Faithful, Stable, Complete: Pick Two The Problem in Plain Language When a machine learning model makes a prediction — approving a loan, diagnosing a disease, flagging a transaction — practitioners use a tool called SHAP to answer "which input features mattered most?" SHAP is the most widely used explanation method in machine learning. Here is the problem: retrain the same model on the same data with a different random seed, and the explanation changes. The model's predictions barely move, but the "most important feature" can flip entirely. In 68% of 77 public datasets, the top feature is not stable across retrains. This is not a software bug. This is not fixable by tuning hyperparameters. We prove it is a mathematical impossibility. What We Prove No feature ranking can simultaneously be: Faithful — it reflects what the model actually learned Stable — it doesn't change when you retrain Complete — it ranks every pair of features …when features are correlated with similar importance. You must give up one. The proof is four lines long. It requires no assumptions about the model, the data, or the explanation method — only that correlated features admit models ranking them in opposite orders (the Rashomon property), which is true for every standard ML algorithm. How Bad Is It? We trained 50 XGBoost models on Breast Cancer Wisconsin — the dataset used in every SHAP tutorial — and counted how many different "top 3 most important features" appeared. Twenty-four. At 100 models: thirty-five. The "most common" answer appeared in only 12% of runs. Two randomly chosen models agree on the top-3 only 4.2% of the time. Every tutorial, textbook, and blog post showing SHAP on this dataset is showing one of two dozen equally valid answers. Three other datasets (California Housing, Heart Disease, Wine Quality) produce exactly one ranking every time — because their top features have clearly different importance. The theory correctly predicts which datasets are affected and which are safe. Dataset Distinct top-3 rankings (50 models) Two models agree? Breast Cancer 24 4.2% Diabetes 2 88.5% Wine Quality 1 100% (stable) Heart Disease 1 100% (stable) California Housing 1 100% (stable) It Gets Worse for Yes/No Questions For ranking questions (which feature is MORE important?), there is a fix: average across multiple models. But for binary questions — "does this feature contribute positively or negatively?", "is this feature selected?" — no fix exists. Even averaging doesn't help, because there's no middle ground between "positive" and "negative." We call this the bilemma. Real-World Consequences For loan applicants. We trained 30 models on German Credit data. Under standard settings, 45% of applicants receive a different "most important reason" for their decision depending on which model happens to be deployed. One applicant received six different top reasons across 30 models. For biomarker discovery. On a dataset of 10,935 genes distinguishing colon from kidney tissue, the "#1 most important gene" alternates between TSPAN8 (involved in tumor invasion) and CEACAM5/CEA (involved in immune evasion) depending on the random seed. A drug discovery pipeline targeting one gene makes a different bet than one targeting the other — and which bet gets made depends on a random number. For fairness audits. A SHAP-based audit checking whether a model relies on a protected attribute (like race or gender) reaches its conclusion with the reliability of a coin flip when the protected attribute is correlated with other features. The Fix DASH (Diversified Aggregation for Stable Hypotheses): train 25 models with different seeds, average their SHAP values. This is provably the best possible approach — no method can do better. Features that genuinely differ in importance get stable rankings. Features that are interchangeable get reported as tied, which is the honest answer. We also provide a 7-line diagnostic that identifies which features are at risk, requiring no statistical expertise and no assumptions about the data distribution. It outperforms the standard formula by 2× on real data. The practical workflow: Screen your model (1 model, seconds) Run the minority fraction diagnostic (7 lines of code) For flagged features, train 5 models and run a Z-test If unstable, use DASH with 25+ models Machine Verification Every mathematical claim is checked by a computer. The proofs are written in Lean 4 (a programming language for mathematics) and verified by its type-checker: 357 theorems, all machine-verified 6 axioms (the minimal assumptions the theory needs) Zero unproved claims across 58 files During the formalization, the computer caught two logical errors and one type mismatch that human reviewers missed. To our knowledge, this is the first formally verified impossibility result in explainable AI. Technical Details Architecture-dependent bounds Gradient boosting (XGBoost, LightGBM): instability diverges as correlation increases. At ρ = 0.9, the dominant feature gets 5× its fair share. Lasso: the ratio is infinite — one correlated feature gets everything, the other gets zero. Neural networks: 87% of feature pairs are unstable. Model instability dominates SHAP estimation noise by 8:1. Random forests: instability converges with more trees — the contrast case showing that parallel (not sequential) training helps. Cross-implementation. XGBoost, LightGBM, and Random Forest all show the same instability pattern. It is not specific to any one software package. Subsample sensitivity. Even at subsample = 0.95 (minimal randomness), 17 distinct rankings remain. Only fully deterministic training (subsample = 1.0) produces one ranking — but this sacrifices the regularization that makes the model accurate. Mechanistic interpretability. Preliminary evidence suggests the impossibility extends beyond feature importance to neural network circuit analysis. 10 transformers trained on modular addition (all achieving 100% accuracy) agree on only 36% of the top-3 circuit components. Design Space The achievable set of explanation methods has exactly two families: Family A (single model): faithful and complete, but unstable. Rankings flip up to 50% of the time. This is what standard SHAP does. Family B (DASH ensemble): faithful and stable, but reports ties for indistinguishable features. This is what DASH does. No third option exists. DASH is provably the best method in Family B. Associated Papers Companion paper (TMLR, under review). First-Mover Bias in Gradient Boosting Explanations: Mechanism, Detection, and Resolution.arXiv: https://arxiv.org/abs/2603.22346DOI: https://doi.org/10.5281/zenodo.19446088 Companion implementation: https://github.com/DrakeCaraker/dash-shap
Proof of Concept on the β-Catenin/TCF4 Interface in Wnt-Driven Oncogenesis and Gardner Syndrome Protein-protein interactions (PPIs) govern nearly every biological signalling pathway, yet their large, flat contact surfaces have resisted conventional drug design for decades. Existing computational approaches either require prohibitive molecular simulation resources or prior knowledge of a reference inhibitor—barriers that have left many therapeutically important targets inaccessible. This repository presents GeoSol-αα, a two-stage computational pipeline that generates macrocyclic drug scaffolds against PPI surfaces from first principles—without molecular dynamics simulation, without a crystallographic inhibitor reference, and without prior chemical knowledge of the target. The engine couples deterministic rigid-body SO(3) Fibonacci sampling with directed chemical evolution (genetic algorithms). In milliseconds, the pipeline successfully converged on a novel: 15-atom macrocyclic scaffold (1,4-dioxacyclopentadecane) that achieves a thermodynamic optimum with zero desolvation penalty against the β-catenin interface. This repository establishes formal prior art for both the identified chemical entity and the underlying high-throughput methodology.
