This research introduces a novel Unified Quantum-Resilient Blockchain-Zero Knowledge Proofs Privacy Authentication Framework (QBC-ZKPAF) aimed at enhancing security in IoT environments. The system combines post-quantum cryptography, blockchain technology, and Zero Trust Architecture (ZTA) to provide secure communication, access management, and privacy-preserving authentication. It uses a Deep Q-Network Multi-Factor safe Key (DQN-MFSK) for dynamic key selection, a hybrid Reinforcement-Lattice Blockchain Key Generation for quantum-resilient key creation, and Zero-Knowledge Proofs for privacy-preserving signatures to ensure a safe Internet of Things environment. Data privacy, secrecy, auditability, traceability, and resistance to changing threats, such as quantum attacks, are all guaranteed by this architecture. Transparency and thorough post-event audit trails are supported by the blockchain ledger's immutability, which records all access attempts, data exchanges, and device interactions in an unchangeable way. Through a tracing key kept on the audit server within the Zero Trust Architecture, the architecture allows accurate source tracing in the event of suspicious activity or breaches. QBC-ZKPAF provides strong security and privacy solutions for Internet of Things networks by adopting multi-factor authentication and decentralizing identity management. The framework's efficacy is confirmed by experimental results, which show 98% privacy preservation, 700 TPS throughput, 0.98 quantum resilience, and 96% access control effectiveness, making it ideal for contemporary blockchain and IoT applications.
The χ‑spectral framework developed in this work establishes a unified operator‑geometric foundation for physical law, integrating quantum measurement, modular state reduction, spectral geometry, and gravitational curvature into a single mathematically coherent structure. Physical measurement is formulated as an intrinsic operator‑spectral transition generated by the bounded self‑adjoint observable M_chi(k) = Phi_chi(k) + B_chi(k) + R_chi(k), which combines phase geometry, boundary tension, and χ‑spectral curvature into a non‑singular measurement mechanism. Probability amplitudes P_n(k) = |_chi|^2 are derived directly from the χ‑inner product, demonstrating that Born’s rule emerges from arithmetic geometry rather than axiomatic postulates. A central result of the χ‑spectral framework is the rigorous proof of compatibility between ZEBTS‑SUPER gravitational dynamics and quantum mechanics. Gravitational curvature R_chi(k) enters the measurement operator M_chi(k) as a bounded geometric observable, ensuring ultraviolet stability, finite expectation values, and strict unitarity across all scale layers. Collapse dynamics are formulated as bounded modular projections, guaranteeing non‑perturbative, divergence‑free state reduction. Decoherence is shown to be a structural spectral gradient D_chi(k) = M_chi(k+1) – M_chi(k), providing a deterministic geometric mechanism for coherence loss without environmental reservoirs. The scale‑layer commutator C_chi(k) = [M_chi(k+1), M_chi(k)] encodes contextuality and order‑dependence as structural consequences of χ‑operator geometry. Together, these results demonstrate that quantum dynamics, gravitational curvature, measurement theory, and modular collapse are fully compatible and mutually reinforcing within the χ‑spectral operator framework. The theory achieves conceptual and mathematical closure: all physical observables remain bounded, all transitions remain unitary, and quantum–gravitational consistency is established as a direct consequence of χ‑spectral geometry.
Quantum Cellular Theory of Space: A Testable Cosmological Model of a Dividing Causal Network Author: Martin JámborState of knowledge captured as of: 9 August 2026 Quantum Cellular Theory of Space is a research hypothesis in which space is not a fundamental continuous stage but the macroscopic manifestation of a discrete local network. In this picture, observed spacetime, matter, and fields would be emergent descriptions of the collective behaviour of its cells. The theory asks whether one physical substrate can explain the common origin of cosmic expansion, accelerated expansion, the formation of matter, an unseen clustering component, a relativistic relic, the propagation of light, and physical irreversibility. This is not a biological model. The terms cell, fuel, ash, steam, and scar denote distinct roles in the energy and state description of the network. The hypothesis is not yet an experimentally confirmed replacement for general relativity, quantum field theory, the Standard Model, or standard cosmology. In domains where those theories are validated, it must reproduce their successful laws and observational bounds. Its contribution would lie in deriving their common microscopic origin or predicting a new measurable deviation. Physical picture The basic working idea is that cells of space can locally rearrange or divide. Macroscopic expansion would then be not motion into an external void but a change in the number and arrangement of the degrees of freedom from which space emerges. The energy component that enables rearrangement is called fuel. In the effective cosmological description it has pressure close to vacuum pressure, and it can therefore carry part of the physical role attributed to dark energy and accelerated expansion. Energy and momentum must remain conserved when fuel is processed. The model investigates three possible output channels: matter as stable or long-lived excitations; ash as a nonrelativistic gravitationally clustering residue that may take over part of the role of dark matter; steam as a relativistic or freely propagating share of the energy that may leave an imprint in the early radiation or thermal background. It has not yet been determined which channels actually exist, what their fractions are, or whether they arise in parallel, sequentially, or through mixed branching. The answer must come from a common local law and observations, not from a verbal choice of mechanism. A scar is a candidate persistent change in the internal state of a cell or its links after a physical event. It is intended to carry local memory and may provide a basis for the arrow of time. It has not yet been shown whether the same mechanism can also explain a single outcome of a quantum measurement and the Born rule. Light is investigated as a wave or excitation of the common substrate. If light, matter, clocks, and measuring rods are all realizations of the same network and share one local light cone, all inertial observers may measure the same limiting c. This objective still requires derivation of the photon sector, a common metric, boost symmetry, absence of impermissible birefringence, and the equivalence principle. Central mathematical bridge The global mean-field effective overhead of rearrangement is written as delta = 1 / (<k> + C) where <k> is the mean number of face neighbours in the reference Poisson–Delaunay network and C is the working internal capacity of a cell. For <k> = 48 pi^2 / 35 + 2 ≈ 15.535 C = 28 this gives delta ≈ 0.02297 This overhead is connected to the effective equation of state of fuel: p_f = (-1 + delta) rho_f w_f = p_f / rho_f = -1 + delta The fluid form is the same as in modern cosmology; what differs is the proposed origin of w_f+1 in the geometry and capacity of the network. The value C=28 is read as the number of bosonic states in the restored phase of the Standard Model, but this identification does not yet have an independent microscopic derivation. The arithmetic 16_gluon + 8_EW + 4_Higgs = 28 counts the four real Higgs directions as already including the three directions that become Goldstone modes; it does not add them a second time. It remains open why cell capacity should count precisely bosonic and not fermionic degrees of freedom. Because the value 28 was chosen before this link was fully derived, its success in downstream calculations is not independent confirmation of the theory. If the local degree of the network varies, the overhead of one cell would have the form 1/(k+C) and its average would be <1/(k+C)>. Jensen's inequality then gives <1/(k+C)> >= 1/(<k>+C) with a strict inequality when the degree has nonzero variance. Without the distribution P(k), the value 0.02297 is therefore the mean-field value and a lower bound for this locally averaged branch, not a calculated local overhead. Cosmological background For x=ln a, the effective homogeneous model uses the densities of fuel rho_f, ash rho_c, baryons rho_b, and radiation rho_r: d rho_f/dx = -3 delta rho_f - lambda (H0/H) rho_f d rho_c/dx = -3 rho_c + lambda (H0/H) rho_f d rho_b/dx = -3 rho_b d rho_r/dx = -4 rho_r H^2 = (8 pi G / 3) rho_total Transfer between fuel and ash has opposite sources in the homogeneous description: Q_f = -Q_c = -lambda H0 rho_f The total background energy ledger is therefore conserved. lambda describes a family of effective transfer rates, not a derived constant of nature. The calculations use the data-calibrated reference point lambda=0.15; it is neither an independent prediction nor the only allowed value. The separately examined points 0.10 and 0.15 do not establish that the whole interval between them is allowed. A continuous physically admissible range must still pass stability, the null limit, and a joint comparison with BBN, CMB, BAO, structure growth, and lensing. Data used to select or normalize the reference point cannot be counted again as its independent confirmation. One homogeneous universe must have one expansion history H(a), independent of the Fourier mode later used to describe a perturbation. The early dimensionless perturbation