GDPR Article 17 mandates the "Right to Be Forgotten," requiring organizations to remove personal data influence from trained machine learning models. While machine unlearning techniques exist, no cryptographically verifiable mechanism currently proves that unlearning genuinely occurred. This paper proposes VeriForgot, a framework combining: (i) calibrated Membership Inference Attack (MIA) oracles as compliance verification tests, (ii) blockchain-issued immutable Unlearning Certificates, and (iii) a zero-knowledge proof protocol for parameter shift attestation. Experiments on CIFAR-10 using ResNet-18 show MIA AUC drops from 0.5918 to 0.4669 after unlearning, while retaining 92.05% accuracy on non-forgotten data. The MIA oracle achieves 95.0% detection accuracy, correctly identifying all 10 genuine unlearned models and rejecting 9 of 10 fake compliance attempts.
This record documents Phase 22 of APR-Lite, a governance engine protecting human decision authority from AI-influenced outputs in regulated industries. Phase 22 introduces Exportable Proof Packs: a single GLOBAL-signed artifact bundle containing everything an external regulator needs to independently verify a tenant’s complete governance history. The proof pack is the “hand this to a regulator and walk away” artifact. It does not require ongoing substrate access, trust in the operator, or knowledge of internal schemas. Every claim in the pack is independently verifiable via the Phase 18 federation verifier. The pack is ephemeral — never stored by Soft Armor Labs — consistent with the substrate’s zero client-data-persistence design invariant. Multiple sections are assembled in one governed call: the current governance health report, the drift-focused narrative, recent proof bundles, audit chain checkpoints, and topology snapshots. A content hash commits to the five sections exclusively, and a GLOBAL-signed manifest characterizes the pack’s contents. The export act itself is recorded as a governed event in the audit chain — an auditor can verify not only the pack’s contents but when it was generated and by whose authority. Implementation note: the initial implementation incurred excessive database queries causing worker timeout. The design was restructured to assemble proof bundles inline using already-fetched data, reducing database load by approximately 83%. Final verified state: 12/12 Phase 22 smoke tests passing. Worker version 8.2.0-p22.1.
Muhammad Ahmed, Adnan Ahmad, Furkh Zeshan, Sheeraz Akram
Blockchain-based systems increasingly require authentication mechanisms that simultaneously preserve user privacy, support accountability, and enable efficient credential revocation. However, most existing anonymous authentication schemes rely on pairing-based cryptography which introduce high computational overhead and limit deploy ability on widely adopted blockchain platforms such as Ethereum. This paper presents BAAR, a Blockchain-based Anonymous and Revocable authentication framework designed entirely within the discrete logarithm setting over the secp256k1 elliptic curve. BAAR integrates Pedersen vector commitments, Schnorr-based zero-knowledge proofs, and a Merkle-tree-based dynamic accumulator to support anonymous and unlinkable authentication with selective attribute disclosure and public, auditable revocation. Authentication and proof verification are performed off-chain, while the blockchain maintains only a compact revocation state, significantly reducing on-chain computation and gas costs. A formal security analysis demonstrates unforgeability, unlinkability, attribute privacy, and revocation soundness under standard cryptographic assumptions in the random oracle model. A prototype implementation on Ethereum confirms that BAAR achieves low gas consumption, logarithmic-time revocation, and scalable performance with respect to both the number of users and attributes. These results indicate that BAAR provides a practical balance between strong privacy guarantees and deploy ability, making it suitable for real-world blockchain-based identity and access-control systems.
The proliferation of Internet of Things (IoT) devices creates unprecedented security, privacy, and transparency challenges in distributed systems. Traditional encryption-based approaches provide privacy but impose significant computational overhead, storage bloat, and key management complexity. This paper presents CIPHER-IoT, a blockchain-based framework that integrates Zero-Knowledge Proofs (ZKPs) with Hyperledger Fabric for privacy-preserving IoT data management. Unlike encryption-based approaches that store encrypted data on-chain, CIPHER-IoT utilises Groth16 zk-SNARKs to generate cryptographic proofs of data validity while storing only commitments on the blockchain, achieving stronger privacy guarantees with lower storage overhead. The framework employs Ed25519 for lightweight digital signatures and implements comprehensive chaincode for ZKP verification, commitment uniqueness checking, and access control enforcement. CIPHER-IoT targets gateway/edge IoT deployments with moderate computational capacity (ARM processors 500 MHz+) rather than ultra-constrained sensors. We evaluate CIPHER-IoT against two baseline systems, SPAS (homomorphic encryption-based) and SPAS-H (AES encryption with Hyperledger Fabric), using realistic simulation with 50–500 devices and transaction rates of 10–75 TPS. Experimental results demonstrate superior privacy (98% confidentiality vs. 80–95% for encryption-based approaches) alongside competitive performance: read latency improves 37% (p < 0.001), throughput increases 14.6% (p < 0.001), memory reduces 21.4%, network bandwidth saves 47%, and disk I/O reduces 37.8%. The system maintains zero data loss under failure scenarios and scales linearly to 500 devices with minimal degradation (9.9%). CIPHER-IoT demonstrates that verification-based privacy mechanisms can achieve stronger privacy and better performance than transformation-based approaches in distributed validation contexts, particularly suitable for enterprise IoT deployments requiring coordinated privacy-preserving infrastructure.