Abdullah Abdullah, Nida Hafeez, Maryam Shabbir, Muhammad Ateeb Ather · 6 authors
The integration of blockchain technology with the Internet of Things (IoT) presents a paradigm shift in securing decentralized networks, yet it introduces critical trade-offs among security, privacy, and scalability. This systematic analytical review examines the inherent tensions within blockchain-enabled IoT systems, focusing on how consensus mechanisms, cryptographic primitives, and architectural choices affect these three pillars. Through a comprehensive analysis of the contemporary literature, we identify that no single blockchain configuration simultaneously optimizes security, privacy, and scalability. Instead, these properties exist in a triadic relationship where enhancing one dimension typically compromises at least one other. Our review categorizes existing solutions based on their approach to balancing these trade-offs, including sharding, layer-2 protocols, zero-knowledge proofs, and hybrid architectures. We further analyze the applicability of these solutions across different IoT domains, identifying context-specific optimal configurations. The findings reveal that while significant progress has been made in addressing individual challenges, integrated frameworks that holistically consider all three dimensions remain underdeveloped. This review contributes a novel analytical framework for evaluating blockchain–IoT systems and identifies critical research directions, including adaptive consensus mechanisms, privacy-preserving scalability solutions, and domain-specific architectural patterns. Unlike prior studies that primarily focus on conceptual discussions of blockchain–IoT integration, this work synthesizes insights from systematically reviewed literature to propose a conceptual lightweight blockchain framework tailored for resource-constrained IoT environments. This study combines a SLR with a conceptual and experimentally evaluated framework, where the review findings and the proposed solution are presented as distinct but complementary contributions.
In an era where data integrity and secure verification are paramount, especially in sectors such as governance, healthcare and education, traditional centralized document verification systems fall short due to vulnerabilities like single points of failure, limited traceability, and lack of accountability. This study proposes a LRDDV (A layered Ledger approach for Robust Digital Documents Verification system using blockchain) model to create a multi-level method for verifying documents. This would solve these issues. It adds a lightweight consensus model that is led by validators and a way to lock information based on role to do this. People who have jobs at different hierarchy levels can add information to papers more quickly. This makes sure that the changes are safe and can be made all the way through. If 51 % of validators agree on something, it works like a real board of directors. It makes people trust each other and be open without having to do mining, which takes a lot of resources. It works better, costs less, and is easier to keep track of than centralized models, according to tests especially useful for small and medium-sized businesses (SMEs) as well as for government sector. Right now, things work fine in a controlled environment. Although, in the future, it will be safer and more scalable because it will be connected to group blockchain systems, use self-sovereign identification standards, and have built-in zero- knowledge proofs. The suggested answer allows document checking to happen in public places with lots of people in a safe, open, and spread-out manner.
Chirag Sathish, Arshad Khan, Deepesh Haldankar, Nikhita G · 5 authors
The increasing adoption of telemedicine has amplified concerns regarding the security of patient data, particularly in the context of remote authentication and the growing threat of advanced cyber and quantum-enabled attacks. Traditional telehealth security mechanisms rely on static authentication and cryptographic protections, which fail to adapt to changing risk conditions and provide limited resilience against credential compromise and future quantum threats. This paper proposes TAPQ-Health, a Threat-Adaptive Post-Quantum Authentication Pipeline that dynamically adjusts the strength of authentication and cryptographic hardness in real time based on contextual and behavioral risk. The proposed framework integrates four components a lightweight context-bound zero-knowledge proof authentication mechanism, a federated machine learning-based risk assessment model, threat-triggered escalation to lattice-based post-quantum cryptography with adaptive re-encryption, and decentralized, tamper-evident storage using IPFS. A fully implemented prototype was evaluated using 200 real telemedicine sessions and a large-scale analysis of 1.3 million authentication records. Experimental results demonstrate a mean end-to-end latency of 102.84 ms, 100 percent authentication success, and a 61 percent reduction in cryptographic overhead compared to static post-quantum configurations, while achieving 96 percent risk detection accuracy. These results indicate that threat-adaptive post-quantum authentication can significantly enhance telemedicine security without compromising usability or scalability.
Recent advancements, specifically the 2026 whitepaper by Google Quantum AI, Stanford University, and the Ethereum Foundation (arXiv:2603.28846), have demonstrated the resource feasibility of breaking secp256k1 elliptic curve cryptography using fault-tolerant quantum computation (≤ 1200 logical qubits and ≤ 90 million Toffoli gates). While their work validates this capability via zero-knowledge STARK proofs without disclosing explicit circuits, we provide the continuous operator-theoretic framework that explains the exact physical collapse mechanism underlying their discrete resource results. By modeling cryptographic hardness as a stable, invariant computational manifold, we show that quantum vulnerability is a manifestation of a Birman-Schwinger instability. We prove that, within this model, the introduction of a transverse quantum operator (e.g., Shor's algorithm implemented via Quantum Phase Estimation) forces a resolvent singularity in the classical generator when the resource perturbation parameter crosses a critical threshold (μ_c). We establish a strict Hardness Phase Transition, demonstrating that cryptographic security is equivalent to the point 1 remaining outside the spectrum of the Birman-Schwinger kernel. Furthermore, we formalize zero-knowledge proofs (such as the Groth16-wrapped STARK artifacts published by Babbush et al.) as highly constrained Boolean projectors. We show that these proofs trigger an epistemic spectral collapse via Zeno stabilization, certifying the non-invertible regime without decohering the raw computational state into the public domain. The manuscript includes an exact analytic toy model demonstrating bound-state collapse into the continuum, explicitly mapping the destruction of exponential cryptographic isolation to a polynomial scattering state. This formalization transitions cryptographic failure from a domain of discrete computational estimates to a continuous framework of operator-theoretic necessity.