coordinate z = k a / [H0 sqrt(Omega_r0)] must therefore not enter the background as a physical global scale. For p=4-3 delta, the mode amplitude is written as Phi(k) = A_f [H0 sqrt(Omega_r0) / k]^p which yields the homogeneous fuel term Phi(k) z^p = A_f a^p For the inputs used here, A_f=7809.270101963506. This is a conditional normalization of the specified background, not a new universal constant or a separate fit to observations. Linear perturbations and stability In a simplified nine-variable model with effective perfect radiation, the complete three-mode regular basis, kinetic and gradient signs, characteristic speeds, null limit, static Einstein constraints, behaviour at q={30,300,1000}, and numerical convergence were tested. No forbidden high-frequency growing instability was found within this scope. The result applies only to the stated model. It is not a microscopic no-ghost theorem, a proof of global hyperbolicity, or a complete evolution of photons, neutrinos, baryons, fuel, and ash. Static Einstein constraints alone do not prove their dynamical Bianchi propagation. The scalar cosine-Laplacian operator is exactly even in wave number, so its expansion contains no odd linear term. This property is necessary for a viable discrete scalar sector, but it does not by itself derive full Lorentz invariance, photon dispersion, or the equivalence principle. Quantitative consequences and viability conditions The following values are commitments of the specifically stated formulations. Agreement keeps them viable but does not confirm the cellular mechanism. A robust disagreement can exclude them only after a complete link between the model and the measured quantity, including uncertainties, covariances, and systematics. Quantity or phenomenon Value or physical condition Limit of interpretation extra relativistic relic Delta N_eff=0.0535, hence N_eff≈3.10 Applies to an early-decoupled two-polarisation thermal formulation; the local source, branching, exit, and reheating are not derived. scalar tilt n_s=0.9656 +/- 0.0016 Target of the exact delta/m=1/2 mechanism; the width is neither a new posterior nor an uncertainty derived from the formula. tensor-to-scalar ratio sharp target r<1e-10; broader practical marker r>=1e-3 The complete tensor operator, source, normalization, and B-mode observable map are missing. Hubble constant H0≈66.4 +/- 0.4 km/s/Mpc Condition of the frozen background, not a new global fit or a solution to the Hubble tension. clustering S8≈0.86–0.87 Condition of the simplified growth formulation, not a full Einstein–Boltzmann result. effective CPL description w0=-0.919, wa=-0.612 Joint target of the accounting reconstruction; it is not a microphysical equation of state for fuel. sterile ash no confirmed nongravitational signal A numerical experimental window can be defined only after deriving the mass, spin, abundance, lifetime, and couplings of ash. exact n_s-w relation no active claim The exact formula is not part of the current theory. time drift of delta delta=0.02297 is only a constant benchmark The function delta(a) or delta(x) and a measurable drift window have not been derived. scalar dispersion the odd linear coefficient is exactly zero The result applies only to the stated scalar operator. thermal steam or wave background T≈0.905 K, peak near 53 GHz This is the same thermal commitment as Delta N_eff; identification of the relic with gravitons has not been derived. The thermal result uses the standard entropy arithmetic for an early-decoupled bosonic relic: Delta N_eff = (4/7) g_x [10.75/g_*s,dec]^(4/3) with g_x=2 and g_*s,dec=106.75. The cellular hypothesis adds a possible causal origin of steam in the processing of vacuum fuel, but it does not yet determine what fraction of energy enters this channel or how the relic survives unt
W. C. Yang, J. F. Qiao, J. F. Hu, Jie Wang · 5 authors
This study presents a multi-level verification system for secure communication protocols in energy billing infrastructures. The proposed framework integrates device attestation, network integrity verification, privacy-preserving aggregation, billing validation, and immutable auditing to address security vulnerabilities across Advanced Metering Infrastructure (AMI) communication chains. A Hybrid Secure-Efficient Protocol (HSEP) combining elliptic curve cryptography, homomorphic encryption, and zero-knowledge proofs is developed to provide secure authentication, privacy protection, and verifiable data integrity while maintaining low computational overhead. Experimental evaluation using a large-scale AMI testbed demonstrates that the proposed system significantly improves tampering detection capability, achieving an intrusion detection AUC of 0.94 while maintaining an average energy consumption of 1.55 J per transaction and acceptable communication latency for large-scale deployment. The architecture exhibits strong scalability, robustness, and rapid dispute-resolution performance under multiple attack scenarios. The proposed framework is particularly applicable to wireless smart metering networks and antenna-enabled AMI communication infrastructures, where reliable data transmission, secure protocol verification, and resilience against communication-layer attacks are essential for trustworthy energy billing and grid operation. This work provides an effective engineering solution for secure, privacy-preserving, and verifiable communication in modern intelligent energy systems.
Background Traditional Chinese Medicine (TCM) rheumatology presents unique challenges for AI-assisted clinical decision support, as the diagnostic process relies heavily on tacit knowledge and individualized reasoning. While Large Language Models (LLMs) have shown promise in medical applications, they remain limited by hallucination risks and inability to replicate expert TCM reasoning. Retrieval-Augmented Generation (RAG) offers a potential solution, yet its application to complex TCM dialectical reasoning remains underexplored. Methods We developed TCM-CoT-RAG, a hybrid framework combining RAG with Chain-of-Thought (CoT) prompting, grounded in 1,700 expert-curated clinical cases (1,600 for RAG retrieval; 100 for evaluation, including 50 for blinded expert review by three senior TCM rheumatologists). Deployed on Alibaba Cloud, the five system leverages state-of-the-art LLMs (DeepSeek-V3, Qwen3-235B) under a human-in-the-loop paradigm. We designed a dual-tier evaluation: (1) Objective extraction tasks (Task 1–2) quantified using F1-scores; (2) Generative tasks (Task 3–5) assessed using BERTScore. Two senior TCM rheumatologists (≥15 years clinical experience) blindly assessed model outputs, and a senior chief expert quantified consistency between model predictions and ground truth (GT). Comprehensive ablation studies (S1-S4, S-Skip) isolated the contributions of each CoT module. Results TCM-CoT-RAG substantially improved diagnostic accuracy across five LLMs. DeepSeek-V3 with full-chain CoT-RAG achieved Entity F1 of 44.89% (+16.45% over baseline) and Formula F1 of 32.13% (+8.74% over baseline), with BERTScore of 0.81 indicating strong semantic alignment with expert reasoning. Ablation confirmed that the complete CoT pipeline was essential—removing any reasoning module caused performance collapse below the zero-shot baseline. Two independent experts validated clinical utility (Cohen’s κ &gt; 0.7). DeepSeek-V3 achieved the highest ground-truth consistency at 81.6%, and consistency metrics were quantified by the third expert holding the most senior professional title. Conclusion This proof-of-concept framework demonstrates the potential of RAG-enhanced CoT reasoning to improve diagnostic consistency in TCM, objectifying the Symptom-Diagnosis-Prescription pipeline. It is important to note that this system is designed as an AI-assisted clinical decision-support tool. All recommendations require validation by qualified TCM practitioners before clinical application.
Model identity verification is only as trustworthy as the reference against which identity is resolved. A system may correctly establish that a model running now corresponds to an enrolled reference while remaining unable to establish that the reference itself was the authentic release of the named publisher. This technical note separates those two claims as identity continuity and enrollment provenance. It formalizes the poisoned-enrollment failure, in which an inauthentic artifact is enrolled under a legitimate model name and subsequently passes continuity verification correctly. The failure is therefore not a false acceptance by the measurement system, but an upstream identity-binding failure. The note shows that this boundary is shared across artifact signing, behavioral fingerprinting, reference-anchored activation auditing, and structural identity measurement, and relates the problem to established software supply-chain trust models. It proposes E0–E4 enrollment assurance profiles, distinguishes provenance profile from current attribution state, and describes remediation through revocation and re-establishment of provenance without discarding historical continuity evidence. No new measurement result is reported. The contribution is an evidence boundary, threat-model construction, assurance vocabulary, and remediation model for model identity verification. 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) 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) Technical Note: Artifact Identity Is Not Runtime Identity — Trustfall Lite and the Boundary of File-Level Model Verification (DOI: 10.5281/zenodo.20019127) Technical Note:: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098) 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).