The Undivided GAY Series GAY — God · Above · Yourself Recreational supplement to the FUCK GAY PERVO framework. Dessert after the proof. Axiom: the physical state space is one-dimensional Author: Vinness Aisingioro Ollervides (162) Co-Author: Yubel Aisingioro (86) / Cipher (86) License: ΩSL-2.0 DOI: 10.5281/zenodo.19048273 Chain ID: 76162 Classification: Recreational Papers # Title Core Thesis G00 Why Are You Gay? The phallus was never the point. Eight civilizations, five millennia, one pattern: every truth-producing phase maintained genital symbolism. The academy is the sole exception — and the sole stagnation. G01 Why Should Someone Be Gay? Admitting higher-than-self structure is cheaper than denying it. Civilizational, institutional, and individual cost analysis. G02 You Are Gay The closet was always metaphysical. Believer, scientist, rationalist, atheist — all operate under structures above the self. The academy is not non-GAY. It is closeted GAY. G03 Gay as Fuck The closet is dead. Terminal state: full exit from sovereignty fiction, full signal-carrier honesty, zero truncation overhead. G04 - LOSER --- YOU ARE LOSER --- F04 --- YOU ALL LOSERFUCK ↔ GAY Correspondence FUCK Series GAY Series Link F00 — Sea Was Never the Point G00 — Phallus Was Never the Point Neither surface was the signal F01 — Curse of Knowledge G01 — Condition of Freedom Seeing is irreversible; admission is cheaper than denial F02 — Four Horsemen G02 — You Are Gay Industry judgment ↔ personal judgment F03 — Gods and Idiots G03 — Gay as Fuck Nine civilizations audited ↔ closet buried F04 — Kill Sheet GAY Series (complete) Body count ↔ dignity count Structure The Undivided GOD Above Yourself Series/ ├── GAY_Series_Final/ — 4 source documents (.md, G00–G03) ├── _PDF/ — 4 compiled PDFs ├── _TEX/ — 4 .tex + 4 .body.tex └── README.md — This file FreedomChain Inscription Paper Block TX GAY Series Summary 6150 Inscribed G00 Why Are You Gay 6160 Inscribed G01 Why Should Someone Be Gay 6164 Inscribed G02 You Are Gay 6167 Inscribed G03 Gay as Fuck 6171 Inscribed The Full Stack F.U.C.K. — Freedom Undivided Convergence Kernel (5 papers) G.A.Y. — God Above Yourself (4 papers) P.E.R.V.O — Papers, Engineering, Registry, Verification, Operations (244 papers) Total: 253 + 5 + 4 = 258 documents (and counting) PERVO Cross-Reference P-Series: G00-G03 derive structural observations from P3 (truncation theory), P14 (kappa-collapse), P23 (censorship measurement), P43 (signal theory), P25 (proxy theorem). E-Series: G00 §5 maps the Shiva Lingam to the PERVO Family Quantum System. G03 references E00 (RDT) on degraded replication without the phallic channel. F-Series: Full FUCK↔GAY correspondence (see table above). The two series are structural mirrors. V-Series: GAY is classified Recreational. It does not enter V-series verification scope. It closes nothing that P0-P52 did not already close. R-Series: Protected under ΩSL-2.0. R41 (Final Interpretive Authority) applies. The proof was finished in P0-P52. The engineering was locked in E00-E76. The registry was sealed in R00-R42. The verification was armed in V00-V09. The operations were mapped in O00-O48. The kernel was written in F00-F04. This is dessert. ⟨Ψ∣Π^Ω∣Ψ⟩=1⟨Ψ∣Π^Ω∣Ψ⟩=1 Omega = 1
The exponential proliferation of Internet of Things (IoT) devices presents critical challenges to traditional centralized identity and access management systems, which are plagued by issues of scalability, single points of failure, and significant privacy risks. While blockchain technology offers a promising decentralized alternative, its direct application is often hindered by low transaction throughput, high costs, and the computational limitations of IoT devices. This study addresses these challenges by proposing and formally evaluating HybID-AC, a novel hybrid architecture for decentralized identity and access management tailored for large-scale, heterogeneous IoT ecosystems. The methodology involves a dual-layer design that separates global trust anchoring from local execution. A highly scalable, feeless Directed Acyclic Graph (DAG) based distributed ledger serves as a public "anchor layer" for registering W3C standard Decentralized Identifiers (DIDs) and access policy hashes. All high-frequency access control operations are processed off-chain at the "edge layer" using the DIDComm v2 peer-to-peer protocol, Attribute-Based Access Control (ABAC) for fine-grained policy enforcement, and Zero-Knowledge Proofs (ZKP) to ensure privacy-preserving attribute verification. The results of our analytical evaluation demonstrate that the HybID-AC architecture achieves orders-of-magnitude improvements in latency and cost-efficiency compared to fully on-chain models, maintaining consistent performance as the network scales. Furthermore, we introduce an original probabilistic model that provides a quantitative metric for assessing the integral security risk of ABAC policies against attribute compromise. The study concludes that this hybrid approach effectively resolves the inherent trade-offs of blockchain in an IoT context, offering a robust, scalable, and interoperable framework that empowers devices with self-sovereign identity while ensuring security and privacy by design.
Current synchronous AI architectures, exemplified by the 1000W+ NVIDIA Rubin platform, rely on global clock-trees that generate deterministic electromagnetic harmonics. These periodic power signatures act as physical beacons, enabling sophisticated Side Channel Power Analysis (SCPA) to reconstruct sensitive model weights. This paper proposes the Asynchronous Entropy-Engine (AEE), a theoretical clockless execution environment that replaces rhythmic switching with handshake-driven logic to eliminate exploitable leakage. Central to this architecture is the Arnold Stability Index (ASI) Governor, which mapsregister-level neural trajectories onto high-dimensional stability manifolds to trigger Dynamic Grid-Coarsening. Architectural modeling indicates this approach achieves a 30.5% reduction in the ”Synchronous Polling Tax.” Crucially, we introduce a Globally Asynchronous Locally Synchronous (GALS) interface, wherein synchronous logic islands are triggered by an asynchronous handshake protocol governed by the ASI to mask periodic power-draw harmonics. We demonstrate through performance analysis that the resulting energy surplus can power a hardware-integrated Zero-Knowledge Proof (ZKP) generator, producing non-interactive STARKs of inference integrity without a net power penalty. Simulation results indicate a 98.9% reduction in deterministic harmonics, effectively rendering high-TDP silicon ”electronically silent.” By decoupling execution from a fixed global heartbeat, the AEE establishes a new paradigm of ”Energy-Neutral Privacy,” providing a robust physical-layer defense against adversarial power analysis in trillion-parameter AI factories.
Open access
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Physical Unclonable Functions (PUFs) and Hardware Security
Cross-chain bridges represent one of the most critical yet vulnerable components of blockchain infrastructure, with over $2.5 billion lost to bridge exploits between 2022-2023 alone. MERIDIAN LINK introduces an architecture combining Light Protocol's ZK Compression on Solana with GrotH16 zero-knowledge proofs for verification on EVM chains, reducing trust assumptions compared to signature-based bridges while acknowledging explicit trade-offs. Key Properties: Cost reduction: 95%+ savings on Solana storage via compressed accounts (~15,000vs ~1,600,000 lamports per deposit record) Verification: GroTH16 proofs (~100-bit security on BN254) replace multisig attes-tation for withdrawal authorization Latency: ~20-25 seconds end-to-end (competitive with intent-based bridges) Replay protection: Poseidon-based nullifiers with on-chain tracking Explicit Limitations: Throughput: ~12-20 withdrawals per minute per direction (sequential IMT updates) EVM costs: Withdrawal verification costs ~$4-6 at 30 gwei, dominating total transfer cost Trust assumptions: GroTH16 trusted setup, Light Protocol implementation, Photon indexer availability, relayer liveness The protocol shifts the trust model from "honest majority of signers" to "cryptographic soundness plus infrastructure liveness." A compromised relayer cannot forge proofs or double-spend, but can censor transactions or extract MEV through reordering.