This paper argues that India's Goods and Services Tax Network has already produced, through tax incentive rather than cryptographic consensus, the supply chain properties — traceability, transparency, fraud reduction, and audit trail — that the blockchain literature proposes to deliver through distributed ledger technology. The argument is not that blockchain does not work. It is that the mechanism that produces tamper-resistance is the incentive, not the technology, and India already has that mechanism at national scale. The paper's original theoretical contribution is a two-player simultaneous-move game formalizing the bilateral incentive structure that the VAT self-enforcement literature has assumed in prose but never derived from primitives. The unique Nash equilibrium (F,D) — formal supplier, demanding buyer — is obtained by iterated elimination of weakly dominated strategies and sustained by a single precise condition: τv > c_B, the input tax credit exceeds the buyer's cost of sourcing from a registered alternative. No audit is required at the transaction level. The ITC does the work that enforcement cannot. The upstream formalization cascade — empirically documented by Patnaik (2026) as a doubling of effects over five years — follows directly as this equilibrium applied iteratively upstream, tier by tier, without government intervention at each stage. To the author's knowledge, this micro-foundation does not appear elsewhere in the VAT literature. Pomeranz (2015), Kleven et al. (2011), and de Paula and Scheinkman (2010) treat the self-enforcement intuition as motivation or derive aggregate implications; none writes down the strategic form game or states the equilibrium condition in falsifiable form. The empirical case rests on scale. FY2024-25 gross collections of Rs. 22.08 lakh crore (approx. USD 263 billion). April 2025 single-month record of Rs. 2.37 lakh crore (approx. USD 28 billion). 1.51 crore active registered taxpayers. Six phases of e-invoicing threshold reduction from Rs. 500 crore to Rs. 5 crore, directionally toward universal pre-validated coverage. GST 2.0 implemented September 22, 2025. The Production Linked Incentive scheme disbursing billions to Apple's contract manufacturers on the basis of GSTN-verified production data — the sovereign proof that the infrastructure is trusted for the highest-stakes commercial verification the government performs. The implication for Indian FMCG, pharmaceutical, and logistics firms is direct: private blockchain consortia built to solve domestic supply chain transparency problems are solving a solved problem at non-zero cost.
This paper argues that India's Goods and Services Tax Network has already produced, through tax incentive rather than cryptographic consensus, the supply chain properties — traceability, transparency, fraud reduction, and audit trail — that the blockchain literature proposes to deliver through distributed ledger technology. The argument is not that blockchain does not work. It is that the mechanism that produces tamper-resistance is the incentive, not the technology, and India already has that mechanism at national scale. The paper's original theoretical contribution is a two-player simultaneous-move game formalizing the bilateral incentive structure that the VAT self-enforcement literature has assumed in prose but never derived from primitives. The unique Nash equilibrium (F,D) — formal supplier, demanding buyer — is obtained by iterated elimination of weakly dominated strategies and sustained by a single precise condition: τv > c_B, the input tax credit exceeds the buyer's cost of sourcing from a registered alternative. No audit is required at the transaction level. The ITC does the work that enforcement cannot. The upstream formalization cascade — empirically documented by Patnaik (2026) as a doubling of effects over five years — follows directly as this equilibrium applied iteratively upstream, tier by tier, without government intervention at each stage. To the author's knowledge, this micro-foundation does not appear elsewhere in the VAT literature. Pomeranz (2015), Kleven et al. (2011), and de Paula and Scheinkman (2010) treat the self-enforcement intuition as motivation or derive aggregate implications; none writes down the strategic form game or states the equilibrium condition in falsifiable form. The empirical case rests on scale. FY2024-25 gross collections of Rs. 22.08 lakh crore (approx. USD 263 billion). April 2025 single-month record of Rs. 2.37 lakh crore (approx. USD 28 billion). 1.51 crore active registered taxpayers. Six phases of e-invoicing threshold reduction from Rs. 500 crore to Rs. 5 crore, directionally toward universal pre-validated coverage. GST 2.0 implemented September 22, 2025. The Production Linked Incentive scheme disbursing billions to Apple's contract manufacturers on the basis of GSTN-verified production data — the sovereign proof that the infrastructure is trusted for the highest-stakes commercial verification the government performs. The implication for Indian FMCG, pharmaceutical, and logistics firms is direct: private blockchain consortia built to solve domestic supply chain transparency problems are solving a solved problem at non-zero cost.
Proof of Concept on the β-Catenin/TCF4 Interface in Wnt-Driven Oncogenesis and Gardner Syndrome Protein-protein interactions (PPIs) govern nearly every biological signalling pathway, yet their large, flat contact surfaces have resisted conventional drug design for decades. Existing computational approaches either require prohibitive molecular simulation resources or prior knowledge of a reference inhibitor—barriers that have left many therapeutically important targets inaccessible. This repository presents GeoSol-αα, a two-stage computational pipeline that generates macrocyclic drug scaffolds against PPI surfaces from first principles—without molecular dynamics simulation, without a crystallographic inhibitor reference, and without prior chemical knowledge of the target. The engine couples deterministic rigid-body SO(3) Fibonacci sampling with directed chemical evolution (genetic algorithms). In milliseconds, the pipeline successfully converged on a novel: 15-atom macrocyclic scaffold (1,4-dioxacyclopentadecane) that achieves a thermodynamic optimum with zero desolvation penalty against the β-catenin interface. This repository establishes formal prior art for both the identified chemical entity and the underlying high-throughput methodology.