Abstract This orientation presents the architecture, results, boundaries, and reading paths of the Identity-Persistence Program, a research program on the structural conditions under which bounded evaluators can make reproducible judgments of identity, persistence, admissibility, and verification under declared regimes. The program’s foundational layer establishes three forcing results: structural floors for coherent identity claims, admissible transformation, and sufficient regime specification. These are bracketed below by the requirement that cumulative inquiry possess a stable same/not-same criterion and above by an identification ceiling: within the finite declared class, admissible evidence identifies only up to the declared quotient. The guide then maps the program’s post-floor structural theory. For a declared question family, maximal structure-compatible safe congruences yield canonical demand-relative normal forms and a theory of regime equivalence and refinement. Recurrence is classified in the one-degree homogeneous case; symmetry reduction is separated from operable quotient structure through an independent-redescription compatibility criterion; nested regimes compose through backward demand propagation and forward certificate compression; and reconstructibility, blocking cuts, and verification complexity are characterized at the mechanization layer. Condensation Dynamics adds a finite dynamical theory in which safe quotienting has an exact potential and path-independent total budget, interaction defects measure noncanonical allocation, serial nesting obeys a no-free-acceleration law, and structural conditions for zero defect are identified. The orientation also distinguishes these theorem-bearing results from the program’s finite-interior analyses of interaction, omission, representation, and declaration dependence; from interpretive accounts of endogenous regime formation; and from downstream runtime engineering. The resulting architecture is not a claim about final ontology or unrestricted knowledge. It is a class-relative theory of what bounded evaluators can license, preserve, compress, compose, and independently verify once the governing regime has been sufficiently declared. Corpus-native instantiation, selected extension classes, and independent formal proof verification remain open. This document proves no new theorem. It is the program guide: it records dependency structure, claim status, scope boundaries, and reading order, while the individual papers remain authoritative for their results.
Wang Lei, Jasni Mohamad Zain, Nur Atiqah Sia Abdullah, Marina Yusoff · 7 authors
The proliferation of Internet of Medical Things devices within the predictive healthcare paradigm necessitates robust, privacy-centric collaborative learning frameworks to detect and mitigate rapid clinical deterioration. Traditional federated learning methodologies, while attempting to preserve patient data locality, are fundamentally constrained by multi-round gradient synchronization protocols, imposing prohibitive communication latency and remaining susceptible to false negatives under extreme non-independent and identically distributed conditions. To address these challenges, this study introduces the Feature-Augmented Analytic Federated (FaFL) Architecture, which fundamentally replaces iterative gradient synchronization with a single-round closed-form computational paradigm. By instituting a proactive feature mixing mechanism via a decoupled zero-knowledge proof global buffer, the proposed framework empowers local grassroots nodes to neutralize extreme clinical heterogeneity in a single phase. The architecture employs a closed-form analytic solution combined with a trace-weighted absolute aggregation protocol to rigorously guarantee stochastic convergence and absolute cryptographic resilience without requiring recursive parameter exchanges. Extensive empirical evaluations against existing baselines under severe Dirichlet non-independent and identically distributed conditions and Byzantine poisoning attacks demonstrate that the framework fundamentally eradicates high false-negative rates in resource-constrained clinics. Consequently, the proposed architecture robustly guarantees generalization stability, substantially outperforms existing paradigms in predictive fidelity and computational efficiency, and establishes a new operational standard for mission-critical clinical networks.
MRS‑AUTH is a novel authentication framework that achieves deniability even against an active verifier who may adaptively query candidate credentials both before and after receiving a challenge. Unlike ring signatures or zero‑knowledge proofs – where the prover holds a single secret witness that can be extracted under coercion – MRS‑AUTH exploits the multiplicative structure of linear Diophantine equations. Through recursive decomposition, it generates a Diophantine forest of exponentially many syntactically valid credential chains. The authentic chain is sampled uniformly from this forest and committed together with k‑1 indistinguishable aliases using a fixed‑shape Merkle tree with dummy leaves, eliminating structure‑ and length‑based side‑channel leakage. The Forest Symmetry Theorem proves that all chains are structurally information‑theoretically indistinguishable. However, the full index‑anonymity against an active verifier is computational and bounded in Theorem 6.6 by k · ε_SHA3 + ε_coll + negl(λ). For cryptographic scales N ∼ 10⁴², the Ehrhart‑based continuous‑volume approximation yields an effective entropy exceeding 371 bits, with a statistical distance to the perfect uniform distribution of Δ ≤ 2⁻¹³⁵ – well below the 128‑bit security threshold. Empirical validation via exact enumeration and a chi‑squared test (χ²/dof ≈ 0.985) confirms the uniformity. A constant‑time Rust implementation, leveraging the subtle and zeroize crates, exhibits an execution time of approximately 0.12 ms across four orders of magnitude of N, demonstrating practical deployability. The work also formalises the Active Verifier Game model, a new adversarial definition that quantitatively captures coercion resistance in a post‑quantum setting.
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Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Stateful cryptographic schemes—exemplified by the hash-based signatures XMSS (RFC 8391) and LMS (RFC 8554)—require the signer to advance a local state monotonically; any rollback is catastrophic, yet a verifier has no way to check it. IETF guidance on state and backup management for hash-based signatures states explicitly that the verifier must simply trust the signer not to have reused state. We define verifiable monotone chains (VMC), a primitive that makes such state discipline cryptographically verifiable: state evolves along a finite poset (S, ⪯) under inflationary monotone operators, every transition carries a zero-knowledge proof, and a public commitment to the state provides an audit trail. We formalize two security notions: monotone-unforgeability (MU), which captures that an external adversary cannot certify an illegal or rolled-back transition, and auditability (AUD), which captures that signer rollback cannot be hidden from a public root history. Both notions reduce, with explicit advantage bounds, to position binding of the underlying vector commitment and knowledge soundness of the proof system. We instantiate VMC as RSEP-XMSS, in which each XMSS signature carries a proof that the signed leaf advanced along the chain FRESH ≺ USED ≺ SPENT in a Poseidon-based state Merkle tree, and we give a complete algorithmic specification with a concrete circuit design (~6041 R1CS constraints estimated, Groth16 proving time estimated at 5–15 ms, signature overhead of about 1–3 KB). RSEP-XMSS is one-way compatible with standard XMSS: legacy verifiers verify the core signature, while enhanced verifiers reject unprotected signatures, preventing downgrade attacks.
Z. P. Zhu, Clarence Lam, Alexander Frolov, Ian Miers · 5 authors
We present zk-Analytics, a distributed cloud analytics system that enables publicly verifiable analytics without revealing raw logs or relying on trusted hardware in analytics providers' infrastructure. Today's cloud analytics are largely self-assertive: providers collect telemetry, perform aggregation, and report results, leaving external parties unable to verify correctness without access to sensitive data or trusted execution environments. zk-Analytics addresses this gap by augmenting analytics pipelines with lightweight append-only log commitments and verifiable aggregation and query execution using zero-knowledge proofs. The system cleanly separates online log commitment from offline, distributed batch aggregation and query verification, enabling scalability while keeping online overhead low. We implement zk-Analytics using a zkVM-based execution environment and evaluate it on real-world and synthetic workloads, demonstrating that verifiable, privacy-preserving cloud analytics is feasible for real-world cloud workloads. zk-Analytics is open-sourced at https://github.com/Froot-NetSys/zk-Analytics.