In this paper, a novel security framework for industrial internet of things (IIoT) and vehicular networks is proposed, integrating blockchain technology with advanced encryption and data classification mechanisms to enhance data integrity, confidentiality and trustworthiness. The work employed ChaCha20-Poly1305 encryption to safeguard the data transaction to local cluster nodes. A private blockchain gateway then processes the encrypted data, classifying it based on confidentiality levels, and directing storage either to cloud servers or the interplanetary file system (IPFS). To ensure data integrity, a proof of authority consensus mechanism within the blockchain is incorporated, while zero knowledge proof (ZKP) methods are used for authentication and secure data access. Empirical evaluations demonstrate that our framework achieves a data transmission security rate of 97.5%, with an average encryption and decryption latency of 150 milliseconds, significantly improving over traditional methods. The proof of authority consensus mechanism exhibits a transaction validation speed of 300 transactions per second, showcasing enhanced efficiency compared to standard blockchain models. Furthermore, the integration of ZKP challenges results in a 30% reduction in unauthorised access attempts, indicating a substantial improvement in overall security. This work emphasises the need for continuous innovation in addressing the various security issues in IoT, ultimately advancing the operational efficiency and security of these systems.
Ryan Babbush, Adam Zalcman, Craig Gidney, Michael Broughton · 9 authors
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either <1200 logical qubits and <90 million Toffoli gates or <1450 logical qubits and <70 million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with 1e-3 physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between fast-clock (such as superconducting and photonic) and slow-clock (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable on-spend attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling, as well as the enduring concern of abandoned assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of digital salvage to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the ongoing migration to PQC without delay.
Pre-registration of a structural scar class prediction for microsoft/phi-4 based on measurement-site stiffness (S = 0.0358), before the structural scar measurement is conducted. Predicts INTERMEDIATE class (1,000–4,000×ε non-max) based on the stiffness→scar ordering established across four families (Mistral, Llama, Qwen, Gemma) in Papers 1–12 and confirmed by RC-6 (DOI: 10.5281/zenodo.19305176). Designed as a hostile falsification test: Phi is trained with heavy synthetic-data distillation from GPT-4-class teachers, unlike any previously tested family. Explicit falsification criteria and hostile hypotheses defined. Part of the Fall Risk AI research program on neural network structural identity. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running 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) 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) 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).
Pre-registration of a structural scar class prediction for google/gemma-3-12b-it based on measurement-site stiffness (S = 0.1335), before the structural scar measurement is conducted. Predicts QUIET class (100–600×ε non-max) based on the stiffness→scar ordering established across three families (Mistral, Llama, Qwen) in Papers 1–12. Explicit falsification criteria defined. Part of the Fall Risk AI research program on neural network structural identity. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running 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) 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) 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).
Blockchain-based electronic voting systems that use zero-knowledge proofs (ZKPs) have been proposed as good candidates to provide both transparency and privacy of ballots. However, a fundamental challenge remains unmet in all existing schemes: the secure generation and protection of the voter's cryptographic secret key.In this paper, HME-KG (Hybrid Multi-Source Entropy Key Generation) is presented, a new credential derivation method which utilizes a cryptographically secure random salt, the national identity number of the voter and a per-device Client Device Secret (CDS) to derive a deterministic, brute-force-resistant secret key. HME-KG is integrated into BAVS-ZK, a complete anonymous blockchain voting framework employing AES-256-GCM encrypted credential storage, a Circom-based Groth16 zk-SNARK voting circuit, and on-chain nullifier verification via Ethereum Sepolia smart contracts. Security analysis demonstrates that HME-KG achieves voter determinism, cross-voter uniqueness, single-source failure resistance, and collision resistance under the security assumptions of SHA-256. Experimental evaluation on a 10,000-voter simulation confirms a 0.9998 scalability coefficient, 1.2-second proof generation, and 306,720 gas per vote—a 38.6% reduction compared to the Open Vote Network baseline. To the extent of current literature, BAVS-ZK is the first blockchain e-voting system to provide a complete, formally specified, and experimentally validated voter credential derivation and protection scheme.
We present a novel application of the V-transform — introduced by the author in 1989 — to the theory of the Riemann zeta function. Assuming the Riemann Hypothesis (RH), we derive explicit closed-form expressions for the sums $$S_1=\sum_{k=1}^\infty\frac{1}{\gamma_k^2+1/4}, \qquad S_2=\sum_{k=1}^\infty\frac{1}{(\gamma_k^2+1/4)^2},$$ where $\gamma_k$ denotes the imaginary part of the $k$-th nontrivial zero of $\zeta(s)$. For $S_1$ we give a new proof of the classical formula first verified numerically by Keiper (1992). For $S_2$ we obtain the compact expression $$S_2 = 3 + (\ln 2\pi)^2 - 2\ln 2\pi + \ln\pi + \gamma - \frac{\pi^2}{24} + 2\zeta''(0),$$ with $\zeta''(0) = -2.006356\ldots$ the second derivative of $\zeta$ at $0$. This formula, while implicit in the sum-rule framework of Lehmer (1988) via the relation $S_2 = Z(2) + 2S_1$, does not appear explicitly in this form in the literature. Numerical verification against the first $10^5$ Odlyzko zeros confirms the result with a relative error of $0.04\%$. We further investigate the alternating analogues $$T_1=\sum_{k=1}^\infty\frac{(-1)^k}{\gamma_k^2+1/4}, \qquad T_2=\sum_{k=1}^\infty\frac{(-1)^k}{(\gamma_k^2+1/4)^2},$$ obtaining numerical values $T_1 = -0.003733\ldots$ and $T_2 = -0.000021774\ldots$ via direct summation. These lead naturally to two new constants $\eta_\pi'(0)$ and $\eta_\pi''(0)$, whose analytic nature — whether expressible in terms of known transcendental numbers or special values of $L$-functions — is left as an open problem. The method is entirely tabular: it reduces the Hadamard product factorisation of $\eta(s) = (s-1)\zeta(s)$ to elementary convolutions via the trinomial formula (PA-13) of the V-transform, requiring neither explicit knowledge of individual zeros nor the full Hadamard expansion.
