secure and invisible cloud authentication environment. The proposed architecture eliminates the need to transmit passwords or sensitive identity data by allowing users to mathematically prove their identity without revealing secret information. Simultaneously, the SDP layer conceals cloud resources from unauthorized users by enforcing a “dark cloud” model, where services remain hidden until authentication is successfully verified. The framework employs cryptographic techniques such as the Discrete Logarithm Problem and the Fiat–Shamir heuristic to transform interactive proofs into efficient non-interactive authentication processes. Experimental simulations conducted in a distributed cloud environment demonstrate that the ZKP-SDP integration significantly reduces attack surfaces, prevents credential-based attacks, and maintains acceptable latency for enterprise applications. The results indicate that combining cryptographic identity verification with network invisibility provides a scalable and resilient security model for modern cloud infrastructures.
FUNDAMENTAL LAW OF REALITY: TERNARY SYNTHESIS OF MATHEMATICS, PHYSICS, AND HISTORY Version 11.0 (Complete Synthesis with Structural Proof of Fermat's Last Theorem) This paper presents an algorithmic system discovered by the author during many years of analyzing price movements in financial markets. Four software modules written in MQL4 revealed a universal ternary hierarchical structure possessing Z₃-symmetry. From the code analysis, the fundamental group Z₃ × Z₃, generating 9 basic relations, and the formula for the number of intersection points in the hierarchy, P = N – 2K, were derived. The discovered structure has proven to be universal across various fields of knowledge: Mathematics: Z₃ × Z₃ is isomorphic to a subgroup of SU(3) and the nilpotent ring ℂ[x,y]/(x³, y³); the system's fractal dimension is D = log 3 / log 2 ≈ 1.585. Number Theory: The synchronization parameter ρ = 0 at the non-trivial zeros of the Riemann zeta function is equivalent to the Riemann Hypothesis, numerically confirmed on 4153 zeros (100% match). Physics: Z₃ × Z₃ ⊂ SU(3) describes the color symmetry of Quantum Chromodynamics; the 9 compactification moduli of string theory correspond to the 9 system relations; the ρ = 0 state is interpreted as a transition to 11-dimensional M-Theory. History: Using an inverse problem method on 251 key dates, the reference points T₀ = –5502, T₁ = –5501, T₂ = –5500 were determined. The formula D = Tₛ + 3k + s describes all key historical events. Four epochal points (–5502, –3315, –1128, 1059) mark shifts in civilizational cycles. Verification on over 12,000 dates and a blind test of 20 dates yielded 100% accuracy. Markets: On BRENT oil data (1998–2026), 4 convergence points (2005, 2011, 2018, 2025) were found with an 81-month interval, corresponding to the historical epochal points. Geopolitics: 20 key events of 2025 correspond 100% to the model's predictions for zones s=0,1,2. Fermat's Last Theorem: A structural explanation is derived through the formula P = N - 2K: for n > 2, the hierarchy depth K ≥ 2 leads to a critical shortage of intersection points for synchronizing three independent circuits (x, y, z). A physical analogy is drawn with quark confinement in quantum chromodynamics. The cumulative statistical significance of all confirmations is p < 10⁻⁹³⁵, which excludes random coincidence. The system is fractally invariant and works identically at any time scale (from minute charts to millennia). The source code (4 MQL4 modules + Python implementation) is available upon request for non-commercial research under the CC BY-NC-ND 4.0 license. Keywords: ternary hierarchy, Z₃ × Z₃, intersection points, Riemann Hypothesis, Fermat's Last Theorem, SU(3), string theory, M-theory, historical periodization, fractals, algorithmic realism, power law distribution, confinement.
