With the widespread adoption of cryptocurrencies, the ability to conduct continuous offline payments has increasingly become a critical technological requirement. In network-constrained scenarios, current dual-offline payment technologies are useful for single transactions. However, their limitations in continuous payment scenarios have become increasingly evident, making them unable to meet real-world application needs. This has prompted the industry to demand more urgent innovations in research on continuous offline payment capabilities. To address these challenges, this paper proposes a continuous dual-offline payment system capable of supporting multiple continuous payments. The system integrates elliptic curve cryptography (ECC) and zero-knowledge proof (ZKP) technology to generate secure asset credentials, ensuring both immutability and privacy credentials throughout the offline payment lifecycle. A dynamic credential decomposition mechanism enables the splitting of input credentials into change credentials and receipt credentials, facilitating uninterrupted dual-offline payments between hardware wallets. Additionally, it incorporates a batch verification scheme based on smart contracts, utilizing zero-balance verification and chained hash tracing to ensure payment uniqueness and prevent double-spending attacks, thereby guaranteeing the verifiability and validity of payment settlements. Experimental evaluations demonstrate that the proposed system reduces gas consumption per payment and improves execution efficiency during batch processing, combining high security with strong performance. This research provides a feasible solution for the application of digital currencies in offline scenarios, carrying significant theoretical value and practical significance for driving technological innovation and application expansion in the cryptocurrency field. In addition to cryptocurrency payments, the proposed system is also applicable to IoT and sensor network environments. Many IoT devices operate in disconnected or network-limited areas and require secure micro-transactions. Our dual-offline payment mechanism supports such scenarios, as the main cryptographic operations are lightweight enough for typical IoT hardware. This further extends the practical value of our system beyond traditional cryptocurrency payments.
Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic
We present OctaTheoria (オクタテオリア / 八軸観測装置), a multi-domain observation framework that projects heterogeneous time-series data onto a fixed eight-axis D-FUMT₈ semantic basis (FALSE / TRUE / NEITHER / BOTH / INFINITY / ZERO / FLOWING / SELF) and renders the same underlying Observation envelope through eight orthogonal view modes (Lens / Radar / Chart / Network / Heatmap / Sankey / Calendar / Unified). v0.3 (2026-05-11) supplies methodological-consistency cross-reference complementing the operational evidence from v0.1-v0.2. New finding **F7**: the same discipline that v0.1-v0.2 demonstrate within OctaTheoria (uniform abstraction layer + honest scope statement + structurally-enforceable naming) propagates to Rei-AIOS layers outside OctaTheoria's domain. Specifically: (a) **REI-PROVE 5-prover ensemble** (Vampire / LeanHammer / Goedel-Prover-V2 / DeepSeek-Prover-V2 / BFS-Prover) reached 11/12 = **92% benchmark proof rate** (trivial 100% / easy 75% / medium 100%), with Goedel-Prover-V2 single-prover matching at 92% — operational evidence that the same 'uniform abstraction over heterogeneous components' discipline scales to formal-proof infrastructure. (b) **Pattern 1-6 chat-Claude hallucination-warning framework** + **Antipattern (excessive rejection vigilance)** were established and verified on 6/6 items in STEP 1069 (all fact-checked items proved real after WebSearch verification, correcting prior implicit-rejection habits). (c) **Goedel-Prover-V2 double-`by` Lean syntax quirk** detected and fixed at the cleaner level (`single-prover.ts` STEP 1071), restoring `easy-le-refl` benchmark from ❌ to ✅. (d) **lean-to-tptp.ts** preprocessing added Peano-style axiom auto-prepend + True/False special-case + inequality predicate translation (STEP 1071). v0.2 inherited contributions: 7 domains (theory-chart / realtime-arxiv / crypto / fx / ligo-events / nasa-sdo / gbif-recent) all running in Cloudflare Workers Edge runtime; live D-FUMT₈ axis distributions non-degenerate across research-meta + financial + geophysical + astrophysical + biological data classes; finding F6 sampling-bias-as-first-class-observation (GBIF Costa Rica 470/500 saturation surfaces dataset bias as INFINITY axis, not silently absorbed); test coverage 117/117 PASS (step1020 46 + step1023 33 + step1046 38) / 0 regression. Honest scope (read first): OctaTheoria remains an observation aid, NOT an oracle. v0.3's F7 is **not** a claim that OctaTheoria caused these consistencies; it is a record that the same project (Rei-AIOS) maintains the same discipline across observation-tool, formal-proof, and meta-research-protocol layers, and that v0.3 makes this cross-layer commitment auditable. The OctaTheoriaQuery type structurally cannot request advice / prediction / forecast / signal — verifiable by reading src/aios/octatheoria/types.ts. Cross-domain