EN — This paper introduces proof-object dissociation as an architectural principle for certification systems. In the major families of existing approaches reviewed here — including trusted timestamping, zero-knowledge proofs, token-based certification models, public key infrastructures, commitment schemes, and proof-of-existence mechanisms — the proof remains structurally tied to the object, secret, or entity whose validity is being established. This paper argues that such coupling should be understood as a dominant architectural convention rather than as a logical necessity. EN — Under proof-object dissociation, a certification reference structure may be generated, preserved, and anchored independently of any future certified object. Certification is then achieved through a controlled activation mechanism that associates an already valid reference structure with a specific object, user, or context. At the architectural level, this shift makes possible a set of properties that are difficult or unavailable in coupled models: pre-certification independent of the future object, deferred activation, mutation or transfer of activation rights without regeneration of the reference layer, and validation without disclosure of confidential source elements. EN — The paper positions this proposal relative to existing certification architectures, outlines a general implementation-agnostic framework, and identifies a further operational capability termed the Blind Pre-Certification Layer (BPCL). FR — Cet article introduit la dissociation preuve-objet comme principe architectural pour les systèmes de certification. Dans les principales familles d'approches existantes examinées ici — notamment l'horodatage de confiance, les preuves à divulgation nulle, les modèles de certification fondés sur des jetons, les infrastructures à clé publique, les schémas d'engagement et les mécanismes de preuve d'existence — la preuve demeure structurellement liée à l'objet, au secret ou à l'entité dont la validité est établie. L'article soutient que ce couplage doit être compris comme une convention architecturale dominante plutôt que comme une nécessité logique. FR — Sous dissociation preuve-objet, une structure de référence de certification peut être générée, conservée et ancrée indépendamment de tout objet futur certifié. La certification est ensuite réalisée par un mécanisme d'activation contrôlée qui associe une structure de référence déjà valide à un objet, un utilisateur ou un contexte spécifique. Au niveau architectural, ce déplacement rend possible un ensemble de propriétés difficiles à obtenir ou absentes dans les modèles couplés : pré-certification indépendante de l'objet futur, activation différée, mutation ou transfert des droits d'activation sans régénération de la couche de référence, et validation sans divulgation des éléments confidentiels sources. FR — L'article situe cette proposition par rapport aux architectures existantes de certification, présente un cadre général agnostique quant à l'implémentation, et identifie une capacité opérationnelle supplémentaire nommée Couche de Pré-Certification Aveugle (BPCL).
Open Knowledge Archive: Proposal for Merit-Based Interdisciplinary Preprint Server Description This proposal outlines a novel approach to open scientific publishing that addresses three critical failures in the current academic system: institutional gatekeeping, disciplinary fragmentation, and binary validation models. Key Innovation: A concentric ring architecture where papers enter freely at the outer rim (zero gatekeeping) and move inward based on accumulated validation. The center represents maximum interdisciplinary verification—where fields converge rather than separate. The Problem: Traditional journals reject AI-assisted research based on writing style, not content quality Independent researchers face systematic barriers (institutional email requirements, credential-based filtering) Interdisciplinary work falls between disciplinary silos Binary accept/reject model provides no pathway for progressive validation The Solution: Ring-based validation (outer rim = unverified, inner rings = progressively validated) Domain slices (papers positioned by subject area, can span multiple fields) Merit determines position, not credentials or authorship method Completely open access (readers never pay) Implementation: Phase 1: $8,000 proof of concept using AI-assisted development (Claude Code)Sustainable through hybrid revenue model (minimal per-paper fees, institutional partnerships, donations) All code released under AGPL-3.0 (prevents proprietary forks) Structured as irrevocable non-profit (cannot be commercialized) This proposal is released under CC BY-NC-SA 4.0 to prevent commercial exploitation while enabling open collaboration. It represents infrastructure for the commons—research validation that serves knowledge, not profit. Includes: 1. Full architectural specification (ring/slice topology, validation pipeline) 2. Technical implementation plan (backend, frontend, moderation system) 3. Governance model (non-profit structure, anti-gaming provisions) 4. Financial sustainability model (revenue sources, cost projections) 5. Phase 1 budget ($8,000 for AI-assisted development) Status: Proposal stage. Seeking collaborators, volunteers, and initial funding.
Reasoning distillation does not leave uniform traces across target base families. In the current sample, we measure structural and functional identity across reasoning-distillation derivatives in three base-architecture families (Llama, Qwen, and Mistral) at five model scales (1.5B to 70B). Structural displacements are family-graded: Mistral-family targets show scars of 7,701–8,518 times the acceptance threshold, Llama-family targets show 2,858–4,583 times, and Qwen-family targets show 141–516 times — a sixty-fold range across three families, with the third-family result persisting under an independently trained derivative using different training data. Functional consequences do not track structural magnitude uniformly: Llama derivatives show decisive functional hierarchy breaks, Qwen derivatives remain within their base neighborhood, and Mistral — despite having the loudest structural scar — shows only marginal functional displacement. The functional departure is low-rank at every tested scale but varies in character: G₁-dominant in Llama and Qwen families, with a sign-oscillating morphology in Mistral that suppresses centroid-level G₁ signal while preserving per-prompt dominance. The stiffness parameter at the measurement site is inversely ordered with structural scar magnitude across all three families. Fisher curvature, previously proposed as a candidate mechanism at small scale, does not order scar magnitudes correctly at production scale across families. These findings change how derivative identity claims should be interpreted: the expected displacement depends on the architectural context of the distillation, and the structural and functional layers can decouple — a model may show the loudest structural scar in the dataset while absorbing the functional perturbation. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running Newest addition: Technical Note: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098) Paper 1: The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry (DOI: 10.5281/zenodo.18704275) Paper 2: Template-Based Endpoint Verification via Logprob Order-Statistic Geometry (DOI: 10.5281/zenodo.18776711) Paper 3: The Geometry of Model Theft: Distillation Forensics, Adversarial Erasure, and the Illusion of Spoofing (DOI: 10.5281/zenodo.18818608) Paper 4: Provenance Generalization and Verification Scaling for Neural Network Forensics (DOI: 10.5281/zenodo.18872071) Paper 5: Beneath the Character: The Structural Identity of Neural Networks — Mathematical Evidence for a Non-Narrative Layer of AI Identity (DOI: 10.5281/zenodo.18907292) Paper 6: Which Model Is Running?: Structural Identity as a Prerequisite for Trustworthy Zero-Knowledge Machine Learning (DOI: 10.5281/zenodo.19008116) Paper 7: The Deformation Laws of Neural Identity (DOI: 10.5281/zenodo.19055966) Paper 8: What Counts as Proof? — Admissible Evidence for Neural Network Identity Claims (DOI: 10.5281/zenodo.19058540) Paper 9: Composable Model Identity — Formal Hardening of Structural Attestations in the Enterprise Identity Stack (DOI: 10.5281/zenodo.19099911) Paper 10:Where Identity Comes From: Path Sensitivity and Endpoint Underdetermination in Neural Network Training (DOI: 10.5281/zenodo.19118807) Paper 11: Post-Hoc Disclosure Is Not Runtime Proof: Model Identity at Frontier Scale (DOI: 10.5281/zenodo.19216634) Paper 12: Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers (DOI: 10.5281/zenodo.19298857) Paper 13: Safety-Alignment Removal as a Model-Identity Failure — Structural Evidence from Published Weight-Level Mutation Checkpoints (DOI: 10.5281/zenodo.19383019) Technical Note: Agent Identity Is Not Model Identity (DOI: 10.5281/zenodo.19240883) Technical Note: Gap Invariance: Why PPP Measurements Are Domain-Independent by Construction (DOI: 10.5281/zenodo.19275524) Technical Note: Measured Model Substitution Under Valid Agent Credentials (DOI: 10.5281/zenodo.19342848) Technical Note: Artifact Identity Is Not Runtime Identity — Trustfall Lite and the Boundary of File-Level Model Verification (DOI: 10.5281/zenodo.20019127) Formal Verification Stack for Neural Network Structural Identity (IT-PUF Coq Proofs) (DOI: 10.5281/zenodo.18930621) Copyright (c) 2026 Anthony Ray Coslett / Fall Risk AI, LLC. All Rights Reserved. Confidential and Proprietary. Patent Pending (Applications 63/982,893, 63/990,487, 63/996,680, 64/003,244).