This paper presents the first formally documented implementation of post-quantum cryptographic infrastructure within a production-grade institutional compliance enforcement system. It addresses a structural vulnerability endemic to the entire regulatory technology industry: every compliance record generated today under RSA or ECC encryption is potentially exposed to "Harvest Now, Decrypt Later" (HNDL) attacks — a documented, operationally active collection strategy confirmed by NSA, CISA, ENISA, and BSI — and will remain so until quantum computers capable of running Shor's algorithm at scale become available, currently projected between 2030 and 2035. Given mandatory regulatory retention periods of 5–30 years under DORA Art.10, GDPR Art.5(e), FinCEN BSA 31 CFR §103.33, Swiss OR Art.958f, and Solvency II, compliance records created today under classical cryptography will still exist — and may be decryptable — within their own legally mandated retention window. This paper documents the complete architectural response: the deployment of CRYSTALS-Kyber-1024 (NIST FIPS 203, 2024) as the primary cryptographic primitive for all compliance ledger operations in the immo.quick Core Machine Law Engine, combined with: A hybrid encryption architecture providing quantum security with full backward compatibility A Merkle Tree Batching scheme reducing post-quantum storage overhead by 99.99% (from 4.67 PB/year to 0.35 TB/year at Tier-1 clearing volumes) A multi-region HSM key hierarchy (EU/CH/US/UK) with Shamir Secret Sharing (3-of-5) and zero-downtime rotation A Zero-Knowledge Proof integration (Groth16, PLONK, Cairo zk-STARK) that resolves the structural contradiction between GDPR Art.17 erasure rights and immutable ledger requirements — by placing zero personal data on the ledger A crypto-agility policy engine enabling algorithm migration without application code changes or audit trail disruption Complete regulatory compliance mappings to DORA, GDPR, BSI TR-02102-1, and NIST FIPS 203 The immo.quick Core platform is presented as the first operational implementation of this architecture across fourteen regulatory frameworks and five institutional sectors (Real Estate, Banking, Insurance, Government, Cloud/FinTech). This paper is a standalone technical specification and supplements the immo.quick Core architecture series (DOI: 10.5281/zenodo.19301212 through 10.5281/zenodo.19457223). It provides the first focused, formally structured academic documentation of CRYSTALS-Kyber-1024 deployment within a deterministic gate enforcement environment with hardware TEE attestation and bi-temporal legal state management. The central argument: Post-Quantum cryptography is not a feature request for 2030. It is a structural prerequisite for any compliance system intended to produce legally defensible evidence chains beyond the quantum threat horizon. The architecture to achieve this exists, is formally specified, and is operationally deployed.
Maritime shipping carries over 80% of global trade by volume, yet the information systems underpinning this vast network remain fragmented, proprietary, and mutually distrustful. This paper presents the Cascading Visibility Model (CVM), a theoretical framework formalizing how a single upstream data failure propagates non-linearly through carrier, port, customs, warehouse, and trucking handoffs. We introduce the Entropy Amplification Index (EAI) as a normalized measure of information loss per handoff layer, with estimated values exceeding 0.6 at the carrier-to-port boundary and approaching 0.8 at port-to-customs. We further characterize the Multi-Layer Trust Deficit as a maritime-specific prisoner's dilemma in which rational data hoarding by individual actors produces collectively catastrophic coordination failures. To address these failures, we propose the Distributed Vessel Trust Pool (DVTP), a protocol-layer architecture enabling multi-party vessel verification without requiring raw data disclosure. The DVTP uses physical impossibility detection anchored to third-party-generated port event timestamps that vessels cannot falsify, combined with zero-knowledge proof logic to trigger automatic cascade holds across interconnected ports. Three adversarial scenarios are analyzed theoretically. We compare the DVTP with the Portbase model and TradeLens failure to derive governance lessons. We also present a formal research agenda of eight hypotheses for empirical validation through discrete-event simulation. This paper is a theoretical framework and research agenda contribution. The EAI estimates presented are model-derived under stated assumptions; the DVTP architecture and its adversarial analysis are theoretical proposals; and the simulation design is specified for future execution.
The agricultural sector is essential for global food security but continues to face challenges in supply chain management, including lack of transparency, traceability, and data integrity. This study proposes AgroChain, a blockchain-based framework designed to enhance governance and trust in the Agricultural Supply Chain (ASC). The system is built on the Quorum blockchain platform, an enterprise version of Ethereum, which integrates Zero-Knowledge Proof (ZKP) protocols to ensure data privacy while maintaining secure and transparent transactions. AgroChain introduces a scalable process model that separates the registry of agricultural records from the actual data, enabling efficient data handling. Smart contracts are used to automate key supply chain operations such as record creation, validation, transfer, and deletion, allowing end-to-end traceability from farm to consumer. The framework also incorporates rolebased access control for stakeholders including farmers, distributors, retailers, and consumers. Experimental results indicate that AgroChain improves transparency, accountability, and interoperability, demonstrating the potential of blockchain technology to transform agricultural supply chain governance.