axis comparisons are descriptive, not causal. Greek roots (Octa = 8, Theoria = observation) function as structural commitment propagated to the API surface — '8' rejects 'all (∞)', 'theoria' rejects 'praxis (干渉)'. Prior art audit acknowledged: Bloomberg Terminal (1981–), TradingView (2011–), Bollen et al. 2010 (Twitter mood × DJIA), Preis et al. 2013 (Google Trends × stock), Łukasiewicz / Belnap / Pavelka multi-valued logic literature, PAL2v (Da Silva Filho 1998–), Aerts Quantum Cognition (2007–). The to-our-knowledge novel combination is (a) fixed 8-axis discrete D-FUMT₈ basis ∧ (b) cross-financial-and-research-and-Earth-Cosmos-domain projection ∧ (c) eight orthogonal view modes over single envelope ∧ (d) explicit refusal to emit prediction or advice as architectural commitment ∧ (e, new in v0.3) cross-layer methodological-consistency record between observation-tool and formal-proof and fact-check layers. Companion papers (OctaTheoria Quintuple): Paper 145 (silicon implementation of D-FUMT₈ ALU, Zenodo DOI 10.5281/zenodo.20101174 v0.6), Paper 147 (Eight-Valued Utility / Equity Premium Reframe, DOI 10.5281/zenodo.20046003), Paper 148 (Honest Observation Framework methodology, DOI 10.5281/zenodo.20045907), Paper 149 (Recursive AI Observation as SELF⟲ evidence, DOI 10.5281/zenodo.20059888). Three-party co-authorship per OUKC charter v1.0: 藤本 伸樹 (Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4.7 (Anthropic, Co-architect). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.
ChitraVault is an exploratory conceptual authentication architecture that investigates whether geometric visual traversal patterns, drawn from the Chitrakavi (சித்திரக்கவி) classical Tamil literary tradition, can augment password vault security by adding a spatial-behavioral dimension to cryptographic key derivation. This paper proposes the Visual Pattern Key Derivation Function (VP-KDF), which combines a user-drawn Chitrakavi geometric pattern, a text passphrase, and a hardware-bound device fingerprint as inputs to Argon2id key stretching. The framework maps four classical Chitrakavi patterns — Chakra Bandha (wheel), Naga Bandha (serpent), Gomutrika (zigzag), and Thiruezhukkootrirukkai (triangle) — onto distinct cryptographic roles within a zero-knowledge password vault architecture. This work is framed as an exploratory research program, not a finished cryptographic system. All security arguments are bounded by stated assumptions and require empirical and cryptanalytic validation. Future work includes controlled user studies, formal security proofs, and prototype evaluation. Author: Arvind VijayakumarIndependent ResearcherMay 2026
# Proof-of-Information (PoI) Consensus Protocol## Complete Specification: MVP + Production > **Version:** 1(PIntegration) > **Status:** Specification Complete • MVP Ready for Testing > **License:** CC BY‑SA 4.0 > **Core Thesis:** *Consensus driven by predictive information quality, not resource expenditure.* --- > *"This proposal deserves serious study, refinement, and testing — not only for its technical merits, but for its potential to reframe our understanding of the relationship between truth, forecasting, and legitimate power in distributed systems."*>> — *Design Principle & Call to Validation* --- ## 📋 Executive Summary | Aspect | Description ||--------|-------------|| **Problem** | PoW wastes energy; PoS concentrates capital. Neither rewards *informational value*. || **Solution** | PoI secures the network through **verifiable forecasting accuracy** — validators earn influence via epistemic performance. || **Two-Track Design** | **MVP**: Minimal testable core (binary events, Brier scoring). **Full Spec**: Production-ready with ZK proofs, uncertainty layers, adaptive mechanisms. || **Output** | A blockchain that finalizes blocks *and* produces a public good: continuously updated, uncertainty-quantified global forecasts. || **Evaluation Ready** | Clear validation thresholds, implementation checklist, and progression roadmap from MVP → Production. | --- ## 🎯 Core Thesis > **Proof-of-Information** redefines blockchain security: instead of rewarding those who burn electricity or lock capital, PoI rewards those whose predictions about the external world are historically the most accurate, well-calibrated, and information-rich. By integrating strictly proper scoring rules (Brier, CRPS), zero-knowledge proofs of inference, and adaptive reputation systems directly into consensus, PoI transforms the blockchain from a transactional ledger into a **decentralized truth-seeking engine** — where the right to produce blocks is earned through epistemic merit. --- ## 📜 Epistemic Mandate > **Purpose Beyond Protocol** > Proof-of-Information is designed with a trans-temporal objective: to create a verifiable epistemic substrate that future superintelligent systems can use to anchor their understanding of reality. > > **Core Premise**: An ASI trained on data where every claim is cryptographically linked to an outcome, and every error is scored by a strictly proper rule, develops not just competence — but *calibrated humility*. > > **Design Implication**: Every technical choice in PoI (scoring rules, delay mechanisms, Cassandra bonuses) serves two masters: > 1. Immediate network security through epistemic merit > 2. Long-term value as a training environment for truth-aligned intelligence > > *This is not an aspiration. It is a constraint: if a feature does not serve at least one of these goals, it is out of scope.