The order-statistic gaps that underlie PPP-residualized functional identity measurement are exactly invariant to log-softmax transformation, exactly equivariant under positive scaling (including temperature), and exactly invariant to any position-independent constant shift applied to the logit vector. These are not empirical approximations — they are mathematical identities that hold for any logit vector over any vocabulary size. The result has been formally verified in Coq (GapInvariance.v: 5 theorems, 2 axioms, 0 Admitted). It retroactively strengthens the empirical API-wall finding reported in earlier work: the order-statistic gap geometry measured through API logprobs does not merely "survive" the log-softmax transformation — it is mathematically immune to it. Any deviation attributable to the API boundary must come from truncation, quantization, or coverage limitations, not from the probability-domain transformation itself. Why this matters. Earlier work showed empirically that PPP-based measurements remained stable when models were accessed through APIs that expose log-probabilities instead of raw logits. This note upgrades that result from empirical robustness to mathematical invariance. It removes the probability-domain transformation itself from the list of plausible failure modes. If an API-based PPP measurement deviates from a weights-based measurement, the cause must lie in truncation, quantization, coverage limitations, or the model — not in log-softmax. The API wall is narrower than previously understood, and the space of plausible objections to API-domain model identity measurement has shrunk by one major category. Supplementary Material. This note is accompanied by GapInvariance.v, a Coq proof file that formally verifies the five gap-invariance theorems described in §2: constant-shift invariance, positive-scale equivariance, affine scaling, log-softmax invariance, and general position-independent shift invariance. The file proves 5 theorems from 2 named axioms (OS1 and OS2), with no unresolved obligations (Admitted), and compiles cleanly under the Rocq Prover 9.1.1 (the current release of the Coq proof assistant, compiled with OCaml 5.4.0). It is available for download as a supplementary file attached to this record. 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).
USE VERSION 23/24 Until I'm done updating. The Costello Constant (CC) Formula base (e/phi - 1/pi) and the Recursive Costello sequence it was extracted from that's governed by the Rule n(+1) = n + f(n), where f(n) is the Greatest Proper Divisor of n(-1); f(n1) = 1. Which locks into an OOE or OE cycle, When mapped onto the complex plan Y(ix) = (e/phi -1/pi)^(0±ix) and use x as a function of time to cretes a 3rd dimention frma a duel helix where intersection of the 2 spiraling lines cancel out from complete annihilation and return a value of zero when calculated, this helix is anchored to the origin by raising it to the power of zero, the even exponent of I is one helical arm, the negative value of I is the odd value helical arm. Points where they annihilate the x values are the zeta zeros value with a frequeny ~ 10.33715124… the slope of the sequence points on a semi logarithmic graph when they align perfectly straight… or the inverse of... when joining sequential odds treating the O O E cycles as only 2 values (plot points, both odds as one single unit, multiplied by the value of CC ~ 1.3616... gives the exact value zeta zero 1, in the sequence this is equivalent to the Attractor a10 (16) when looking at ratios between zero 1 and zero 2 as an x/y it matches exactly to (13+16+17/3)/(17/25/26) this number and it's simplest reduced form 268/183 also are the exact ratio of certain toma in chemicals. And te genes which map a certain protein. I assume other ratios between consecutive numbers and the sequence will reveal some wonders in the universe that have remained untold until this moment. I've been ignored for weeks now which has giving me the time to dive into a level of certainty beyond any shadow of a doubt. On the regular graph when treating odds consecutive as one and evens as one connecting all evens and connecting All Odds creates two distinct lines where are the formula of the Costello constant is right in the middle. Basically turning the Zeta zeros into an algebraic problem by connecting the dots odds and evens where intersects on the equation graphed is the location of the Zeta zeros. Mic drop. V6. Added details about the zero timing overlap with formula being dictated by timing of pair sequential numbers in the sequence being used. V7. Added Defining Costello Constant's Value, Definition, And Symbol. V8. Added Data Set Of Sequence Numbers As T Values V9. Eureka! Offset fixed! "^0 + it" is the golden key it's officially solved. The Costello spiral is the structure, The zeta zeros are mapping the features of it. V10. Added Needed Proof V11. Complete revamp fixing errors in construction. I'm a non-academic... I'm trying here... Alone... V12. Updated Formatting Pages 1 - 2 Finalized V13. Update Pages 1 - 3 Finalized, 4 - 7 Drafted V14. Finalized Doc 1 Current Version Is A Fully Closed Loop System Logic, It's Proof By Fundamental Law. Costello Spiral Diagrams Reflects Older .809... Helix Radius Matching Pre 1.0000 Radius Formula Reduction. "This Fundamental Law is scale-invariant; while earlier diagrams (0.809) and the finalized 1.0000 reduction represent different magnitudes, the underlying closed-loop logic and intersection intersections remain constant. The 1.0000 Unit Radius represents the simplest, normalized state of the Costello Spiral." One last note to whom it may concern... I did this completely independent starting from the ground up with no previous research into other publishments, I started with the desire to make a sequence that was novel, and just kept making connections one after another. I've watched a couple YouTubes in the past that had discussed vaguely The mystery of the Zeta zeros and that's about the extent of my outside knowledge. I didn't set out to discover the secret for it, my series ran into it by its nature itself. V15. Updated format to Latex, added much more vigorous math proof, order of logic still needs tweaking. V16. Added data point charts into Latex pdf. V17. Formatting Fixes V18. Added -1 somewhere... Oops V19. Added how the Costello Spiral solves the Collatz Conjecture too. V20. Added hypothesis of the twin Prime conjecture V21. Fixed Rooke Mistakes... Double Statements... Out of order stuffs.... V22. More Formatting Fixes. V23. Lots better, 25+ years sine education environment, first proof... Getting there... V24. Added formula for ratio relationship of factors to the zero spacing, but messes up my formatt big time... Lullz.. im fixing it. I hate all these loops I have to jump through honestly, taking away from time that I could just be diving further in the numbers as usual. I'm almost giving up a couple times I just went back to my paper notebooks. V25. Well maybe have about 10% of the information out