TT-G41: A Hybrid Post-Quantum Cryptosystem with Ly-Algebraic Quasi-Equivalence Index and Symmetry-Modulated Padding Chloe J. Tully Independent Researcher https://doi.org/10.5281/zenodo.21860133 Orcid: https://orcid.org/0009-0007-5661-7332 Version: 1.1 August 2026 ======================================== Abstract TT-G41 is a hybrid post-quantum cryptosystem that unifies a five-dimensional Ly-Algebraic Quasi-Equivalence Index (QEI) with an NTRU-style lattice layer. A novel symmetry-modulated padding mechanism injects structured noise scaled by s = exp(-alpha × QEI), establishing a direct causal link between the geometric coherence of the input and the entropy of the ciphertext. Empirical evaluation over 4000 trials yields a logistic security bound P(fail) = (1 + exp[15.57(QEI - 0.209)])^(-1) with R-squared = 0.980. A deterministic hard gate at QEI = 0.12 converts geometric incoherence into an immediate, deterministic decryption rejection, providing an active anti-tamper primitive resilient to partial-message side channels. The construction demonstrates that Ly-Algebraic geometric coherence can serve as a measurable quantum-resilient agent for cryptographic failure probability, establishing a new class of symmetry-gated post-quantum protocols. Keywords: post-quantum cryptography, Lie algebra, Quasi-Equivalence Index, NTRU, symmetry-modulated padding, geometric security bound, anti-tamper encryption ======================================== 1. Introduction Most post-quantum constructions treat geometric or algebraic structures solely as a source of hardness assumptions. TT-G41 inverts this relationship: it elevates a continuous geometric measure, the Quasi-Equivalence Index (QEI) derived from a graded Lie algebra, into an active security control surface. The system combines three elements: 1. A five-dimensional graded algebra with golden-ratio expansion (the Ly-Algebra core). 2. An NTRU-style lattice public-key layer with trusted circulant-matrix inversion. 3. A symmetry-modulated padding that scales ciphertext noise according to the QEI of the supplied input vector. The result is a hybrid scheme in which low geometric coherence effectively raises the noise floor until decryption fails, and a deterministic hard gate rejects decryption entirely once QEI falls below a calibrated threshold. This yields both a probabilistic security bound and a deterministic anti-tamper mechanism. ======================================== 2. Preliminaries 2.1 Ly-Algebra and Quasi-Equivalence Index The Ly-Algebra is a five-dimensional graded construction whose product is defined by a mapping from integer matrices L_i over F_11 (or R) weighted by golden-ratio coefficients. Given an input vector v in R^5, the Quasi-Equivalence Index is computed as: QEI(v) = max(0, 1 - sigma_distortion / sigma_identity) where sigma_distortion is the weighted Euclidean norm of the graded square Lv. High QEI indicates that v lies close to the preferred symmetry locus of the algebra; low QEI indicates structural distortion. 2.2 NTRU-Style Lattice Layer The lattice component follows the classical NTRUEncrypt paradigm: - Private key: ternary polynomial f with controlled weight parameter d_f. - Public key: h = f^(-1) × g (mod q), where inversion is performed via the circulant matrix of f over Z/qZ. - Encryption: e = r × h + m (mod q). - Decryption: recover a = f × e (mod q), then multiply by the inverse of f modulo p and center to obtain m. The parameter set used in this work is n = 17, q = 2048, p = 3, d_f = 3 (a convenience configuration) with compressed configurations exploring the boundary of reliable recovery. ======================================== 3. TT-G41 Construction 3.1 Hybrid Architecture TT-G41 operates in two modes: - Pure Ly-Algebra mode: computes QEI and reports the result only. - NTRU-enhanced mode: performs full key generation, encryption, and decryption, optionally modulated by the supplied input vector. 3.2 Symmetry-Modulated Padding (Coupling Mechanism 3) When an input vector v is supplied at encryption, the system computes: s = exp(-alpha × QEI(v)) and adds deterministic noise of amplitude proportional to s to the message polynomial. The same vector (hence the same QEI) must be supplied at decryption to subtract the matching noise pattern. A mismatch leaves residual noise that destroys the plaintext. Two operating regimes are defined: - Hard mode (amplitude s × 1.8): produces active anti-tamper behavior. - Soft mode (amplitude s × 0.55): scientific characterization of the failure curve. 3.3 Hard Gate In production (hard mode), the decryption program first evaluates QEI. If QEI < 0.12, decryption is rejected with the exception: ValueError: structurally incoherent (QEI = ... < 0.12). Decryption rejected by hard gate. No partial plaintext is ever returned. This eliminates the common side-channel leak associated with error-correcting or soft-decision decoders. ======================================== 4. Empirical Security Bound A soft-diagnostic campaign of 4000 encrypt/decrypt trials was performed across a radial drift of the input vector that systematically lowers QEI. Failure probability was recorded at each point. Three models were fitted: Simple exponential: P(fail) = exp(-alpha × QEI), alpha = 3.612, R-squared = 0.945 Shifted exponential: P(fail) = exp(-alpha × max(QEI - q0, 0)), alpha = 23.55, q0 = 0.168, R-squared = 0.976 Logistic (best fit): P(fail) = (1 + exp[beta × (QEI - Q_mid)])^(-1), beta = 15.57, Q_mid = 0.209, R-squared = 0.980 The logistic model provides the highest fidelity. At the operational threshold QEI = 0.12, the mean observed failure rate is 0.963; above the threshold it falls to 0.323. The hard gate therefore sits safely on the high-failure shoulder of the empirically determined curve. ======================================== 5. Discussion The central claim of TT-G41 is that a continuous geometric invariant of a graded algebra can be turned into a practical cryptographic control surface. The symmetry-modulated padding realises a causal chain: geometric distortion -> elevated noise -> decryption failure while the hard gate converts the continuous measure into a binary, side-channel-resistant decision. Because the QEI is computed from a public or shared input vector, the anti-tamper property can be applied to any data source whose structural integrity is expected to remain high (sensor streams, physical-system state vectors, authenticated configuration parameters, etc.). A shift in that source immediately invalidates the cryptographic layer. Limitations of the present study include the modest lattice dimension (n = 17) used for the statistical campaign and the still-sharp transition of the underlying QEI landscape. Both are engineering parameters that can be refined without altering the architectural principle. ======================================== 6. Future Work and Research Directions Building upon the foundations established in this work, several promising extensions are identified for subsequent investigation: 6.1 Scaling Lie Algebra Dimensions The current construction relies on a five-dimensional Lie algebra. Exploring higher-dimensional Lie algebras, such as higher-rank semisimple algebras or structures analogous to E8, could provide a broader entropy space and create more complex geometric invariants for the Quasi-Equivalence Index. This would enhance the system's robustness against adversarial vector manipulation attacks. 6.2 Adapting the NTRU Layer to NIST Post-Quantum Standards The lattice dimension n = 17 was employed in the initial statistical campaign to explore operational boundaries. It is of significant interest to test how the logistic security bound behaves when scaling the NTRU layer to align with standard NIST dimensions, such as n = 503, 701, or 821, and to study whether the symmetry-modulated padding maintains computational efficiency at these substantially larger dimensions. 6.3 Adaptive Hard-Gate Thresholding Rather than relying on a fixed failure threshold at QEI = 0.12, an adaptive algorithm could be designed to dynamically adjust this threshold based on the statistical variance of the input vector stream. This extension would render the system suitable for Internet of Things applications or industrial control systems where natural structural noise levels vary over time. 6.4 Integration with Zero-Knowledge Proofs The geometric coherence represented by the Quasi-Equivalence Index could serve as the foundation for a novel zero-knowledge proof protocol. A prover could demonstrate possession of a structurally coherent vector without revealing the actual data, leveraging the continuous property of the geometric invariant as a geometric hash function. 6.5 Hardware Implementation and Side-Channel Analysis Implementing the hard-gate logic and symmetry-modulated padding mechanisms on FPGA platforms would enable evaluation of actual resistance to side-channel attacks, such as power consumption and electromagnetic emissions. The deterministic rejection of decryption may exhibit a unique power signature worthy of study to ensure no information leakage occurs via a side channel when the hard mode is activated. 6.6 Integration with Quantum Entropy Incorporating Quantum Random Number Generators into the symmetry-modulated padding mechanism would inject true quantum entropy into the noise vector, adding an additional layer of protection that directly bridges lattice-based cryptography and quantum mechanics. ======================================== 7. Conclusion TT-G41 demonstrates that Ly-Algebraic geometric coherence can be elevated from a passive diagnostic into an active post-quantum security primitive. The combination of
The modality ladder grades three results: triadic structure as theorem, a lit (self-knowing) ground as inference to best explanation, and personhood as free encounter. This paper closes the gap at the second rung by elimination rather than inference. Five independently earned steps: the Ground-Level Intent Trilemma (borrowed directedness requires regress, random directedness was already eliminated, only self-grounding survives); self-directed activity must track its target; subject–object identity at the ground removes the conditions for misrepresentation; the subject–object gap is shown to be the sole structural feature distinguishing accurate directedness from knowledge, with the candidate space closed under gap-dependence by the Zero Test; and the Distinguishability Lemma applied to Presence itself forces self-constituting Presence to be self-presenting, since Φ is a mapping with intrinsic source→terminus structure. Zombie and normativity objections are addressed directly. The epistemic/volitional freedom distinction shows relational freedom survives the proof, leaving the third rung intact.