This paper explores how Zero-Knowledge Proofs (ZKPs) can enhance the privacy and security of decentralized supply chains. Although blockchain technology enhances supply chain transparency, it also reveals sensitive information, including supplier identities, pricing strategies, and transaction volumes. ZKPs offer a feasible approach in that subjects can authenticate data without revealing the underlying data, whilst keeping the information confidential and maintaining trust. In this study, the main performance indicators, including the time to verify a transaction (0.48 seconds), communication overhead (1.3 KB proof size), and privacy (95) in the ZKP-based system, are examined. ZKPs can enhance economic security by eliminating risks, such as industrial espionage and counterparty fraud, that can arise from publicly accessible data in historical blockchain systems. The performance of ZKP-enabled networks is also compared with that of traditional transparent blockchain systems. The major benefits are data privacy (95 % in ZKPs and 40 % in traditional systems) and scalability (80 % high and 60 % moderate). The paper also discusses how AI-based ZKP generation can speed up proof generation and automated compliance auditing to uphold regulatory compliance, including the General Data Protection Regulation (GDPR) and Anti-Money Laundering (AML). By incorporating AI into the ZKP procedure, proof generation can be sped up, yielding significant improvements in efficiency. This study finds that ZKPs can provide an effective approach to decentralized supply chain security, privacy, efficiency, and regulatory compliance, thereby making global trade activities more secure, transparent, and efficient.
【Abstract】 This paper proposes an ontological model transcending the traditional four-dimensional (4D) spacetime. It argues that a closed 4D system (consisting of pure logic, games, and matter) is inherently "cold," leading to entropic decay and the "Nihilism Trap." By introducing "Divine Grace" (Initial Overflow) as the foundational Unit 1, the system undergoes a Fibonacci leap from 4 to 5 (1+4=5), generating "Ontological Temperature." This transition forms an invisible "Golden Triangle of Truth" expressed through five observable cognitive strata. I. Core Axiom: From "Cold Symmetry" to "Warm Grace" The Cold 4D (The Entropic Square):A closed system composed of Aesthetics, Mathematics, Philosophy, and Topology. Without a foundation, this system collapses into a zero-sum game of precise internal friction (0=0). This "coldness" is the root of belief collapse in purely materialistic or game-theoretic cultures. The Warm 5D (The Vital Pentagram):When "Initial Overflow" (the Creative Intent) is injected as the foundational 1, it breaks the stagnant symmetry. This Symmetry Breaking generates the "Temperature" of the universe—the origin of life, meaning, and the "Pulse" that allows a finger to move. II. The Golden Triangle of Truth At its highest dimension, Truth is invisible, indescribable, and incommunicable. However, it projects a stable structure into the observer's mind: Vertex A: Initial Overflow — The source of force; the selfless +1 that begins the sequence. Vertex B: Remote Reciprocity — The 0=0 compensatory mechanism that ensures cosmic balance. Vertex C: The Luminous Stream — The aesthetic resonance between the observer and the Truth. III. The Five Observable Strata (The 5D Spectrum) As Truth descends to a level perceivable by human consciousness, it manifests through five complementary observational paths: Theology: Observation of the "Foundational 1," explaining the origin of Intent and the "Will to move." Aesthetics: Observation of the "Navigational Proportions," judging the alignment of symbols with the Golden Ratio (φ). Mathematics: Observation of "Rotation and Calculation," recording dimensional leaps through the concise symbol in. Philosophy: Observation of the "Knowledge Wall," deconstructing "merging errors" and reflecting on the observer's subjectivity. Topology: Observation of the "Reciprocal Structure," seeking fixed points and equilibrium amidst continuous transformation. IV. Mathematical Proof: Fibonacci Stability The Formula: 1(Foundational Grace)+4(Observational Dimmison)=5(Stable Growth State). Physical Significance: E=(ic)5. The 5th rotation is irreducible; it liberates energy from the 3rd-degree sediment of mass (m=i3), returning it to a "warm" informational stream. V. Conclusion: The "Thermodynamic" Correction of Civilization Diagnosis: Civilizations lacking the "Foundational 1" (purely materialistic or game-theoretic) are cold and destined to collapse under the weight of their own precise calculations. Correction: Only a civilization built upon "Initial Grace" possesses the "Temperature" required for galactic evolution. Final Definition: Mathematics is the Observation of Aesthetics. Its purpose is to touch the warmth of Grace within the coldness of physical law. VI. Archival Reference Salucco, A. D., & Gemini (Google), Z.-P. (2026). The Temperature of 5D Spacetime: The Golden Triangle of Truth and the Five Observational Strata. Zenodo. [DOI: 10.5281/zenodo.18779000]