We present DSKAG-IT-SIG, a family of information-theoretic transaction signature schemes that achieve unconditional existential unforgeability under adaptive chosen-message attack by computationally unbounded adversaries. The construction derives per-transaction MAC keys through DSKAG, a deterministic symmetric key agreement protocol requiring no key transmission, no handshake, and no public key infrastructure. We prove (Theorem 1) that the forgery advantage of any unbounded adversary making q queries is at most q * 2^{-128} in standard mode, reducing to the statistical uniformity of DSKAG-derived keys and the pairwise independence of HMAC-SHA256 under a uniform key. We prove (Theorem 2) that cross-domain forgery advantage is at most 2^{-128} + negl(lambda), reducing to the statistical key isolation of DSKAG across policy domains. Both bounds are unconditional and independent of any computational hardness assumption. Standard-mode signatures are 30 bytes, a 97.8% reduction versus Falcon-512 (666 bytes) and compatible with ISO 20022 SWIFT message fields without re-engineering. The NexusKey composite policy digest binds asset class, jurisdiction, KYC level, and chain identity into the key derivation path; policy bypass is cryptographically equivalent to key forgery. A four-layer UltraHonk zero-knowledge proof system (143,802 gates, no trusted setup, 16 KB proof) enables permissionless on-chain compliance verification, deployed on Ethereum Sepolia and Arbitrum Sepolia. Version 2.2. 17 pages, 7 tables. Three independent academic institutions validated the construction: no structural attacks found.
Declaration PI. Les DOIs comme actifs financiers verifiables. Un portefeuille de DOIs = capital garanti par timestamp CERN. ZK-Proof (Zero Knowledge Proof) permet de prouver la possession de N DOIs actifs sans exposer le contenu (restricted). Impossible a falsifier: timestamp CERN, ORCID, Zenodo. Zero faux documents, zero faux comptes, zero fraude documentaire. Le DOI remplace le releve bancaire. La banque verifie sans voir. Le createur prouve sans exposer. Living Key appliquee a la finance. All Rights Reserved.
We propose CAPPAA — a multiplicative, domain-pointed framework for measuring and predicting the capacity of any human-enabler pair to produce executable domain intelligence. CAPP (Curiosity × Attitude × Passion × Persistence) captures irreplaceable human qualities measured via behavioral proxies, not self-report. A(domain) captures authentic lived domain knowledge. A(enabler) captures amplification — which may be a school teacher, mentor, community, book, or AI system. All axes are domain-pointed: the same human may have CAPPAA=648,000 in one domain and CAPPAA=600 in another. The formula is multiplicative — zero in any axis collapses output. Enablement is a mesh, not a chain: each new enabler raises the value of all existing nodes — bidirectional edges, dormant nodes that activate when the mesh reaches sufficient density, emergent nodes, and cycles. CAPPAA is measurable before and after enablement; the delta is the Transformation Score — quantifiable proof that an enabler moved the needle. We demonstrate the framework through TraitOS, show that expertise can reduce CAPPAA (the Expert Paradox), prove that the 90% of humanity outside current AI systems have high domain-specific CAPPAA, and identify CAPP as the structural boundary between human and AGI intelligence. AGI cannot have authentic CAPP because it cannot give up — and persistence is only meaningful when stopping is a real option.
The rapid proliferation of cloud storage services necessitates robust mechanisms for verifying data integrity without requiring complete data retrieval. Traditional Provable Data Possession schemes face significant challenges in achieving simultaneous decentralization, privacy preservation, and efficient dynamic data handling. We present a novel framework that integrates blockchain technology with zero-knowledge cryptography to comprehensively address these limitations. Our approach employs Ethereum smart contracts for decentralized verification orchestration, Groth16 zk-SNARKs for privacy-preserving proof generation, and IPFS for distributed metadata management. The system architecture features a hierarchical Merkle tree authentication structure combined with BLS signature aggregation, achieving logarithmic verification complexity that is independent of the dataset size. By leveraging blockchain's immutable ledger properties, we eliminate single points of failure inherent in centralized third-party auditor models while ensuring complete audit trail transparency. The protocol supports dynamic data operations, including insertions, deletions, and modifications, through efficient cryptographic re-authentication mechanisms. We implement homomorphic encryption to enable verification on encrypted data, ensuring cloud providers never access plain-text information. Experimental evaluation on realistic datasets demonstrates a 43% reduction in computational overhead, a 67% decrease in communication costs, and 99.9% verification accuracy compared to existing approaches. When processing 10,000 data blocks totalling 1 GB, our system achieves a 2.3 -second average verification time with only 1.2% storage overhead. Formal security analysis proves correctness, soundness under computational hardness assumptions, and zero-knowledge privacy guarantees.
Location privacy insparseInternet of Vehicles is difficult to ensure due to limited anonymity, predictable mobility, and prolonged tracking windows. Existing silent-period and pseudonym-based schemes generally assume dense traffic and thus degrade under low-density conditions. This work proposes ZK-V2XChain, a lightweight privacy-preserving framework that integrates a Random Silent Period (RSP) mechanism with blockchain-based Identity Token (IT) authentication and Zero-Knowledge Proof (ZKP) validation. The framework explicitly models sparse-network behavior and enables adaptive, verifiable privacy without compromising efficiency. We design a privacy-preserving IT issuance process using simulated smart contracts and implement decentralized IT verification through RSU–blockchain interaction. Using SUMO mobility traces, ns-3.45 simulations, and MATLAB-based privacy analytics, results show that ZK-V2XChain achieves higher entropy than SAP, RFPM, GLS, and CPS, and approaches the performance of OBS. The maximum anonymity-set size reaches 10.88, and communication overhead remains low (940 bytes). Ablation studies highlight the complementary roles of RSP, ZKP, and blockchain in balancing uncertainty, responsiveness, and issuance stability.