now... Main problem is I don't know what's most important to show I don't know what the world knows or not... Like I don't know what to add next the list is too big... Semi-prime Costello sequence numbers that are close together align with Zeta zeros close together.. eg., 7171... So much work... I've tried showing my math and I get laughed at... I'mma just keep on pushing... It may not be conventional to add your thoughts or whatever... But I'm a break the fifth wall right now... From two weeks now I've tried reaching out... All skepticism.. it just hit me tonight... It's because it's all sounds too good to be true... I didn't know that... I'm trying to do too much at once... I mean on top of my work that I'm doing I had to learn the formal language... I've had to learn how to code... I've had to learn Python script so I can run my old numbers... And for 2 weeks now I've been pushing... To show people ONE of my creations. Maybe the world is just not ready.... .. .. . Maybe. It's hard to forget, everything I regret. So why do I neglect, the chances that I get, To make those things correct... When I've tried to reflect... I just lost more respect... How did i ever let my mindset behind set get so inept. While im On the subject if I may be direct. I digress... It is best to get the rest of my chest. Im blessed but made a mess whats more or less my nest. I feel i failed my quest, I have failed my own test. It's a sure bet soon I'll take my last breath. Back to work... V26. Gtting there... Please use V23 complete copy until i stop mesing up my work with copy pasts twice deleed everything. V Edition2 V27. New formatt next few additions should be coming back to back to back as I string the old with the new. Refer to V22/23 for older complete outline, V Edition2 V28. Brought over some data from my research pfd, order and simplification are needed. V Edition2 V29. Stitching in the dimensional transitions from the number line to a real plane to complex plane to the manifold. Still need smooth transitioning. V Ediion2 V30. Added a good chunk to complex/manifold section, I just want to get it uploaded, I still have to prune it and smooth it. And make sure the stuff at the end is stated the way it's supposed to before I can remove it. Editiom2 V31. Added 10.3 frequency of spiral is the slope of sequence on log xy. Deleted doubles. Edition2 V32 Added dada set at end, refining python code number generator to add next. Edition2 V33 Changed Description on Zenodo added some info to I - III, refer to Ver 23 in tandem as f now after reading to complete the info aquired. Lots more to come... Edition2 V33.2 Keep Pushing Unil The World Listens... Changed Sequence Formula Formatt of f(n) Fixed Order still have to move over more sections from research Pdf. Including making sure pdf reflects duel helix is intersecting as counter clockwise 1 string and clockwise the other, reforming old 180° opposition, to actual intersection. At 0° Edition2 V34. Updated High Precision Value Of Slope using 500 sequence Values, Added bar graph for delta 2 equalization, other minor adjustments. Edition2 V35. Fixing all formulas to compensate for the change of what f(a_n) is.. as befor the rule a_n+1 = a_n + f(a_n-1) when f(a_n) meant a_n's GPD.. but for clearity f(a_n) now means a_n-1's GDP... To remove a LAG extra thought... Royal pain but a necessity.... Almost done converting everything. Edition2 V36 Formalized Pages 1-2 of actual proof after index, added rigor and made it more succinct. Eution2 V37. Showed how 10.337... slight miss alignment snap perfectly to 10.333 and perfectly aligned to zz1 now that start up terms 1-9 are removed from calculations. Edition2 V38 Formed formulas using the costello constant for prime density and how many primes exist in any limit, gives exct answer at 1,000,000. Edition2 v39 Finalized pages 1-4 Edition3.1 Finalize Format Starting To Translate. Page 1 done, Page 2 in progress Edition3.2 Actual Professional Formatt Learned And Applied.Pae 1/2 almost good. Should be a quick transition building back a strong base from dra in previous versions. Edition3.3 Added .6 Parity Limit, Growth Factor & Graph. Edition3.4 Added Symmetry/2-adic Sections & Tables Edition3.5 added the singularit Edition3.6 Formatt ambiguities removed, added minor info, Organized Zenodo Ledger, Edition3.7 Unified formatt formatt & variables, added log/non lomgrph real graphs, n more. Edition3.8 Added Changed To Font/Formatt Added Graphs Other Minor Additions Edition3.9 Bulletproofed Logic up to Lambda parity Density 0.6, 2:3. Edition3.10 Defined Lambda and lambda, added parity density equations and table Edition3.11 Added High Precision Lambda Values, 2 Graphs (1 Custom Expanding Y Axis} Edition3.12 Learned Python... Wrote and added script for producing Verifiable Data, Include plain txt file and 2 Appendix to PDF with Program and sample data. Edition3.13 Streamlined f function by introduction of spa divisor set mapped to n. Defined Tau and some other minor stuffs. Edition3.14 Added plain txt documents of raw Latex Code And Python Sequence Engine Edition3.15 Added Infinit tetration of B = C,, LogB(C) =
Older versions more complete but.... Umm less complete. I'm hopefully putting the pieces back together for the final edition. The Costello Constant (CC) base (e/phi - 1/pi), and Costello sequence governed by n(+1) = n + f(n), f(n) is the Greatest Proper Divisor of n(-1); f(n1) = 1, mapped onto the complex plan Y(ix) = (e/phi -1/pi)^(0±ix) using x as a time function for an. added dimention, forms a single helix that bifurcrates into. duel helix where intersection of the 2 spiraling lines cancel out from complete annihilation at value of the first zero~(14) this helix is anchored to the origin by raising the base to the power of zero, The even exponent of i are one helical arm, the negative value of i is the odd value helical arm. Points where they annihilate the x values are the zeta zeros value with a frequeny ~ 10.33715124… the slope of the sequence on a semi logarithmic graph align perfectly straight… or the inverse of... when joining sequential odds treating the O O E cycles as only 2 values (plot points, both odds as one single unit, multiplied by the value of CC ~ 1.3616... gives the exact value zeta zero 1, in the sequence this is equivalent to the Attractor a10 (16) when looking at ratios between zero 1 and zero 2 as an x/y it matches exactly to (13+16+17/3)/(17/25/26) this number and it's simplest reduced form 268/183 also are the exact ratio of certain toma in chemicals. And te genes which map a certain protein. I assume other ratios between consecutive numbers and the sequence will reveal some wonders in the universe that have remained untold until this moment. I've been ignored for weeks now which has giving me the time to dive into a level of certainty beyond any shadow of a doubt. On the regular graph when treating odds consecutive as one and evens as one connecting all evens and connecting All Odds creates two distinct lines where are the formula of the Costello constant is