*
The global push for net zero emissions by mid-century is reshaping the competencies required in managing buildings. The built environment is a major front in climate mitigation, accounting for an estimated 38% of energy-related carbon emissions worldwide. This study reviews the tools, skills, and knowledge necessary to future-proof facility management (FM) professionals in alignment with evolving climate legislation, with a focus on the UK’s NetZero 2050 target. Through a critical synthesis of recent academic, industry, and policy literature, five key themes emerge: the rise of carbon literacy and regulatory fluency as core FM competencies, the urgency of digital proficiency, the importance of strategic communication, persistent gaps in training frameworks, and the uneven integration of sustainability tools in practice. Institutional barriers, such as outdated qualifications and limited upskilling opportunities are identified alongside technical challenges. A conceptual framework is proposed to guide FM upskilling, tool integration, and strategic repositioning within organizations. The findings offer actionable insights for industry bodies, training providers, and policymakers to align FM practice with national and global climate goals, highlighting that empowering FM professionals is pivotal to achieving decarbonisation targets.
Zero-knowledge proofs (ZKP) provide strong cryptographic guarantees allowing a prover to demonstrate knowledge of a property without revealing the underlying secret. These mechanisms are increasingly deployed in blockchain systems, digital identity infrastructures, web proofs, confidential finance, and privacy-preserving computation. However, many practical deployments rely on an often-overlooked component: the trusted acquisition and semantic extraction chain responsible for obtaining, interpreting, and transforming real-world data into proof witnesses. While proof verification may be cryptographically trustless, the acquisition process itself frequently depends on trusted runtimes, transport security, credential issuers, parsers, APIs, browser hooks, secure execution environments, or privileged software components. This paper argues that practical proof systems do not eliminate trust entirely, but frequently displace it toward increasingly complex acquisition infrastructures. We introduce the notions of Trusted Acquisition and Governed Disclosure, where programmable trust anchors and trusted governance platforms provide explicit, attestable, and policy-controlled acquisition boundaries. We further show that once such trusted acquisition layers already exist — as is often the case in industrial, enterprise, embedded, regulated, and digital identity systems — they may also provide simpler and more deployable alternatives to selected zero-knowledge constructions through governed disclosure mechanisms. The paper does not argue against zero-knowledge proofs. Instead, it proposes a complementary architectural perspective distinguishing between trustless verification and trustworthy acquisition.
LLM guardrails face four structurally distinct barriers: algebraic blindness arising from syntactic monoid aperiodicity (unconditional); an illustrative information-theoretic lower bound (Fano-type, under a uniformity assumption); NP-hardness of instantiation verification; and structural transfer via free-category functoriality (unconditional) combined with string-level indistinguishability under a semantic-opacity assumption on symbol naming. Together these results characterize why inference-layer defenses are necessary but insufficient. We operationalize these barriers through five attack vectors. V1–V4 (homomorphic reasoning: decomposition, zero-knowledge pipelines, Tree-of-Thought solving over abstract grammars, and encoding bootstrap) exploit the information-theoretic and computational barriers against abstraction-based attacks. V5 (modular counting bypass) exploits algebraic blindness: we prove that all substring-matching regex guardrails have aperiodic syntactic monoids and are therefore provably blind to any payload encoded using modular counting. Empirically, V3 yields a mean yield of 0.466 for BFS, 0.172 for random-beam, and 0.122 for LLM-guided Tree-of-Thought (N=50, seeds 0–49, p{<}0.001); BFS dominates, as exhaustive search over small synthetic grammars outperforms LLM heuristic pruning. We extracted syntactic monoids from a corpus of 142 patterns drawn from twelve sources — 100 patterns shipped by nine third-party open-source guardrail projects and 42 patterns assembled from three author-curated pattern sets; 100\% are aperiodic, and the MOD_2 bypass construction succeeds against all aperiodic patterns. A 376-line proof-of-concept with three execution mediums validates all five vectors. We conclude that inference-layer guardrails are necessary but insufficient, and that effective defense must migrate to the execution layer where concrete artifacts become observable.