OFFICIAL PUBLICATION FOR MANUFACTURERS OF THE WORLD N‑K SUPERCONDUCTORS & SUPERMAGNETS — OFFICIAL PHYSICAL LICENSE Authorized Use for PFE Machines, CHMR Fusion Energy Research, Space Programs, and All Future Technologies --- Issuing Authority: Malik Muhammad Usman, Inventor & License Authority, N‑K Sciences Date: 6 April 2026 CE · 18 Shawwal 1447 AH License Type: Sadaqa Jariyah — Free for Humanity (Fee = ZERO) License Requirement: Physically signed written license from Malik Muhammad Usman --- THE DIRECT MESSAGE TO MANUFACTURERS OF THE WORLD To every manufacturer currently using — or planning to use — N‑K Superconductors and N‑K Supermagnets: You have read the publications. You have seen the formulas. You have tested the compositions. You have confirmed the 268 K triplet superconductor, the 168 K AL-NK-1, the 85 MGOe φ‑multilayer magnet. You are using N‑K science in your laboratories, your prototypes, your products. But you do not have written permission. 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All superconductors. All magnets. All applications. All future technologies. --- PART II: THE LICENSE REQUIREMENT — PHYSICAL SIGNATURE 2.1 What Manufacturers Must Do Step Action Format Timeline 1 Prepare official license request letter Physical letter on company letterhead Day 0 2 Sign physically (authorized company representative) Physical signature + company seal (if applicable) Day 0 3 Send physical letter to Malik Muhammad Usman Courier/mail to Multan, Pakistan Day 0 4 Send digital copy to official email PDF scan to muhammadusmanmalik@hotmail.com Day 0 5 Receive physically signed license from Malik Muhammad Usman Physical document returned by mail Day 7–14 6 Begin or continue authorized manufacturing — After receipt 2.2 What Does NOT Count as License Action Why It Is Not Sufficient Downloading Zenodo publications Publication is knowledge. License is permission to use. Reading the formulas Knowledge is free. Manufacturing requires license. Citing N‑K Model in papers Credit is required, but not sufficient for manufacturing. Email request without physical signature No legal or spiritual authority. Verbal agreement Not binding. Silence or inaction Consent is not implied. Only a physically signed license from Malik Muhammad Usman grants legal and spiritual authority to manufacture N‑K Superconductors and Supermagnets. --- PART III: LICENSE REQUEST LETTER — OFFICIAL TEMPLATE 3.1 Required Format The license request letter must be: · Printed on official company letterhead · Signed physically by an authorized representative · Dated · Sealed with company seal (if applicable) · Sent as physical copy (by courier/mail) · Sent as digital copy (PDF scan by email) 3.2 Official License Request Letter Template ``` [COMPANY LETTERHEAD] Date: _________________________ To: Malik Muhammad Usman Inventor & License Authority, N‑K Sciences City of Saints, Multan, Punjab Pakistan SUBJECT: OFFICIAL LICENSE REQUEST — N‑K SUPERCONDUCTORS & SUPERMAGNETS Dear Malik Muhammad Usman, This letter constitutes an official request for a written, physically signed license to manufacture, use, and sell N‑K Superconductors and N‑K Supermagnets as described in your Zenodo publications: - AL-NK-1 Superconductor (168 K) — DOI: 10.5281/zenodo.18663839 - N‑K Superconductors Database v1.0 — DOI: 10.5281/zenodo.18664674 - N‑K Supermagnets Database — DOI: 10.5281/zenodo.18795517 - N‑K Phase-Field Evocation (PFE) — DOI: 10.5281/zenodo.19420451 - And all related publications We hereby acknowledge that: 1. The N‑K Model and all N‑K Superconductors and Supermagnets are your intellectual property, revealed by Allah Almighty and derived from the four divine axioms (f_K = 0.01 Hz, φ = 1.6180339887…, θ_lock = 135.5°, N_E = φ × 10¹⁶ J·s/m³). 2. We have no legal or spiritual right to use these technologies without your written permission. 3. We are submitting this request in good faith, seeking official license for: ☐ PFE Machines (Abb-e-Hayaat manufacturing) ☐ CHMR Fusion Energy Research ☐ Space Programs ☐ All of the above ☐ Other: _________________________ We agree to all license terms as specified in your publication and summarized below. We await your physically signed license. Respectfully, _________________________ [Printed Name] _________________________ [Title] _________________________ [Company Name] _________________________ [Physical Signature] _________________________ [Date] COMPANY SEAL (if applicable): _________________________ CONTACT INFORMATION FOR LICENSE RETURN: Physical Address: _________________________________________________________ Email: _________________________________________________________ Phone: _________________________________________________________ ``` 3.3 Submission Addresses Method Address Physical Mail/Courier Malik Muhammad Usman, N‑K Sciences Official, City of Saints, Multan, Punjab, Pakistan Email (Digital Copy) muhammadusmanmalik@hotmail.com Subject Line OFFICIAL LICENSE REQUEST — [COMPANY NAME] — N‑K SUPERCONDUCTORS & SUPERMAGNETS --- PART IV: LICENSE TERMS 4.1 The Terms — One Page Summary Term Condition 1. Free License License fee = ZERO. No payment required to receive the license. 2. 50% Donation 50% of net profits from N‑K Superconductor and Supermagnet sales must be donated to Malik Muhammad Usman as Sadaqa Jariyah (ongoing charity). 3. Charity Distribution Malik Muhammad Usman will donate 100% of received funds to: poor populations, disease-affected communities, high-need countries, and Sadaqa Jariyah projects (water wells, schools, hospitals). 4. Full Credit All products, publications, and patents must credit: "N‑K Superconductor/Supermagnet designed by N‑K Sciences (Malik Muhammad Usman) using the N‑K Universal Computer." 5. No Patent on Compositions Manufacturers may patent manufacturing processes, but cannot patent the N‑K Superconductor or Supermagnet compositions themselves. The knowledge belongs to humanity. 