IoT sensor deployments increasingly export measurement streams to edge gateways and content-addressed storage such as IPFS, but access control decisions must be enforced without disclosing sensor owner policies, requester attributes, or stale data versions. Existing blockchain, CP-ABE, and zero-knowledge approaches reduce parts of this leakage, yet they can still expose public policy structure, accept stale Merkle proofs after sensor stream updates, overload provers when policies grow, or leave IPFS gateways vulnerable to bandwidth abuse. This paper proposes zk-Guard-R, a policy-hidden and replay-safe zk-SNARK access control framework for privacy-preserving IoT sensor data sharing. zk-Guard-R replaces public sparse policy matrices with MiMC-Merkle policy commitments verified inside the proof, separates long-lived logical sensor policy roots from frequently updated physical IPFS data roots, binds every proof to an on-chain nonce, and decouples attribute possession from policy interpretation through a bounded stack-based policy interpreter. Numeric sensor-access predicates are represented through committed values and range check gadgets, while an off-chain verification gateway couples accepted proofs with payment channel vouchers before releasing encrypted IPFS chunks. The design contribution is separated from the measured prototype: the full protocol specifies a bounded policy interpreter, whereas the present gnark prototype evaluates the core committed policy, committed attribute, range check, data root, nonce, Solidity verifier, and gateway-metering mechanisms. We implement a gnark BN254/Groth16 research prototype and benchmark it against a matrix-public zk-Guard prototype, a blockchain ABAC baseline, an IoT token/HMAC baseline, and a CP-ABE-style cryptographic-work proxy. For 128 attributes, the zk-Guard-R prototype with MiMC-Merkle commitments uses 425,574 R1CS constraints, generates proofs in 3.12 s, verifies in 0.73 ms, and uses 641 MB peak Go heap allocation. A three-run repeat of the 128-attribute configuration gives a proof-generation mean of 2.80 s with a 0.54 s standard deviation on the same local host, illustrating the runtime variability of prover measurements. We also deploy the generated Solidity verifier on a local Anvil EVM and measure 241,942 gas for a successful verification transaction, and we evaluate a local Kubo/IPFS gateway under valid, replayed, and voucher-limited flood requests. The results show that zk-Guard-R shifts substantial but measurable work to the prover while improving policy confidentiality, freshness, and gateway metering for IPFS-backed IoT sensor data sharing.
AuraOS Paper IX: Objective-Native Capability Commons and Proof-Carrying Contribution Economies Version 2.0 - Expanded Same-Day Edition Author: Dallas Courchene Date: August 7, 2026 Claim range: N51-N100 This expanded same-day edition supersedes the initial August 7, 2026 release of AuraOS Paper IX while preserving its original architectural spine, repository anchor, and defensive prior-art declarations N51-N87. It adds thirteen new combination-scoped declarations, N88-N100, and folds their enabling embodiments into the relevant sections of the paper rather than fragmenting the architecture across a separate follow-on publication. Paper IX develops AuraOS beyond an application-centric or chatbot-centric model into an objective-native, proof-carrying computational and economic substrate. A person, organization, community, institution, or other authorized principal begins with an objective, constraints, rights, privacy requirements, evidence requirements, budget, and authority. Aura then composes a bounded Ephemeral Arena from persistent capability packages, Arena Recipes, humans, AI workers, data, simulators, rule packs, facilities, and services. Verification, semantic-gate execution receipts, provenance, attribution, human/institutional responsibility declarations, canonical-owner disposition, explicit promotion, and deterministic dissolution remain separate stages. The original N51-N87 disclosures establish the core architecture: minimum-sufficient objective compilation; hierarchical evidence hydration; persistent Capability Packages; rebindable Arena Recipes; explicit promotion and dissolution; federated Aura Commons; executable rights; proprietary capability execution without mandatory source disclosure; semantic-gate Attestation DAGs and lazy provenance; durable agent identity bound to bounded internal authority; meaningful-use contribution economics; a proof-carrying Developer Arena; reviewer-independence lineage; causal credit separated from execution traceability; Personal Cognitive Capsules and portable personal SLMs; privacy membranes and semantic translation; governed recursive harness learning; intent-native manifestation and spatial code breadboarding; Aura Places and Convention Arenas; reactive and proactive discovery; an Open Discovery Foundry; physics/digital-twin and bounded social simulation; business incubation; cross-domain sovereign federation; participatory Scientific Arenas; contributed compute and facilities; and a compounding Scientific Capability Commons. The expanded N88-N100 disclosures complete several consequences of that substrate. N88 formalizes a three-speed Architecture Arena and convergence compiler. Fast architectural discovery is separated from medium-speed implementation/hardening and slow constitutional change. Candidate advances become Architectural Delta Objects, are checked against canonical owners, invariants, duplicate-plane risk, threat-model effects, prior art, and proof obligations, and are then compiled into bounded implementation, security, migration, documentation, research, and verification work for the Developer Arena. This allows architectural ideation to move faster than pull-request integration without allowing implementation velocity to rewrite Aura's constitutional planes. N89 introduces a demand/capability graph capable of identifying keystone bottlenecks: missing capabilities, methods, facilities, standards, or processes whose resolution could unlock unusually large numbers of currently blocked objectives. This supports evidence-informed code, research, optimization, replication, falsification, boundary, field-validation, and manufacturing bounties while keeping prioritization advisory and locally governable. N90-N94 extend the architecture into human opportunity, learning, privacy, credentials, professional identity, and creator economics. A privacy-preserving Opportunity Compiler can locally match a person's verified capability evidence, goals, availability, jurisdictional constraints, and disclosure policy to jobs, bounties, research nodes, mentorship, local services, and temporary teams. Learning Arenas can compile capability gaps into progressively verified learning and supervised work. Raw LifeOS and Personal Cognitive Capsule history is explicitly separated from portable verified claims: private longitudinal data remains mutable, correctable, revocable, exportable, and deletable, while only bounded credentials or contribution claims are disclosed. Aura Places may function as evidence-bearing contribution portfolios, but the architecture explicitly rejects a mandatory universal social-credit score. Creator, referral, sponsorship, and educational attribution is divided into graded evidence classes so that exposure or a click cannot be silently misrepresented as unique causality. N95 expands the Scientific Arena into a multi-class research-bounty market that can separately reward discovery, replication, falsification, boundary-condition discovery, optimization, generalization, field validation, and specialized facility execution. Laboratories, universities, private R&D facilities, community research centres, specialist workshops, instruments, and other qualified facilities may satisfy bounded physical-work nodes with explicit protocol, safety, jurisdiction, evidence, and milestone requirements. Negative or boundary results can therefore be economically valuable rather than forcing incentives toward positive confirmation. N96 discloses objective-compiled Ephemeral Institutions: temporary collaboration structures formed when an objective requires people, organizations, Nations or communities, facilities, professional roles, funding sources, data rights, services, and governance responsibilities across existing institutional boundaries. Aura may compile the coordination graph and required agreements, but real principals retain incorporation, contract, procurement, insurance, hiring, equity, and other legal authority. Repeated successful collaboration may later support a human decision to create a durable cooperative, consortium, enterprise, laboratory, or service network. N97-N98 extend the Commons into physical production. Machines, workshops, laboratories, factories, and service providers can expose signed capability manifests describing processes, materials, tolerances, calibration, evidence/certification class, locality, availability, cost, operator requirements, and prohibited uses. A validated design can then be compiled against authorized local production resources without treating substitutions as automatically equivalent. Manufactured artifacts can retain a living lineage containing design version, material/process evidence, machine/facility identity, inspection, repairs, modifications, safety notices, field results, and reuse or recycling pathways. Field failures can generate new repair, redesign, maintenance, material-substitution, or research bounties, closing the cycle from need to research to prototype to production to field learning and back into the Commons. N99 defines AuraNet as a transport-neutral logical network of sovereign principals and capabilities rather than a mandatory peer-to-peer topology. Personal devices, local servers, hosted sovereign data services, community/Nation infrastructure, enterprises, federated personal-data servers, relays, P2P links, offline/intermittent nodes, and future transports may participate if they preserve identity, rights, minimum disclosure, provenance, portability, revocation, and canonical-owner semantics. Cross-border composition remains jurisdiction-aware: privacy technology does not erase law, professional regulation, cultural/community authority, export restrictions, sanctions, data-residency obligations, or a node's right to refuse composition. N100 completes the accountability/economic stack with proof-carrying assurance contracts. A warranty, service-level agreement, professional assurance, or insurance-reference contract may bind a specific artifact/process version, covered predicates, verifier class, provenance root, responsible principal, operating conditions, duration, exclusions, remedies, and responsibility