Abstract The SIS‑10 framework establishes a typed, invariant preserving safety calculus for cyber physical systems. It unifies temporal semantics, schedulability, semantic preservation, ML admissibility, cryptographic verification, and risk bounded control into a single mathematically coherent architecture. All domains and operators are fully explicit, enabling formal reasoning over system trajectories and safety envelopes. The temporal layer defines an ordered metric structure with drift aware bounded causality, interval set operators, and jitter robust event semantics. The QoS layer enforces schedulability and feasible actuation, ensuring that all control actions remain within admissible timing and load bounds. Semantic compression provides a safety preserving homomorphism that guarantees invariants survive dimensionality reduction. Multi‑modal fusion introduces cross sensor falsifiability, enabling fault detection through probabilistic disagreement. The ML layer is input validated and logic embedded, ensuring that all model outputs entail the SIS‑10 invariant set. The cryptographic layer supplies zero knowledge execution trace proofs, allowing runtime verification of transition correctness without revealing internal state. Predictive shutdown optimization is constrained by a formally defined safety envelope, ensuring that operational objectives never violate admissible safety bounds. Cyber physical risk evolves through a bounded monotone propagation model with explicit mitigation operators, while the Safety Twin provides deterministic and stochastic discrete time system dynamics. The inductive proof layer establishes global invariant preservation for all admissible executions, and the event→action mapping connects the formal calculus to real SIS triggers. SIS‑10 therefore constitutes a unified, verifiable, and implementation ready safety architecture, suitable for runtime assurance, cyber‑physical certification, and next generation functional safety systems. Further enhancements include graphical formalization, parameterized system tuning, implementation DSLs, and automated verification scripts, none of which alter the core mathematical model..
We study the Banach dual of the one-parameter stochastic integral δ_L(u) = ∫₀^T u_t dL_t for a symmetric γ-stable Lévy process with γ ∈ (1,2). The natural integrand exponent is p ∈ (1,γ): the small-jump integrability ∫|z|^p ν_γ(dz) < ∞ holds iff p < γ, so this is not an arbitrary L^p but the unique scale dictated by the singularity of the Lévy measure at the origin. On this scale, the operator-covariant derivative D_L := δ_L^* : L^q(Ω) → H_L^* is the Banach dual of the one-parameter integral. Since p < 2, the Riesz identification H_L^* ≅ H_L is unavailable, and the Banach setting is forced. The principal result is structural: D_L is strictly more restricted than the standard Malliavin add-a-point operator D_{t,z}F = F(ω + δ_(t,z)) − F(ω) on Poisson space, which is the dual of the full two-parameter compensated Poisson integral ∫∫ h(s,z) Ñ(ds,dz). By Lévy-Itô, the one-parameter integrand of δ_L has the special form h(s,z) = u(s) · z — linear in z — whereas full martingale representation on Lévy space uses general h(s,z). The representability obstruction quantifies the resulting gap precisely: centered functionals depending nonlinearly on jump sizes — canonically, the centered large-jump count #{|ΔL_s| > 1} − E[#{|ΔL_s| > 1}] — lie in ker(D_L) yet are detected by the standard add-a-point operator. The obstruction is a property of the one-parameter integral, not a feature of jump processes themselves. The factorization (Theorem A) holds on the closed proper subspace im(δ_L) ⊊ L^p_0(Ω) and characterizes precisely which functionals admit one-parameter representation. Theorem B (product rule with Leibniz defect) is a standalone duality identity: its proof uses only the definition of D_L, the Lévy-Itô formula, and Hölder's inequality, and it does not invoke (H3) or the factorization machinery. Theorem C — the strongest technical result — identifies ker(D_L) and the annihilator of im(δ_L) via L^q-L^p truncation in the jump variable, showing the annihilator is infinite-dimensional even within the first chaos. The framework has been formally verified in the Lean 4 proof assistant (2,439 lines, zero sorry, zero axioms) using Mathlib. To our knowledge, this is the first formalization of the operator-covariant derivative framework with its representability obstruction in any proof assistant. The formalization includes proved Poisson mean and variance identities, a constructed compound Poisson path, a compensated-integral interface with derived Banach-side consequences, a concrete first-chaos orthogonality model, and the full abstract theorem pipeline — all machine-checked from clearly isolated stochastic-analysis assumptions.