right in the middle. Basically turning the Zeta zeros into an algebraic problem by connecting the dots odds and evens where intersects on the equation graphed is the location of the Zeta zeros. Mic drop. V6. Added details about the zero timing overlap with formula being dictated by timing of pair sequential numbers in the sequence being used. V7. Added Defining Costello Constant's Value, Definition, And Symbol. V8. Added Data Set Of Sequence Numbers As T Values V9. Eureka! Offset fixed! "^0 + it" is the golden key it's officially solved. The Costello spiral is the structure, The zeta zeros are mapping the features of it. V10. Added Needed Proof V11. Complete revamp fixing errors in construction. I'm a non-academic... I'm trying here... Alone... V12. Updated Formatting Pages 1 - 2 Finalized V13. Update Pages 1 - 3 Finalized, 4 - 7 Drafted V14. Finalized Doc 1 Current Version Is A Fully Closed Loop System Logic, It's Proof By Fundamental Law. Costello Spiral Diagrams Reflects Older .809... Helix Radius Matching Pre 1.0000 Radius Formula Reduction. "This Fundamental Law is scale-invariant; while earlier diagrams (0.809) and the finalized 1.0000 reduction represent different magnitudes, the underlying closed-loop logic and intersection intersections remain constant. The 1.0000 Unit Radius represents the simplest, normalized state of the Costello Spiral." One last note to whom it may concern... I did this completely independent starting from the ground up with no previous research into other publishments, I started with the desire to make a sequence that was novel, and just kept making connections one after another. I've watched a couple YouTubes in the past that had discussed vaguely The mystery of the Zeta zeros and that's about the extent of my outside knowledge. I didn't set out to discover the secret for it, my series ran into it by its nature itself. V15. Updated format to Latex, added much more vigorous math proof, order of logic still needs tweaking. V16. Added data point charts into Latex pdf. V17. Formatting Fixes V18. Added -1 somewhere... Oops V19. Added how the Costello Spiral solves the Collatz Conjecture too. V20. Added hypothesis of the twin Prime conjecture V21. Fixed Rooke Mistakes... Double Statements... Out of order stuffs.... V22. More Formatting Fixes. V23. Lots better, 25+ years sine education environment, first proof... Getting there... V24. Added formula for ratio relationship of factors to the zero spacing, but messes up my formatt big time... Lullz.. im fixing it. I hate all these loops I have to jump through honestly, taking away from time that I could just be diving further in the numbers as usual. I'm almost giving up a couple times I just went back to my paper notebooks. V25. Well maybe have about 10% of the information out now... Main problem is I don't know what's most important to show I don't know what the world knows or not... Like I don't know what to add next the list is too big... Semi-prime Costello sequence numbers that are close together align with Zeta zeros close together.. eg., 7171... So much work... I've tried showing my math and I get laughed at... I'mma just keep on pushing... It may not be conventional to add your thoughts or whatever... But I'm a break the fifth wall right now... From two weeks now I've tried reaching out... All skepticism.. it just hit me tonight... It's because it's all sounds too good to be true... I didn't know that... I'm trying to do too much at once... I mean on top of my work that I'm doing I had to learn the formal language... I've had to learn how to code... I've had to learn Python script so I can run my old numbers... And for 2 weeks now I've been pushing... To show people ONE of my creations. Maybe the world is just not ready.... .. .. . Maybe. It's hard to forget, everything I regret. So why do I neglect, the chances that I get, To make those things correct... When I've tried to reflect... I just lost more respect... How did i ever let my mindset behind set get so inept. While im On the subject if I may be direct. I digress... It is best to get the rest of my chest. Im blessed but made a mess whats more or less my nest. I feel i failed my quest, I have failed my own test. It's a sure bet soon I'll take my last breath. Back to work... V26. Gtting there... Please use V23 complete copy until i stop mesing up my work with copy pasts twice deleed everything. V Edition2 V27. New formatt next few additions should be coming back to back to back as I string the old with the new. Refer to V22/23 for older complete outline, V Edition2 V28. Brought over some data from my research pfd, order and simplification are needed. V Edition2 V29. Stitching in the dimensional transitions from the number line to a real plane to complex plane to the manifold. Still need smooth transitioning. V Ediion2 V30. Added a good chunk to complex/manifold section, I just want to get it uploaded, I still have to prune it and smooth it. And make sure the stuff at the end is stated the way it's supposed to before I can remove it. Editiom2 V31. Added 10.3 frequency of spiral is the slope of sequence on log xy. Deleted doubles. Edition2 V32 Added dada set at end, refining python code number generator to add next. Edition2 V33 Changed Description on Zenodo added some info to I - III, refer to Ver 23 in tandem as f now after reading to complete the info aquired. Lots more to come... Edition2 V33.2 Keep Pushing Unil The World Listens... Changed Sequence Formula Formatt of f(n) Fixed Order still have to move over more sections from research Pdf. Including making sure pdf reflects duel helix is intersecting as counter clockwise 1 string and clockwise the other, reforming old 180° opposition, to actual intersection. At 0° Edition2 V34. Updated High Precision Value Of Slope using 500 sequence Values, Added bar graph for delta 2 equalization, other minor adjustments. Edition2 V35. Fixing all formulas to compensate for the change of what f(a_n) is.. as befor the rule a_n+1 = a_n + f(a_n-1) when f(a_n) meant a_n's GPD.. but for clearity f(a_n) now means a_n-1's GDP... To remove a LAG extra thought... Royal pain but a necessity.... Almost done converting everything. Edition2 V36 Formalized Pages 1-2 of actual proof after index, added rigor and made it more succinct. Eution2 V37. Showed how 10.337... slight miss alignment snap perfectly to 10.333 and perfectly aligned to zz1 now that start up terms 1-9 are removed from calculations. Edition2 V38 Formed formulas using the costello constant for prime density and how many primes exist in any limit, gives exct answer at 1,000,000. Edition2 v39 Finalized pages 1-4 Edition3.1 Finalize Format Starting To Translate. Page 1 done, Page 2 in progress Edition3.2 Actual Professional Formatt Learned And Applied.Pae 1/2 almost good. Should be a quick transition building back a strong base from dra in previous versions. Edition3.3 Added .6 Parity Limit, Growth Factor & Graph. Edition3.4 Added Symmetry/2-adic Sections & Tables Edition3.5 added the singularit Edition3.6 Formatt ambiguities removed, added minor info, Organized Zenodo Ledger, Edition3.7 Unified formatt formatt & variables, added log/non lomgrph real graphs, n more. Edition3.8 Added Changed To Font/Formatt Added Graphs Other Minor Additions Edition3.9 Bulletproofed Logic up to Lambda parity Density 0.6, 2:3. Edition3.10 Defined Lambda and lambda, added parity density equations and table Edition3.11 Added High Precision Lambda Values, 2 Graphs (1 Custom Expanding Y Axis} Edition3.12 Learned Python... Wrote and added script for producing Verifiable Data, Include plain txt file and 2 Appendix to PDF with Program and sample data. Edition3.13 Streamlined f function by introduction of spa divisor set mapped to n. Defined Tau and some other minor stuffs. Edition3.14 Added plain txt documents of raw Latex Code And Python Sequence Engine Edition3.15 Added Infinit tetration of B = C,, LogB(C) = C, LogC^(1/C)=B,