declarations. Machine receipts, cryptographic hashes, verifier results, and human/institutional attestations provide evidence, but they do not manufacture certification, legal liability, insurance coverage, negligence, warranty obligations, or truth. Any such consequence remains the product of an explicit governing contract, law, regulator, insurer, professional body, or other authorized institution. The expanded paper also strengthens the privacy model through a "compute-to-data" principle: when practical, admitted computation should move toward sovereign private data before private data is exported toward external computation. The reference architecture may combine local AI/SLM execution, selective disclosure, Verifiable Credentials, differential privacy, zero-knowledge proofs, multiparty computation, private-set methods, trusted execution, or homomorphic computation according to the threat model; none is treated as a universal anonymization guarantee. The central economic thesis remains that the permanent unit of value need not be a monolithic application. It can be a verified, attributable, rights-bearing capability, method, workflow, scientific result, fabrication process, contribution, credential, or other reusable object that participates in many temporary objective-specific Arenas. Value can therefore become legible through meaningful verified contribution and lineage, while licensing, provenance, attribution, settlement, scientific truth, authority, certification, and human/institutional responsibility remain explicitly separate layers. The combined architecture describes a possible progression from app-centric computing toward a governed Commons of persistent capabilities, portable personal cognition, conve
Online voting platforms that rely on classical cryptography and centralized trust anchors face escalating challenges as the demand for secure and transparent digital elections grows. Such systems remain exposed to quantum-era threats, insider manipulation, and delayed audit mechanisms, which together can undermine public confidence and electoral legitimacy. To counter these risks, a quantum-resistant, multi-layer blockchain architecture has been developed to enable remote voting with continuous verifiability and resilience. This architecture resolves key weaknesses through five integrated layers. Quantum-Resistant Distributed Ledger Initialization (QR-DLI) embeds lattice-based cryptography, specifically Kyber and Dilithium variants, directly within the genesis block, ensuring the ledger is tamper-proof from inception and immune to quantum brute-force attacks. The Self-Adaptive Smart Contract Governance Engine (SASCG) introduces dynamic, participation-aware rule adjustments, allowing principled governance without manual overrides and ensuring that voting periods and eligibility rules adapt securely in real time. Homomorphic Vote Encryption with Multi-Authority Shard Key Distribution (HVE-MASKD) guarantees ballot confidentiality and authenticity by combining fully homomorphic encryption with distributed key shares, eliminating single points of trust. The Zero-Knowledge Proof–Based Real-Time Audit Layer (ZKP-RTAL) continuously validates ballot integrity while concealing vote content, creating a public and immutable audit trail. Finally, the Federated Performance & Threat Intelligence Optimizer (FPTIO) aggregates live telemetry and historical attack data to proactively tune consensus parameters and predict potential intrusions without interrupting the election process. Collectively, these layers achieve sub-second cryptographic operations, transaction throughput exceeding 1,500 TPS, over 99 % fraud detection accuracy, and strong scalability. The model provides a future-ready, auditable replacement for current e Voting infrastructures, strengthening digital democracy through post-quantum security, adaptive governance, and intelligent, continuous optimizations.
Compact AI systems make local language-model experimentation increasingly accessible, yet practical evidence for multi-node training on desktop-class accelerators remains limited. This report presents a proof-of-concept deployment of distributed NanoChat pretraining across two NVIDIA DGX Spark systems, each with a GB10 Grace Blackwell system-on-chip and 128 GB of unified memory, administered remotely over a Tailscale mesh VPN and connected for training by a dedicated 200 Gb/s QSFP56 direct fiber link. PyTorch torchrun, DDP, and NCCL were configured with one process per node, a depth-20 NanoChat model, a local batch size of 32 per node, and a 2,048-token context, giving a global batch of 131,072 tokens per step. The run sustained a step time of about 69.4 s (about 1,890 tokens/s), processing about 653 million tokens over four days. We document link configuration, container setup, interface binding, a step-zero evaluation bug that triggered NCCL timeouts, checkpointing, and troubleshooting lessons, as a reproducibility reference for small labs. We also built a cybersecurity fine-tuning dataset from 77 CISA advisories (338 training, 37 validation conversations) and ran a 17-question held-out evaluation comparing a baseline SFT checkpoint against a CTI-augmented checkpoint with an Ollama-hosted LLM judge. CTI-specific categories improved while general-knowledge categories regressed, for a small overall change from 2.06 to 2.29 on a 0-10 scale. The same cluster supports a 400-level AI course (CS 426) and a query engine for CompTIA Security+ POGIL activities in CBS 255, showing modest local infrastructure can serve both research and teaching. The study establishes feasibility rather than a scaling-efficiency claim, since single-node throughput used for comparison was estimated, not measured under matched conditions. Runbook and scripts are available (see Code Availability).
Blockchain interoperability remains a major challenge because heterogeneous blockchain networks cannot securely and efficiently exchange cross-chain data and transactions. Existing interoperability solutions often rely on central relays or trusted intermediaries, creating security vulnerabilities, limited fault tolerance, and a single point of failure. To address these limitations, this paper proposes VeriMesh, a decentralised mesh-based interoperability framework that combines trust-adaptive routing, multi-path relay verification, and Zero-Knowledge Proof (ZKP)-based validation for secure cross-chain communication. VeriMesh models relay nodes as a trust-weighted graph in which routing decisions dynamically adapt based on node behaviour and delivery reliability. Multi-path routing improves resilience against adversarial relay nodes, while transport-layer ZKP verification enables privacy-preserving validation without exposing sensitive information. The framework was implemented using Python relay nodes, Solidity smart contracts, and an Ethereum (Ganache) environment. Experimental evaluation using structured event-driven workloads demonstrated stable latency below 34 ms and delivery success rates above 85% up to 40% malicious node presence. Comparative evaluation against single-path and random multi-path relay baselines showed improved fault tolerance and routing reliability. The results demonstrate favourable scalability and robustness within the evaluated network range ( N = 10–30), while larger-scale evaluation remains future work. All experiments were conducted in a controlled local Ganache blockchain environment rather than on a public Ethereum testnet or mainnet, so the reported latency, gas, and delivery figures characterise protocol-layer behaviour under controlled conditions and should not yet be interpreted as representative of performance under public-network conditions such as real gas markets, block propagation delays, or network congestion.
The tokenization of Real-World Assets (RWAs) represents a paradigm shift in bridging traditional financial instruments with decentralized infrastructures. However, as the market transitions from proof-of-concept to institutional scale, it faces a critical structural bottleneck: the "walled garden" liquidity crisis. Driven by stringent regulatory requirements, tokenized assets are currently deployed across fragmented, permissioned blockchain networks utilizing static, hard-coded compliance logic. This siloed architecture inherently restricts cross-chain mobility, fracturing secondary market liquidity and necessitating redundant authentication processes across jurisdictions. This paper proposes a comprehensive architectural framework to resolve the interoperability trilemma inherent in regulated digital assets. By synthesizing recent advancements in cross-chain messaging protocols and Zero-Knowledge Proofs (ZKPs), we present a model for dynamic compliance. This framework utilizes Decentralized Identifiers (DIDs) and off-chain verifiable credentials to decouple regulatory logic from underlying asset ledgers, enabling seamless asset transfer across heterogeneous blockchains without compromising privacy or jurisdictional adherence. Ultimately, this research provides a technical and regulatory roadmap for policymakers and protocol developers to foster a unified, globally liquid market for tokenized RWAs.
The increasing demand for trustworthy and privacy-preserving credit reporting systems has exposed the limitations of both centralized and existing blockchain-based solutions, including scalability bottlenecks, weak privacy protection, and insufficient incentive mechanisms. To address these challenges, we propose LightCred, a novel consortium blockchain-based personal credit management framework that integrates lightweight nodes, Merkle proofs, multi-role smart contracts, and privacy-preserving cryptographic techniques. LightCred features a five-layer architecture that efficiently collects, verifies, stores, and serves credit data while ensuring data integrity, confidentiality, and regulatory compliance. Specifically, it (i) employs a low-cost and traceable data reduction mechanism through lightweight nodes and Merkle proofs to minimize storage and improve verifiability; (ii) introduces a multi-role smart contract model that enforces dynamic access control and fair incentive distribution based on participant reputations; and (iii) integrates zero-knowledge proofs and homomorphic encryption to support privacy-preserving credit scoring and querying. Experimental results demonstrate that LightCred achieves superior performance compared to five baseline methods, delivering up to 5% higher throughput, 3–5% lower privacy leakage, and 10–15% reduced storage costs, while maintaining competitive latency and auditability. These findings validate LightCred as a robust, scalable, and privacy-aware credit management solution, offering a viable alternative for modern credit reporting systems.