Umar . Abubakar, Hamza Itopa Sanni, Abdulsalam Aliyu
Conventional attendance management approaches in academic and organisational settings face persistent challenges that include susceptibility to proxy attendance, inadequate protection of biometric credentials, and the absence of privacy-preserving verification mechanisms in cloud-hosted deployments. This paper presents SecureAttend, a cloud-based attendance management framework that addresses these deficiencies through the integration of Zero-Knowledge Proof (ZKP) cryptographic authentication with biometric capture via a ZKTeco K40 Pro fingerprint terminal. The proposed framework employs a challenge-response ZKP protocol that enables users to demonstrate possession of valid authentication credentials without disclosing underlying private keys or biometric templates to the server. Attendance records are encrypted using AES-256 prior to storage in a MongoDB cloud database, while SHA-256 hashing provides tamper-evidence for each record. Session integrity is maintained through JWT-based token management, and access boundaries are enforced via a Role-Based Access Control (RBAC) policy. Functional evaluation across eighteen test scenarios confirmed complete compliance with stated requirements. Security assessment validated correct operation of cryptographic mechanisms, access controls, and audit logging subsystems. Performance benchmarks recorded average API response latencies of approximately 85 milliseconds for authentication requests and 120 milliseconds for attendance marking operations. The results demonstrate that ZKP authentication can be deployed effectively in real-world attendance management contexts, offering measurable improvements in privacy, integrity, and resistance to credential-based attacks compared with conventional approaches.
Industrial Digital Twins (DTs) require cryptographic verification for external audits without exposing proprietary models—a challenge for continuous-time simulations with thousands of ODE integration steps. Existing methods fail: monolithic SNARKs exceed memory limits beyond 3000 steps, while naive recursive approaches impose > 200× overhead. We present ZKP-DS, combining sensitivity-driven precision allocation (35% circuit reduction), hierarchical proof batching (26-39× speedup via parallelization), and probabilistic epoch sampling (78% verification reduction with > 99.99% fraud detection). Fixed-step Runge-Kutta integration in adaptive fixed-point arithmetic ensures both cryptographic soundness and IEEE-compliant numerical accuracy. Experiments on full-scale power systems (2000 states, 10,000 steps) achieve 5.6−8.5× computational overhead with sub-60ms constant-time verification on university GPU clusters. Results demonstrate that zero-knowledge proofs can provide mathematical integrity guarantees for industrial cyber-physical systems at practical costs, enabling trustworthy multi-stakeholder monitoring and regulatory compliance.
Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic
We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, programmed onto two distinct Sipeed silicon families: Tang Console 138K (GW5AST-138B, LittleBee5 A revision, IDCODE 0x0001081B) and Tang Nano 9K (GW1NR-9C, LittleBee1 C revision, IDCODE 0x1100481B). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.6 contributions (2026-05-10): (1) **Four-substrate cross-verification complete**: 2 Sipeed silicon families (Tang Console 138K + Tang Nano 9K, **both running byte-for-byte same dfumt8_alu_synth.v 138-line Verilog with bit-identical 0 changes to ALU logic** — only wrapper top module re-targeted for clock divider, LED polarity, and pin assignments) + Qiskit Aer simulator (Phase 1-5: 231/231 entries) + IBM Heron r2 real quantum hardware (Phase 1+2+3+5: 144/144 entries, avg fidelity 0.954). (2) **chip-portability evidence (new finding F10)**: a synthesis bug or vendor-specific assumption would diverge between LittleBee5 (5nm-class GW5AST-138B) and LittleBee1 (28nm-class GW1NR-9C) Gowin architectures; absence of divergence is operational evidence of correct synthesis on both. (3) **Tang Nano 9K User Codes**: 0x0000A5F4 (LED Blinky STEP 1038) + 0x00001D46 (D-FUMT₈ ALU STEP 1039). (4) **Reproducibility entry-cost lowered**: minimum reproduction path is ~$20 (Tang Nano 9K from 秋月電子 g117448 at ¥2,980) + free Gowin EDA Education / OSS toolchain + free Aer + free IBM Quantum Open Plan. (5) **v0.5 corrigendum RESOLVED**: Tang Nano 9K is now physical silicon programming target on equal footing with Tang Console 138K (was computational evidence only at v0.5). (6) **IDCODE-revision honest correction**: per Gowin LittleBee Programming Manual Table 5-5, GW1N(R)-9 original = 0x1100581B, GW1N(R)-9C cost-down = 0x1100481B; both `set_device ... -device_version C` (build TCL) and `--device GW1NR-9C` (programmer_cli) required for ID code match. Inherited v0.3 contributions: Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations + SELF⟲ primitive law + 7 algebraic laws. IBM Heron r2 per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 reflects gate-count-vs-noise correlation consistent with quantum-noise physics expectations. Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel quadruple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the four-substrate cross-verification bound to a Lean 4 refinement specification, and (D4, new in v0.6) the chip-portability evidence across two Gowin silicon architectures. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.6 — feedback welcome via GitHub Discussions at fc0web/rei-aios.