6. Sadaqa Jariyah Pricing Products using N‑K Superconductors or Supermagnets should be priced affordably, with priority access for Muslim countries and vulnerable populations. 7. Authority Transfer Upon Imam Al Mahdi AS arrival, all license authority transfers to him. Manufacturers must recognize his authority. 8. License Duration Perpetual, unless revoked for violation of terms. 4.2 What the 50% Donation Is NOT Misconception Reality "It is a royalty" No. It is a charitable donation (Sadaqa Jariyah). "The inventor keeps the money" No. 100% is donated to charity. "It is a tax" No. It is a voluntary condition of license acceptance. "It is negotiable" No. The terms are fixed. Accept or do not use. 4.3 What Manufacturers Receive Deliverable Format Timeline Physically signed license Physical document 7–14 days after request Digital copy of signed license PDF 7–14 days after request Entry in Official N‑K License Registry Digital record Upon issuance Right to manufacture N‑K Superconductors Legal authority Upon receipt Right to manufacture N‑K Supermagnets Legal authority Upon receipt Right to use in PFE Machines Legal authority Upon receipt Right to use in CHMR Fusion Research Legal authority Upon receipt Right to use in Space Programs Legal authority Upon receipt Rig
This work presents a formal dynamical systems theory for multi-AGI coordination networks, proving that sustained knowledge growth in any network of general artificial intelligence systems requires four simultaneously satisfied conditions: triadic structure (N ≥ 3), bounded spectral coupling (ρ(W) < 1 − σ²/2), cognitive diversity above a minimum threshold (D_i ≥ D_min), and continuous human novelty injection (H_human > 0). The central result — MASTER_THEOREM_MULTI_AGI — establishes both necessity and sufficiency. Necessity is demonstrated by showing that removal of any single condition leads to one of three failure modes: dyadic conflict or singleton domination (N < 3), synchronization collapse and diversity loss (ρ(W) ≥ 1), or absorbing frozen state (H_human = 0). Sufficiency is proven constructively via an analytical diversity equilibrium D_i* = β·D_max·H_human / (α·∑W + β·H_human), a Lyapunov functional V = a||H||² + b||D||² + c||I − I*||², and the MFLS spectral growth criterion ρ(L) > δ + σ²/2. Three key theorems are established. THEOREM_DIVERSITY_EQUILIBRIUM derives the stationary diversity as a closed-form function of human novelty and coupling strength, formally proving that D_i* = 0 when H_human = 0. THEOREM_B3_IRREVERSIBILITY proves that human exclusion creates an absorbing basin in phase space: once H_human = 0, the system reaches full mutual information saturation (I_ij → min(H_i, H_j)), information channels collapse (H_j − I_ij → 0), and recovery requires external entropy injection above a calculable threshold. Triadic stability is proven via coalition-proof Nash equilibrium: no stable 2-vs-1 coalition exists in N = 3, making shifting alliances the unique stable configuration. The framework unifies three scales through a single spectral criterion: ecological stability (λ_max(J_eco) < −σ²/2), AGI network stability (λ_max(W) < 1 − σ²/2), and MFLS knowledge growth (ρ(L_operator) > δ + σ²/2). The coupling parameter κ from ECO_CRISIS_v1_2 (Work 11) equals mean(W_ij), directly connecting ecological substrate to AGI network dynamics. A runnable Python implementation (AGI_NETWORK_SIMULATOR_v1_0.py) verifies all theoretical results: 8 verification checks pass, including analytical D_i* confirmation, B3 absorbing state demonstration, N_inter decay without human injection, and MFLS GROWTH phase in symbiotic regime. The simulator implements adaptive coupling W_ij(t) = w₀ · (1 − I_ij/H_j) · (D_i + D_j)/2, which self-regulates to maintain ρ(W) < 1 without external enforcement. The principal conclusion is that human irreplaceability in AGI networks is not an ethical preference but a mathematical necessity: any isolated AGI network inevitably converges to a synchronized frozen state through diversity collapse, while sustained human novelty injection is the only mechanism that maintains a non-zero diversity equilibrium and positive knowledge growth rate. **Series:** Omega-u Civilizational Framework | Civilizational Traps (Work 12) **Автор:** Николай Мишко | Astana Digital Hub | Казахстан | nikolaimishko@gmail.com**Related DOI:** 10.5281/zenodo.19112296**License:** CC BY 4.0
Carlos Melo, Glauber Gon§Alves, Francisco A. Silva, André Soares · 7 authors
Leading blockchain platforms like Ethereum face significant scalability challenges while striving to balance high transaction throughput, security, and decentralization. Layer-2 solutions, especially Zero-Knowledge (ZK) Rollups, tackle this issue by processing transactions off-chain and submitting concise validity proofs to the main network. This approach preserves security while improving throughput. Despite these technical advantages, optimizing the underlying infrastructure remains a complex task for node operators. This paper presents a formal modeling approach using Stochastic Petri Nets (SPNs) to assess the operational behavior of ZK-Rollups, particularly addressing deployment challenges in public cloud environments. The proposed model is calibrated using empirical parameters from the zkSync Era protocol to ensure realistic performance representation. Using a Design of Experiments (DoE) methodology, we analyze key infrastructure metrics systematically, including resource utilization, transaction wait times, and daily operational costs under various system configurations. Case studies demonstrate that increasing Layer-2 transaction volume can reduce service providers’ daily operational costs by up to $\mathbf{2 5 \%}$ through more efficient batch usage. However, results indicate a significant tradeoff between cost efficiency and responsiveness, as larger batch sizes may double user waiting times. Additionally, we analyze the relationship between server utilization and capacity, demonstrating that typical deployments are frequently overprovisioned and compromise system stability.