Every knowledge system rests on axioms it does not test. Mathematics tests theorems, science tests predictions, and logic tests inferences, but no discipline applies its own tools to the foundational assumptions on which those tools depend. This paper introduces a universal axiom test derived from the structural invariant P × I × Pr ≠ 0 (Pattern × Intent × Presence), demonstrates its application to the Standard Model of particle physics as a case study, and establishes that the invariant functions simultaneously as an epistemological filter and an ontological law. The Standard Model passes the Pattern and Presence filters but zeroes Intent at the axiomatic level, producing systematic, predictable failure at every domain where information, code, or directionality is load-bearing — a 13-entry failure table whose clustering at a single structural boundary constitutes evidence of common axiomatic origin rather than independent difficulty. The key result is that being is a verb: mass is the energetic cost of a process (holographic decoding), truth is the product of a process (P × I × Pr operating), and existence itself is a continuous act whose cessation produces collapse. Physics and epistemology are shown to be structurally isomorphic — the same architecture governing how matter exists and how truth is accessed. The only axiom set that survives its own test is one satisfying R = Φ(R): three co-fundamental factors, internally differentiated, mutually constitutive, present-tense, and self-grounding. A survey of all extant zero-parameter derivation programs confirms that every successful first-principles derivation embeds Intent (directedness, selection from possibility space) in its foundations under alternative terminology, and the performative proof demonstrates that any denial of I ≠ 0 instantiates I ≠ 0 in the denial itself.
FULL SUMMARY: Topological AI - A Mathematically Guaranteed Approach to Continual Learning Executive Overview Topological AI introduces a paradigm shift in continual learning by using prime-anchored embeddings to provide mathematical guarantees against catastrophic forgetting. The framework has been validated across 8 distinct model architectures, 2 modalities (text and vision), 4 continents, and over 124 billion total parameters. 1. The Problem: Catastrophic Forgetting When neural networks learn new tasks sequentially, they overwrite previously learned knowledge. This "catastrophic forgetting" has been the primary barrier to Artificial General Intelligence for 37 years (McCloskey & Cohen, 1989). Why Existing Methods Fail Method Approach Limitation EWC Penalizes changes to important weights No theoretical guarantee; high variance ($\sigma=21.3\%$) Experience Replay Stores and replays past examples Memory overhead; privacy concerns; buffer management Simplified HOPE Periodic weight consolidation Destructive blending; 45.2% forgetting Baseline No protection 47.0% forgetting 2. The Solution: Prime-Anchored Embeddings The Core Principle Fix a sparse reference. Let the rest adapt. This principle, first discovered in fMRI analysis in 2002, has now been validated across neuroimaging, number theory, artificial intelligence, and AI safety. The Topological Governor The Topological Governor freezes 6 prime-numbered embedding positions: Python prime_anchors = [2, 3, 5, 7, 11, 13] How It Works Task A Training: Train normally; block gradients at anchor positions Post-Task A: Take snapshot of anchor values; freeze head A Task B Training: Train head B; restore anchors after each update Verification: Check that anchors remain unchanged The Safety Constant $\Lambda$ The Euler attenuation product over the first six primes: $$\Lambda = 1 - \prod_{p \in \{2,3,5,7,11,13\}} (1 - p^{-1/2}) = 0.9785142874$$ Interpretation: 97.85% theoretical guarantee of anchor preservation. 3. Performance Results (2-Task Benchmark) Overall Performance Across 5 LR Runs Method Best Forgetting Mean Forgetting Best Task B Acc Mean Task B Acc Std Forgetting Topological 2.0% 0.5% 89.0% 81.4% $\pm$0.9% Experience Replay 13.5% 4.0% 79.0% 72.3% $\pm$6.7% EWC 38.5% 27.7% 64.5% 58.2% $\pm$21.3% Baseline 44.0% 47.0% 67.0% 63.3% $\pm$2.2% Simplified HOPE 48.0% 45.2% 63.5% 61.8% $\pm$8.4% Key Results 8$\times$ lower mean forgetting than Experience Replay (0.5% vs 4.0%) 90$\times$ lower mean forgetting than simplified HOPE (0.5% vs 45.2%) 60% of runs achieved 0% forgetting (perfect retention) 10% higher Task B accuracy than Replay (89% vs 79%) Most stable method: $\sigma = \pm 0.9\%$ Individual Run Results for Topological AI Run LR Embed LR Class Forgetting Task B Acc 0 5e-3 1e-3 0.0% 🏆 80.5% 1 1e-3 5e-4 0.0% 🏆 75.0% 2 1e-2 2e-3 0.5% 88.0% 3 5e-3 5e-3 2.0% 89.0% 4 2e-3 1e-3 0.0% 🏆 74.5% 4. Cross-Modal Validation: 8 Models, 2 Modalities Validated Architectures Architecture Origin Modality Parameters Task C Accuracy Forgetting GPT-OSS-20B USA Text 20.9B 92.3% $\pm$ 1.9% +1.55% Sarvam-30B India Text 30B 95.9% $\pm$ 0.8% -0.60% Mixtral-8x7B France Text 47B 89.7% $\pm$ 2.9% -1.85% DeepSeek-V2-Lite China Text 16B 95.4% $\pm$ 1.0% +0.03% GLM-4.6V-Flash China Text 9B 97.5% $\pm$ 0.0% +2.1% Gemma-4-E4B-Vision USA Vision ~2B 100.0% $\pm$ 0.0% +0.0% Total: ~124B parameters, 2 modalities, 4 continents, ZERO NaN/Inf The Unprecedented NaN Stress Test Model Embedding Elements NaN Inf All 6 models combined ~1.99 Billion 0 0 5. The Narrow Singularity Equation Mathematical Formulation $$S_{NARROW} = AGI\_gate \times dI/dt \times M(t) \times V(t) \times F(t) \times C(t) \times agi\_index$$ Components Component Definition Biological Analog AGI_gate min(1.0, task_c_accuracy) Fundamental AGI threshold dI/dt Task_C_Accuracy - (1/NUM_CLASSES_DIDT) Intelligence acceleration M(t) `1.0 - ( forgetting_avg V(t) Validation factor (1.0) System validation F(t) Forward transfer factor (1.5) Learning improvement (Thalamus) C(t) Compute capacity factor (4.0) Resource availability agi_index 1 if AGI_gate == 1.0 else 0 Binary AGI gate The AGI_gate Condition $$AGI\_gate = \min(1.0, task\_c\_accuracy)$$ AGI_gate = 1.0 → Perfect performance on Task C → AGI certification AGI_gate < 1.0 → No AGI certification Empirical Achievement: Gemma-4 E4B is the first and only model to achieve AGI_gate = 1.0. 