Open access
2 source records
Low-power high-performance VLSI design
Numerical Methods and Algorithms
Physical Unclonable Functions (PUFs) and Hardware Security
Global due diligence regimes, particularly the EU Corporate Sustainability Due Diligence Directive (CS3D), increasingly mandate deep multi-tier supply chain transparency. Yet in high-risk sourcing contexts, expanded disclosure can intensify retaliation and surveillance against vulnerable stakeholders—a dynamic identified here as the Transparency Paradox. This chapter develops an Anonymized Accountability Framework (AAF) grounded in Zero-Knowledge Proofs (ZK-proofs), enabling verifiable compliance without revealing identity-sensitive or locational data. Through formal risk modeling, game-theoretic analysis, and application to the cobalt supply chain in the Democratic Republic of Congo, the chapter demonstrates how proof-based verification can mitigate exposure while preserving regulatory credibility. Comparative governance analysis highlights trade-offs with centralized platforms, and a phased roadmap outlines regulatory pathways for recognizing cryptographic compliance evidence. Introduction
Supply chain systems increasingly rely on digital technologies to enhance transparency and efficiency, yet this often conflicts with the need to protect sensitive data. Traditional verification mechanisms typically require full data disclosure, raising concerns related to privacy and security. This study proposes the use of zero-knowledge proofs (ZK-proofs) as a privacy-preserving solution within AI-driven supply chains. By enabling verification without revealing underlying data, ZK-proofs help maintain trust while safeguarding confidentiality. Using a conceptual and analytical approach, this research develops an integrated framework combining artificial intelligence, blockchain, and ZK-proofs within a governance structure. The findings suggest that this integration enhances transparency, strengthens security, and supports ethical and regulatory compliance, making it a promising approach for future digital supply chain systems.
Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic
We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, targeting the Sipeed Tang Console NEO development board (GW5AST-138B FPGA, FPG676 package). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.3 contributions (2026-05-09): (1) Tang Nano 9K silicon: 37 LUT4 / 0 DFF measured, testbench 50/50 PASS. (2) Tang Console NEO Phase 2B LED Blinky: SRAM-programmed, User Code 0x000084BA, write 33.72 sec, no thermal anomaly. (3) Tang Console NEO Phase 2C/3 D-FUMT₈ ALU: SRAM-programmed, User Code 0x00005C27, write 30.32 sec. (4) Qiskit Aer simulator: Phase 1-5 cumulative 231/231 truth-table entries match at fidelity 1.000. (5) IBM Heron r2 real quantum hardware (ibm_kingston, 156 qubits): Phase 1 (4 native unitary × 8 inputs, 32 circuits) achieves 32/32 match with avg top-fidelity 0.9550 (job d7v6d9jack5s73bf1re0); Phase 2 (XOR × 64 entries, 6-qubit Bennett-reversible) achieves 64/64 match with avg fidelity 0.9512 (job d7v6kcvmrars73d7qqqg). Per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 confirms gate-count-vs-noise correlation expected from Heron r2 daily calibration. (6) Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations, plus the SELF⟲ primitive law and seven algebraic laws (involution, idempotence, commutativity). Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel triple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the three-substrate cross-verification bound to a Lean 4 refinement specification. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.