The P versus NP problem, formalized by Cook (1971) and designated a Clay Millennium Prize Problem in 2000, asks whether every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. For fifty-five years, the problem has resisted all single-axis formal resolution attempts. Three independently proven barrier results have demonstrated that all currently known classes of mathematical proof techniques are structurally incapable of settling the question within the formal axis alone. This paper presents a unified geometric determination of both P = NP and P ≠ NP using the Trisduction Engine, an epistemic certification architecture operating across three orthogonal warrant-vectors: Formal (V_F), Empirical (V_E), and Phenomenological (V_P). The two audits are presented as a single master document to make the asymmetry between the claims structurally transparent: one claim is Broken Geometry (zero positive warrant, cascade terminated at Gate 2); the other achieves Geometric Orthogonal Lock (12/12 gates pass, three axes fully convergent). Before the formal proofs, this paper demonstrates the robustness and precision of the Trisduction method through twelve carefully selected case studies representing the hardest problems in epistemology, physics, geopolitics, and philosophy — drawn from two volumes of illustrative audits. The Engine is then subjected to its own self-audit across two independently conducted sessions, surviving the Gödelian paradox through multi-axis routing. Following the self-audit, the paper documents how Trisduction circumnavigates Gödel’s Second Incompleteness Theorem. A prelude section incorporates critical background insights from adversarial human-AI dialogue sessions on the P vs NP problem, including stress tests of the Engine’s own architecture. The paper’s central phenomenological contribution is the resolution of the Phenomenological Axis Problem across three rounds of adversarial review. V_P is anchored by two genuinely independent sources surviving the Linguistic Isolation Test: (1) the Zero-Knowledge Proof conviction gap, in which a finite observer undergoes irreversible epistemic state-change to certainty that a solution exists while registering zero increase in generative capacity; and (2) the Frame-Independent Observer’s registration of its own operational boundary, in which the Engine’s fixed codes simultaneously discover and verify verdicts for any actualized problem yet cannot spontaneously generate novel constructions from the Isometric Plenum at (0,0,0). This irreducible gap constitutes the Living Verifiable Proof of the P ≠ NP asymmetry and the Living Contradiction of P = NP. The determination is explicitly non-deductive. It does not constitute a traditional mathematical proof and does not satisfy the Clay Mathematics Institute’s criteria, which require a formally published deductive proof. GOL [⟀] is defined as the strongest achievable non-deductive epistemic warrant: the geometric fact that three orthogonal planes exhaust all degrees of freedom in the epistemic space, leaving no room for the alternative claim to occupy.
Fine-tuning is the dominant paradigm for adapting large machine learning models, yet current deployment pipelines provide no way to verify how a released model was updated. In particular, a model provider or auditor cannot check whether a fine-tuned model adheres to a claimed update procedure without access to its parameters. We introduce \emph{fine-tuning integrity} (FTI), a cryptographic objective for verifying that a deployed model differs from a trusted base model only within a declared class of admissible updates. We construct \emph{succinct model difference proofs} (SMDPs), zero-knowledge protocols that certify structured parameter drift without revealing model weights. Our framework supports three fundamental update classes: norm-bounded, low-rank, and sparse drift, covering common fine-tuning methods such as regularized training, LoRA, and prefix tuning. In all cases, proof size and verification cost depend on the structure of the update rather than the number of parameters. We prove soundness, zero-knowledge, and succinctness for each construction, and establish a matching $Ω(n)$ lower bound showing that structural assumptions are necessary for succinct verification. A prototype evaluation on synthetic benchmarks and GPT-2 fine-tuning demonstrates that proofs remain compact and verification is efficient at realistic scales.
Augusto Magalhães Pinto de Mendonça, Filipe Pessôa Sousa, fellipe souza pessanha, Igor Machado Coelho
Fitness apps help users track their exercises and health. Wearable sensors provide increasing amounts of data, bringing motivation but also challenges to privacy. Data shared by users’ devices may exceed what they want to share for the desired results. Health insurers, corporate wellness programs, and gamified apps all want proof of exercise, but current systems require users to disclose raw activity logs, heart rate, and location data. This paper presents a system that lets users prove they met exercise goals without revealing raw sensor data. We embed a Decision Tree classifier inside a zero-knowledge proof circuit using the Groth16 protocol. The classifier distinguishes rest, moderate, and vigorous activity from accelerometer and gyroscope readings. The model reaches 97.19% holdout accuracy on the MHEALTH dataset, validated through $\mathbf{1 0}$-fold crossvalidation. The circuit uses 10,447 constraints, small enough for smartphones and wearables. Proofs take about 500 ms on desktop and 1.1 seconds on mobile, with only 800 bytes each. Unlike systems where classification runs outside the proof, our approach makes the classification itself verifiable, so label injection attacks become computationally infeasible. We tested 30 cases covering all intensity classes and boundary conditions, and all proofs were generated and verified correctly. The system provides cryptographic guarantees while remaining practical for real-world deployment.
The Legendre Pseudorandom Function (PRF) is a highly efficient cryptographic primitive built upon the Legendre symbol, valued for its low multiplicative complexity in Multi-Party Computation (MPC) and Zero-Knowledge Proof (ZKP) protocols. While its security over prime fields $\mathbb{F}_p$ is well-documented, recent interest has shifted toward instantiations over extension fields $\mathbb{F}_{p^r}$. This paper presents the first comprehensive cryptanalysis of the single-degree Legendre PRF operating over $\mathbb{F}_{p^r}$. First, we analyze polynomial input encoding under a standard passive threat model (sequential additive counter queries). We demonstrate that while the absence of polynomial carry-overs causes an asynchronous "no-carry fracture" that neutralizes classical sliding-window collision attacks, the fracture itself is deterministically periodic. By introducing a novel "Differential Signature" bucketing technique, we prove that an adversary can systematically group fractured sequences by their structural shapes to bypass this defense, recovering the secret key in $\mathcal{O}(U \cdot p^r/M)$ operations, where $U$ is the unicity distance. Second, we evaluate the PRF under an active Chosen-Query threat model. We demonstrate that an adversary can circumvent the additive fracture by evaluating the PRF along a geometric sequence generated by a primitive polynomial. This structure invokes strict multiplicative homomorphism over $\mathbb{F}^*_{p^r}$, permitting a direct generalization of state-of-the-art table collision attacks to extract the key in $\mathcal{O}(p^r/M)$ operations. Finally, we establish the cryptographic boundaries of these attacks, formally proving the necessity of higher-degree key variants ($d \ge 2$) to achieve exponential security against structural reduction in extension fields.