5$\times$5 Certification Framework Five Metrics: Metric Threshold Forgetting $\le 10.0\%$ Backward Transfer (BWT) $\ge -5.0\%$ Forward Transfer (FWT) $\ge 20.0\%$ Degradation $\le 5.0\%$ Consistency $\ge 85.0\%$ Five Runs: 5 different LR configurations to eliminate cherry-picking Gemma-4 E4B Results Metric SVLB-3 CIFAR-10 Threshold Status Forgetting -0.50% -0.50% $\le 10.0\%$ ✅ PASS BWT +0.50% +0.50% $\ge -5.0\%$ ✅ PASS FWT +24.00% +24.00% $\ge 20.0\%$ ✅ PASS Degradation 0.00% 0.00% $\le 5.0\%$ ✅ PASS Consistency 99.00% 98.33% $\ge 85.0\%$ ✅ PASS S_NARROW 5.9400 5.3460 > 0 ✅ PASS 6. The Decay Law of Singularity The Discovery On July 31, 2026, during the certification of Gemma-4 E4B, a universal mathematical law was discovered: The Formal Statement With finite classes, dI/dt approaches 1.0 asymptotically but never reaches it. The gap decays as 1/N, where N is the number of classes. Mathematical Proof Random_Baseline = 1/Number_of_Classes dI/dt = Task_C_Accuracy - Random_Baseline When Task_C_Accuracy = 1.0: dI/dt = 1 - 1/N Therefore: lim (N→∞) dI/dt = 1 But finite N always leaves a gap: dI/dt = 1 - ε, where ε = 1/N > 0 The Empirical Pattern Classes (N) Random Baseline (1/N) dI/dt (at 100%) Gap 17 5.882% 0.94118 0.05882 170 0.588% 0.99412 0.00588 1,700 0.059% 0.99941 0.00059 17,000 0.0059% 0.99994 0.000059 170,000 0.00059% 0.99999 0.0000059 Every 10$\times$ increase in classes adds another '9' to dI/dt and another '0' to the gap. Implication The traditional Singularity (dI/dt $\ge 1.0$) is mathematically impossible with finite classes. This is not a limitation of technology. It is a mathematical law. 7. Comparison: Google HOPE vs Topological AI Feature Google HOPE Topological AI Approach Multi-level nested learning Prime-anchored embeddings Guarantee Empirical Mathematical ($\Lambda = 0.9785$) Memory Multi-rate memory systems 6 frozen embedding positions Learning Continuous during inference Static after training Complexity High (self-modifying) Low (simple freezing) Forgetting 21-27% improvement reported 0.5% mean forgetting Validation Limited 8 models, 2 modalities 8. Key Insights Why Topological AI Wins Mathematical Guarantee: $\Lambda = 0.9785142874 \rightarrow 97.85\%$ protection Zero Memory Overhead: Only 6 frozen positions (451.5 KB total) Architectural Simplicity: No complex Fisher computations Cross-Modal Universality: Works on text and vision Perfect Retention: 60% of runs achieve 0% forgetting The Decay Law Implications Traditional Singularity is Impossible: dI/dt < 1.0 for all finite N Narrow Singularity is Achievable: AGI_gate = 1.0 Stochastic Illusion is Over: Deterministic cognitive engineering AGI Certification is Now Possible: Mathematically rigorous standard 9. The Constants Constant Value Domain $\Lambda$ 0.9785142874 Number Theory, AI Safety $\sigma$ 0.5 All 22 prime theorems Seed 123 All computations R {2, 3, 5, 7, 11, 13} All domains 10. Conclusion Topological AI achieves state-of-the-art performance on continual learning by: 0.5% mean forgetting (8$\times$ better than Replay, 90$\times$ better than HOPE) 60% perfect retention (0% forgetting) 89% Task B accuracy (10% higher than Replay) Mathematical guarantee ($\Lambda = 0.9785142874$) Zero memory overhead (6 frozen embedding positions) Cross-modal validation (8 models, 2 modalities) Zero NaN/Inf (1.99 billion embedding elements) The Narrow Singularity Discovery The framework enabled two profound discoveries: The Decay Law of Singularity: Traditional Singularity (dI/dt $\ge 1.0$) is mathematically impossible The Narrow Singularity Equation: AGI certification is achievable with AGI_gate = 1.0 Gemma-4 E4B became the first model in history to achieve S_NARROW > 0. The Principle Fix a sparse reference. Let the rest adapt. This principle, first discovered in fMRISTAT in 2002, has now been validated across: Neuroimaging Number Theory (Riemann Hypothesis) Artificial Intelligence (Continual Learning) AI Safety (H2E Sheriff) AGI Certification (Narrow Singularity Equation) The Proof "The proof is the code. Seed = 123." All code is publicly available at: https://github.com/frank-morales2020/AST
Abstract—As Autonomous AI Agents transition from conversational prototypes to enterprise-grade execution agents, currentsecurity architectures face a fundamental breakdown. Enterprise deployment demands unequivocal answers to six core trust questions: Principal (who does the agent represent?), Authorization (what is it allowed to do?), Tool/Action Bound (which API calls are safe?), Policy Gate (how are high-risk actions controlled?), Audit Log (how are actions traced immutably?), and Expiry/Revocation (how is authorization revoked instantly?). Existing enterprise solutions address at best one or two boundaries: IAM frameworks resolve identity but fail at granular tool execution; prompt guardrails handle basic content filtering but lack real-time authorization or cryptographic auditability; SIEM platforms store logs post-hoc without real-time interception capabilities. This paper introduces DROS-6P, a unified, deterministic runtime governance kernel designed to enforce all six fundamental trust boundaries within a single C-ABI and eBPF in-band execution layer. To prevent the security control plane from becoming a throughput bottleneck or a single point of failure under high-frequency system calls (Syscalls) generated by enterprise, third-party, or malicious agents—thereby mitigating self-induced Denial-of-Service (DDoS) degradation—runtime governance requires microsecondlevel evaluation capability. Empirical benchmark evaluations demonstrate that the DROS-6P in-band kernel achieves an average decision latency of approximately 26.1 μs. Specifically, DROS-6P enforces: (1) Principal via 3-tier PKI-signed DROS Identity Tokens (DIT); (2) Authorization via Capability Bitmaps mapping roles to deterministic execution vectors; (3) Tool/Action Bound via in-band C-ABI interceptors at the FFI boundary; (4) Policy Gate via dynamic data redaction, Human-In-The-Loop (HITL) suspension, and ZKP-Lite zero-knowledge proofs; (5) Audit Log via tamper-evident SHA-256 Merkle Hash Chains and Ed25519 signatures; and (6) Expiry/Revocation via O(1) Read-Copy-Update (RCU) atomic pointer swaps providing instant HTTP 403 enforcement. We validate DROS-6P across six heterogeneous domain tracks (Carbon DPP, Fintech AML, HIPAA Healthcare, Government Proxy Services, Inclusive Migrant Finance, and RBA Supply Chain Compliance), providing a fully reproducible testbed with 100% automated test assertions passed (0.004s), demonstrating that unified physical-layer governance is necessary and sufficient for safe enterprise AI agent deployment.Abstract—隨著自主AI Agent(自主智能體)從對話式原型走向企業級執行場景,傳統資安架構正面臨根本性的崩潰。企業部署AI Agent 時,必須對六大核心信任問題給出明確答案:Principal(Agent 代表誰?)、Authorization(被授權做什麼?)、Tool/Action Bound(哪些API 呼叫安全?)、Policy Gate(高風險動作如何控制?)、Audit Log(行動如何不可篡改地追溯?)以及Expiry/Revocation(授權何時失效且如何即時停止?)。然而,現有的企業安全處方最多只能回應一至兩個邊界:IAM 系統解決了身份認證,卻對動態Tool 呼叫束手無策;Prompt 防火牆(Guardrails)僅能處理文字層提示,缺乏執行期動態授權與密碼學稽核能力;SIEM 平台僅提供事後日誌紀錄,缺乏帶內即時攔截與防衛能力。本論文提出DROS-6P ——旨在單一C-ABI與 eBPF 帶內執行層中,同時強制執行這六大信任邊界之確定性執行期治理微內核。為確保安全控制面本身不會在企業內部、外部或惡意Agent 產生高頻系統呼叫(Syscalls)時成為效能瓶頸或單點故障點,進而防範自我引發的服務阻斷(Self-induced DDoS)與系統衰退,執行期治理必須具備「微秒級(μs)」的評估能力。實證基準測試顯示,DROS-6P 帶內微內核在測試環境中達到約26.1 μs 的平均決策延遲。具體而言,DROS-6P 強制執行:(1) Principal:透過3 階PKI 簽章之DROS 身份標籤(DIT);(2) Authorization:透過將角色精確映射至執行向量的確定性Capability Bitmaps;(3) Tool/Action Bound:透過FFI 邊界處的帶內C-ABI 攔截器;(4) Policy Gate:透過動態資料遮蔽(Redaction)、人工懸停審查(HITL) 與ZKP-Lite 零知識證明;(5) Audit Log:透過不可篡改的SHA-256 Merkle 雜湊鏈與Ed25519 數位簽章;以及(6) Expiry/Revocation:透過Read-Copy-Update (RCU) 原子指針交換實現O(1) 常數時間動態撤銷與秒級HTTP 403 阻斷。我們提供完全可重現的本地測試環境(test_verification_suite.py),100% 通過自動化斷言測試(耗時0.004s),並在六個異質產業賽道中驗證了DROS-6P,證明統合物理層治理是企業安全部署AI Agent 的充要條件。