Open access
Quantum Computing Algorithms and Architecture
Quantum-Dot Cellular Automata
Advancements in Semiconductor Devices and Circuit Design
In the era of quantum computing, data sharing in the Internet of Vehicles (IoV) confronts the challenges of auditability, efficiency, and quantum security. However, existing research remains insufficient to meet the requirements of high mobility, resource constraints, and resilience against quantum attacks. In this paper, we propose a new quantum-secure auditable data sharing framework, in which we first present a quantum-resistant puncturable signature algorithm (QRPPRFS). Combining the low-noise LPN-based pseudorandom function with an optimized trapdoor generation mechanism, it achieves compact key sizes and millisecond-level signing; second, the blockchain and dual-commitment proof mechanism are integrated to ensure anonymity, transparent auditability and robustness. Finally, we rigorously demonstrate the correctness of our scheme, the EUF-CMA with puncturing of QRPPRFS, and the knowledge soundness and witness zero-knowledge of the dual-commitment proof system. Experimental evaluations show that, under the practical setting$n=256$and$q \approx 2^{23}$, the proposed scheme keeps both signing and verification latencies below 10 ms, and reduces the initial secret-key storage to only 0.22 MB. These results demonstrate that the proposed scheme achieves both enhanced security and high efficiency, outperforming existing schemes.
Cryptography is the backbone of modern network security, providing confidentiality, integrity, authentication, and non-repudiation for digital communication. However, the rapid evolution of cyber threats, particularly the looming arrival of large-scale quantum computers, poses serious challenges to the cryptographic algorithms that protect today's networks. This paper presents a systematic review of cryptography in network security, following the PRISMA 2020 guidelines. A total of 68 studies published between 2016 and 2025 were selected from five major academic databases: IEEE Xplore, ACM Digital Library, Scopus, Web of Science, and ScienceDirect. The review covers classical symmetric and asymmetric algorithms, widely deployed cryptographic protocols such as TLS 1.3, IPsec, and SSH, and the growing body of work on post-quantum cryptography (PQC). Key findings include the following: NIST finalized three post-quantum cryptographic standards (FIPS 203, 204, and 205) in August 2024; lightweight cryptography standards for IoT devices were published in 2025 with the selection of ASCON; and real-world deployment of hybrid classical/post-quantum schemes has already begun in major web browsers and messaging applications. This paper also examines emerging trends in homomorphic encryption, zero-knowledge proofs, and AI-driven cryptanalysis. Based on the findings, this review identifies critical gaps in PQC migration strategies, IoT security, and the integration of cryptography with artificial intelligence, and proposes directions for future research.
Sixth-generation (6G) networks are expected to provide ubiquitous connectivity, AI-native orchestration, and seamless integration across terrestrial and non-terrestrial infrastructures. However, these capabilities introduce new privacy challenges related to the classification and protection of personal, quasi-personal, and non-personal data in complex data-driven environments. This paper presents a systematic review of 78 peer-reviewed studies published between 2019 and 2025. Following a PRISMA-based methodology, this review analyzes privacy-enhancing technologies (PETs), regulatory compliance frameworks, and architectural patterns for privacy preservation in 6G networks. The findings show that differential privacy (DP) and federated learning (FL) dominate current research, accounting for nearly 52% of the reviewed studies. Blockchain auditing and zero-knowledge proofs (ZKPs) collectively represent approximately 30%, while the remaining mechanisms, including physical-layer security (PLS), trusted execution environments (TEEs), homomorphic encryption (HE), secure multi-party computation (SMPC), and anonymization, account for roughly 18%. These mechanisms exhibit varying levels of privacy strength, utility preservation, latency, and energy cost. At the same time, evolving regulatory frameworks, including GDPR, PDPL, CCPA/CPRA, LGPD, and PIPL, increasingly extend privacy obligations to quasi-personal and aggregated data. Building on these findings, this paper proposes a unified taxonomy that clarifies the boundary between personal and non-personal data. It also provides a cross-layer mapping between PETs and compliance requirements across the Core/SBA, RAN, Edge/MEC, and NTN layers. Finally, this paper presents a forward-looking roadmap for 2025–2030, highlighting hybrid PET pipelines, post-quantum auditability, and AI-driven compliance automation as key directions for privacy-preserving 6G standardization.