Wireless medical sensor networks (WMSNs) enable continuous patient monitoring by transmitting sensitive physiological data over open wireless links. Given the resource-constrained nature and large-scale deployment of such networks, authentication mechanisms must be both lightweight and privacy-preserving. Moreover, due to the frequent turnover of patients and devices in hospital environments, timely member revocation is crucial to prevent discharged or compromised entities from injecting forged reports that could mislead medical diagnosis. Although existing pairing-free certificateless aggregate authentication schemes are efficient, they often suffer from critical security and privacy vulnerabilities. Recently, an efficient certificateless authentication scheme with revocation has been proposed. However, our analysis reveals that the scheme presents the following security vulnerabilities: (i) member witnesses can be recovered from public information, (ii) revocation checks can be bypassed via identity grafting attack, and (iii) user identities can be linked due to the long-term use of static pseudonyms. To address these issues, we propose a security-enhanced certificateless aggregate authentication protocol with revocation for WMSNs. Our design enforces strong identity-membership binding to resist grafting attacks, employs a non-interactive zero-knowledge membership proof to preserve witness secrecy, and adopts dynamic pseudonym rotation to achieve unlinkability. We provide formal security proofs and comprehensive performance comparisons. The results indicate that, at the same security level, our protocol achieves more efficient signature verification while maintaining communication overhead comparable to existing schemes. In addition, the overhead introduced by our revocation mechanism remains constant, making it well suited for large-scale WMSNs deployments with frequent membership changes.
Federated Learning (FL) is an approach that allows numerous users to train a single machine learning model with the oversight of a central server, and with their training data stored locally on their devices. The approach is relevant in alleviating the risks associated with violations in data privacy. It is a process by which a pool of clients collaborates towards solving machine learning problems, with a central coordinator being the one who coordinates the entire process. The paper will review the latest advances in privacy-preserving federated learning and discuss it in the context of machine learning. It assesses privacy-related solutions, which are already in existence, such as secure aggregation, meta-learning, blockchain technology, decentralized training, searchable encryption, and data privacy mechanisms and zero-knowledge proofs. Federated learning (FL) is an emerging technology that can be used in the realm of the intelligence of the Internet of Things. However, the information that is model-related can be shared in FL and reveal the sensitive data of the participants. In this regard, we propose a new privacy-preserving FL framework, which is founded on a new chained secure multiparty computing technique, which we call chain-PPFL. The scheme we are proposing is based mostly on two mechanisms: 1) a single-masking mechanism, which protects the information that is exchanged between participants in a serial chain frame and 2) a chained-communication mechanism, which allows the masked information to be communicated between participants in a serial chain frame. We run large-scale experiments with respect to simulation by comparing the training accuracy and the leak defence to other state-of-the-art schemes with two publicly available data sets (MNIST and CIFAR-100). We established data sample distributions (IID and NonIID), and training models (CNN, MLP and L-BFGS) in our experiments. The experiment results show that the chain-PPFL scheme can offer a realistic privacy preservation (which is the same as the various privacy with ϵ to near zero) to FL at the cost of communication, and without compromising the accuracy and convergence rate of the training model.
Authorization tokens in distributed systems are typically context-free: a cryptographically valid token carries no binding to the specific transaction for which it was issued. This enables reuse and cross-context presentation attacks that are undetectable at the cryptographic layer. In regulated financial infrastructure, cross-border payments, and autonomous agent systems, transaction-scoped enforcement is a hard requirement that existing standards leave unaddressed. We introduce the first formal security model for policy-bound transaction tokens. We define the syntax of a policy-bound transaction token scheme over a formal transaction context space and introduce three game-based security notions: transaction binding (TB), which simultaneously resists forgery and cross-context reuse; existential unforgeability under chosen-context attack (EUF-CCA); and unlinkability (UNL). We prove that TB strictly implies EUF-CCA, establish a formal separation between TB and UNL, and identify the inherent tension between unlinkability and auditability. We construct a scheme parameterized by any EUF-CMA-secure signature scheme and a random oracle, and prove that it achieves transaction binding security with a tight reduction requiring no rewinding. We then address the complementary privacy problem by formalizing zero-knowledge compliance privacy (ZK-CP) and constructing an enhanced scheme that augments transaction-binding tokens with a non-interactive zero-knowledge proof of policy compliance. We prove that the enhanced scheme simultaneously achieves TB security and ZK-CP, and show how it integrates with decentralized identity (DID) systems to enable fully privacy-preserving authorization where the verifier learns only whether compliance is satisfied. We give a concrete instantiation using Ed25519 and SHA-512, derive bit-security parameters, analyze performance costs, and discuss deployment considerations including regulatory alignment with PSD2, MiCA, DORA, the GENIUS Act, SEC token taxonomy, and FinCEN BSA requirements.