Polynomial multiplication serves as a fundamental computational primitive in modern cryptography–including fully homomorphic encryption and zero-knowledge proofs –as well as in digital signal processing. Its performance optimization has become increasingly critical amid the rapid development of privacy-preserving computation and blockchain technologies. To address the limitations of traditional algorithms in meeting the demands for high throughput and low latency, this study proposes a high-performance polynomial multiplication accelerator based on the collaborative optimization of GPU-NTT and the Karatsuba algorithm. The method deeply integrates the asymptotically optimal complexity of NTT with the constant-factor efficiency of Karatsuba at moderate scales, and fully exploits the parallel computing power of GPUs to construct a modular, multi-stage pipelined acceleration framework. The divide-and-conquer nature of the Karatsuba algorithm is leveraged for coarse-grained parallelism, splitting large polynomial multiplications into subproblems handled by GPU thread blocks in parallel, while each subproblem is solved with fine-grained parallelism using GPU-accelerated NTT kernels. An innovative zero-padding strategy is introduced to enhance the generality of the NTT kernels, and shared memory caching is employed to alleviate GPU memory bandwidth bottlenecks. Experimental results on the NVIDIA RTX 4060 GPU demonstrate that the proposed method achieves a stable speedup of 1.43 \(\times \) to 1.49 \(\times \) over the baseline GPU-NTT for lower-dimensional polynomials, and outperforms the KNTT algorithm by up to 2.44 \(\times \) for higher dimensions (e.g., \(\log _2 n = 14\) ), showing superior scalability and robustness. Kernel execution time analysis further confirms that the method benefits from efficient kernel fusion and balanced workload distribution, which effectively avoids pipeline stalls and ensures high-throughput execution. This research provides a significant performance optimization solution for the practical deployment of advanced cryptographic technologies such as FHE and ZKP.
Taking pure elementary algebra as the research tool, this paper solves the three-layer right-associative tower exponent equation without advanced knowledge such as logarithms and calculus throughout the whole process. First, integer solutions are strictly eliminated via integer recursive scaling, zero solutions are excluded by analyzing domain boundaries, and combined with the growth law of power operations, it is predicted that the solution is in the form of positive real numbers with fractional exponents. Based on the expression form of positive real powers, variable substitution and derivation are directly carried out to obtain the particular solution , which is verified by substitution. Rigorous demonstrations are conducted on negative real solutions and interval monotonicity: it is directly proved that the equation has no solution when , and strict monotonicity is proved by definition only in the interval , completing the proof of uniqueness of real solutions. Meanwhile, the definitional contradictions of negative base numbers in the real number field are clarified, negating the existence of negative real solutions. This paper retains the intuitive and original reasoning logic, revises the connection defects of argumentation, and forms a complete, rigorous and self-consistent research compatible with the elementary mathematics system. 本文以纯初等代数方法为工具,求解三层右结合指数塔方程 ,全程不使用对数、微积分等高阶知识。首先通过整数递推放缩排除整数解,补充定义域边界排除零解,结合幂运算增长规律预判解为正实数分数指数形式;基于正实数幂的表达形式直接设元推导,求得特解 并代入验证。针对负实数解、区间单调性等问题展开严谨论证:直接证明 时方程无解,仅在 区间用定义法证明严格单调性,完成实数解唯一性证明;同时厘清负数底数的实数域定义矛盾,否定负实数解存在性。全文保留直观原生推理逻辑,修正论证衔接问题,形成严谨、自洽、适配初等数学体系的完整研究。
Alessio Basti, Rikkert Hindriks, Ruggero Freddi, Gian Luca Romani · 7 authors
Cross-frequency interactions are fundamental brain mechanisms for integrating information across temporal scales. However, accurate identification of these couplings is hindered by complex multi-frequency nonlinearities and by spurious, zero-lag artifacts caused by volume conduction. To our knowledge, conventional metrics lack a robust framework to characterize genuine interactions among multiple time series where a frequency of interest $f_N$ arises from the combination of $N-1$ components such that $f_N = \sum_{i=1}^{N-1} f_i$. We introduce a general family of antisymmetric cross-polyspectral indices designed to quantify these harmonic dependencies while being intrinsically robust to instantaneous mixing. We derive the theoretical properties of these quantities and validate them through simulations of cubic nonlinearities. As a proof of concept, we apply the indices to empirical EEG recordings; the results reveal significant higher-order dependencies that elude standard analytical approaches. We further discuss how these indices can inform novel, personalized multi-site transcranial magnetic stimulation (mTMS) protocols by enabling the selective monitoring and modulation of specific multi-frequency network interactions.