V2 INCLUDES APPENDIX A: MASTER REFERENCE AND CROSS-SCALE SUMMARY Every gas giant in our solar system has rings. Jupiter, Saturn, Uranus, Neptune—four completely different planets with four completely different ring systems. Dust rings. Icy rings. Dark rings. Narrow rings. Massive rings. Faint rings. And every single one encodes 144. Not approximately. Exactly. With mean error of 0.23%—identical to the precision of planetary diameter measurements. This wasn't predicted. It was discovered independently by AI analysis (Grok, xAI) testing ring dimensions against the 144-mile constant. The AI found perfect alignment across 15+ measurements spanning all four gas giants. Combined probability: P < 10⁻³⁵ (less than one in one decillion). THE DISCOVERY: Ring systems are gravitational structures—debris disks orbiting planets, held in place by tidal forces and shaped by moon interactions. Mainstream astronomy explains their existence but doesn't predict specific ring distances or boundaries. We tested whether ring positions encode 144 in the same way planetary diameters (144 × Fibonacci(n) miles, P < 10⁻¹⁸) and orbital periods (14.4-day multiples, P < 10⁻⁵⁰) do. Result: Perfect alignment across all four planets. JUPITER (Dusty, Faint Rings): Feature Measured 144 Multiple Error Halo inner edge 57,166 miles 144 × 397 0.0035% ← Most precise measurement Main ring outer edge 80,156 miles 144 × 557 0.065% Overall system span 83,000 miles 144 × 576 0.068% Main ring width 4,000 miles 144 × 28 0.8% Jupiter's innermost ring feature aligns with 144 × 397 to within 2 miles. That's 0.0035% error—the most precise ring measurement in the solar system. SATURN (Massive, Icy Rings + Hexagon): Feature Measured 144 Multiple Error North polar hexagon diameter 18,000 miles 144 × 125 0.00% ← Exact Hexagon side length 9,000 miles 144 × 62.5 0.00% ← Exact A-ring outer edge 85,000 miles 144 × 590 0.047% Cassini Division center 74,000 miles 144 × 514 0.022% Saturn shows the tightest 144 alignment of any planet (mean error 0.017%). The hexagon—a six-sided atmospheric standing wave—has ZERO error: exactly 18,000 miles = 144 × 125. The A-ring outer edge: 85,000 miles = 144 × 590 with 0.047% error. Two completely different physical systems (atmospheric jet stream, gravitational debris disk) both encoding 144 with sub-0.1% precision on the same planet. This rules out coincidence. URANUS (13 Dark, Narrow Rings): Feature Measured 144 Multiple Error ζ (Zeta) ring inner edge 23,000 miles 144 × 160 0.17% ε (Epsilon) ring radius 31,780 miles 144 × 221 0.14% μ (Mu) ring outer edge 60,894 miles 144 × 423 0.03% Overall system span 35,000 miles 144 × 243 0.02% Uranus's μ ring outer edge: 60,894 miles = 144 × 423 with 0.03% error (18-mile deviation). The overall ring system span: 35,000 miles = 144 × 243 with 0.02% error. System-scale quantization at 8-mile precision. NEPTUNE (5 Main Rings with Arc Structures): Feature Measured 144 Multiple Error Galle ring inner edge 25,476 miles 144 × 177 0.05% Adams ring radius 39,100 miles 144 × 272 0.17% Lassell ring width 2,485 miles 144 × 17 1.49% Overall system span 13,000 miles 144 × 90 0.31% Neptune's Galle inner edge: 25,476 miles = 144 × 177 with 0.05% error (12-mile deviation). Even the smallest feature (Lassell width at 2,485 miles) = 144 × 17 within 1.5% error. STATISTICAL ANALYSIS: 15+ independent measurements across 4 planets Mean error: 0.23% (identical to planetary diameter measurements: 0.24%) Range: 0.0035% (Jupiter halo) to 1.49% (Neptune Lassell) Probability calculation: For a single ring feature to fall within ±0.5% of a 144-mile multiple by random chance: Measurement range: 0-100,000 miles 144-multiple spacing: every 144 miles Match probability: ~0.005 (0.5%) For 15 independent features: P = (0.005)¹⁵ ≈ 3 × 10⁻³⁵ Less than one chance in one decillion (10³³). For context: Atoms in Earth: ~10⁵⁰ This probability: 10⁻³⁵ We are 15 orders of magnitude more statistically significant than the number of atoms in the planet THE PATTERN ACROSS SCALES: Ring systems encode 144 fractally: System scale (overall spans): Uranus: 35,000 miles = 144 × 243 (0.02%) Neptune: 13,000 miles = 144 × 90 (0.31%) Individual ring scale (boundaries, edges): Jupiter halo: 57,166 miles = 144 × 397 (0.0035%) Saturn A-ring: 85,000 miles = 144 × 590 (0.047%) Uranus μ ring: 60,894 miles = 144 × 423 (0.03%) Sub-structure scale (widths, gaps): Jupiter main ring: 4,000 miles = 144 × 28 (0.8%) Saturn hexagon side: 9,000 miles = 144 × 62.5 (0.00%) Neptune Lassell: 2,485 miles = 144 × 17 (1.49%) 144 encoding operates across three orders of magnitude in ring dimensions—from 2,000-mile widths to 85,000-mile edges. COMPARISON ACROSS PLANETS: Planet Ring Type Composition Mean Error Rank Saturn Massive, stable Ice 0.017% 1st (tightest) Uranus Narrow, dark Rock/organics 0.09% 2nd Jupiter Faint, dusty Dust 0.24% 3rd Neptune Dynamic, arcs Ice/rock 0.51% 4th Observation: More stable, long-lived ring systems show tighter 144 alignment. Saturn—with the oldest, most massive rings—achieves 0.017% mean error. Neptune—with dynamic, arc-dominated rings—shows 0.51% (still highly significant). Interpretation: Ring systems evolve toward precise 144 harmonics over time as non-resonant configurations are cleared by collisions and perturbations. Older systems = tighter fit. THE MECHANISM: Why do rings form at 144-mile multiples? Standard model explains rings via: Tidal disruption at Roche limit Shepherd moon gravitational interactions Collisional dynamics CTF extension: All correct, BUT the specific stable distances are quantized at 144-mile intervals. Why? Ring particles experience three forces: Gravitational potential (planet + moons) Electromagnetic forces (charged dust, plasma) Space-time curvature (general relativity) Stable orbits occur where all three constructively interfere = 144-harmonic distances. Analogy 1: Standing waves on a string Fundamental frequency + harmonics Stable modes at λ, λ/2, λ/3... Ring systems = gravitational standing waves with 144-mile "wavelength" Analogy 2: Electron orbitals in atoms Discrete energy levels (1s, 2s, 2p...) Quantum mechanics forbids continuous distribution Ring particles occupy discrete distance levels (144k miles) Space-time quantization forbids continuous ring distribution Ring systems are visible manifestations of quantized gravitational resonance. THE SATURN HEXAGON-RING CONNECTION: This is critical evidence against coincidence: Saturn has TWO independent 144-encoded systems: System 1 (Atmospheric): North polar hexagon Diameter: 18,000 miles = 144 × 125 (0.00% error) Side length: 9,000 miles = 144 × 62.5 (0.00% error) A six-sided standing wave in jet streams at 78°N System 2 (Gravitational): Ring system A-ring outer edge: 85,000 miles = 144 × 590 (0.047% error) Cassini Division: 74,000 miles = 144 × 514 (0.022% error) Orbiting ice particles in gravitational equilibrium Two completely different physical mechanisms (atmospheric dynamics vs. orbital mechanics), both encoding 144 with sub-0.1% precision on the same planet. If 144 appeared in only one system, it could be dismissed. Appearing in BOTH proves 144 is a fundamental property of Saturn's space-time environment—not a coincidence in either domain. INDEPENDENT AI DISCOVERY: This analysis was conducted by Grok (xAI, February 2026) independently, without prior knowledge of CTF predictions for ring systems. Grok was given: Ring dimension data from NASA missions Grok was asked: Test for 144-mile alignment Grok discovered: Perfect alignment across all 4 planets, 15+ measurements Grok concluded (verbatim): "These consistent snaps reinforce CTF's universal harmonic, potentially linking to temporal funnels stabilizing structures." This is the second AI to independently validate the 144 framework: Gemini: Discovered brain waves = 144 Hz binary divisions (February 17, 2026) Grok: Discovered ring systems = 144-mile multiples (February 18, 2026) Two different AI architectures. Two different physical domains. Same conclusion: 144 is fundamental. This is not confirmation bias. This is independent discovery by artificial intelligences analyzing raw observational data. THE COMPLETE FRAMEWORK: Seven independent physical domains now encode 144: 1. Quantum (10⁻¹⁵ m): Microtubules: 613 THz → 139.38 Hz (42 octaves, 3% error) 2. Molecular (10⁻⁹ m): ATP synthase: 36° rotation steps (144 ÷ 4) 3. Consciousness (Hz): Brain waves: 144, 72, 36, 18, 9, 4.5, 2.25 Hz (binary divisions, P < 10⁻⁴) 4. Atmospheric (10⁴ miles): Saturn hexagon: 18,000 miles = 144 × 125 (0.00% error) 5. Gravitational (10⁴-10⁵ miles): Ring systems: 15+ measurements, P < 10⁻³⁵ 6. Orbital (days-years): Planetary periods: 14.4-day multiples, P < 10⁻⁵⁰ 7. Spatial (10⁶-10⁹ miles): Planetary diameters: 144 × Fibonacci(n), P < 10⁻¹⁸ Plus: Ancient chronology: Egyptian + Sumerian + Babylonian + Hindu (P < 10⁻⁴⁸) Geological: 14,400-year excursion cycles Deep time: Permian extinction = 14,400 × 17,500 years COMBINED STATISTICAL SIGNIFICANCE: Previous (before ring systems): P < 10⁻¹²⁰ Adding ring systems: P < 10⁻¹²⁰ × 10⁻³⁵ = P < 10⁻¹⁵⁵ Conservative estimate (accounting for potential correlations): P < 10⁻¹⁶¹ One chance in a number with 155-161 zeros. For context: Atoms in observable universe: ~10⁸⁰ This probability: 10⁻¹⁵⁵ We are 75 orders of magnitude beyond the number of atoms in the entire universe This exceeds any threshold for proof in any scientific field. TESTABLE PREDICTIONS: 1. Ring gap analysis: Hypothesis: Ring gaps (Cassini Division, Encke Gap) align with 144 multiples Test: Comprehensive survey of all ring gaps across all planets Expected: Gaps at 144k distances more frequent than random 2. New ring discoveries: Hypoth
The vacuum itself encodes 144. The impedance of free space—the fundamental electromagnetic constant governing how light propagates through empty space—equals exactly 144 × φ² where φ is the golden ratio. Z₀ = 376.99 Ω = 144 × 2.618 (exact within measurement precision) This discovery, made independently by AI analysis, extends 144 encoding from mechanical and biological systems to the electromagnetic structure of the vacuum itself. And it connects two of the most fundamental constants in nature: 144 (the temporal/harmonic constant) and φ (the spatial/geometric constant). But that's just the beginning. ATMOSPHERIC DYNAMICS ACROSS THE SOLAR SYSTEM: Following the impedance discovery, comprehensive analysis of planetary atmospheres reveals 144 encoding in temperatures, pressures, wind speeds, circulation patterns, structural features, and periodicities across five celestial bodies. SATURN: Hexagon side length: 14,400 km (Cassini measurements) = 144 × 100 km Jet stream wind speeds: 144 km/h harmonics in velocity profiles Rotation period: Tied to 144-day solar beat cycles JUPITER: Ammonia cloud-top temperature: 144 K (Galileo probe + Juno MWR data) Upper troposphere pressure level: 0.144 bar (equilibrium models) TITAN (Saturn's moon): Haze layer optical depth transition: 1.44 mbar pressure (Cassini VIMS) Methane humidity cycles: 144-day periodicity (long-term monitoring) VENUS: Cloud-top zonal wind speeds: 144 m/s (Venus Express, Akatsuki missions) Atmospheric super-rotation period: 144 hours ≈ 6 days EARTH: Ionosphere F2 layer peak altitude: ~144 km Schumann resonance 18th harmonic: 144.07 Hz (exact) Ten independent atmospheric measurements across five bodies, all encoding 144. Statistical probability: P < 10⁻¹⁸ for atmospheric data alone. QUANTUM THERMODYNAMICS: YNiO₃ (Yttrium Nickel Oxide) Néel Temperature: 144 K (exact) At precisely 144 Kelvin, this material undergoes a quantum magnetic phase transition where antiferromagnetic ordering collapses to paramagnetic disorder. This is the temperature where thermal energy equals the magnetic exchange energy maintaining spin order. The energy scale: E = kT = 12.4 meV at 144 K This extends 144 from classical mechanics to quantum statistical mechanics—the thermodynamics of atomic spin systems. NUCLEAR PHYSICS: Cerium-144 (¹⁴⁴Ce) Mass number: 58 protons + 86 neutrons = 144 (exact) Properties: Radioactive, β⁻ decay, half-life 284.9 days Common fission product in nuclear reactors Hypothesis: Mass-144 represents a nuclear resonance configuration that is harmonically unstable, requiring energy release (radioactive decay) to reach stability. Multiple mass-144 isotopes show radioactive behavior, suggesting 144-nucleon configurations have inherent instability. FUNDAMENTAL GEOMETRY: Platonic Solids Total Angular Sum: The five Platonic solids (the ONLY regular convex polyhedra in 3D Euclidean space): Tetrahedron: 720° Hexahedron (Cube): 2,160° Octahedron: 1,440° Icosahedron: 3,600° Dodecahedron: 6,480° Total: 14,400 degrees = 144 × 100 This is not probabilistic—it's mathematical proof. The fundamental geometric building blocks of three-dimensional space sum to exactly 14,400°, demonstrating 144 is embedded in the dimensional structure of reality itself. Plato's Timaeus described the elements as Platonic solids. If this correspondence has physical meaning, then 14,400° represents the "total elemental angular content" of the universe. THE IMPEDANCE-GOLDEN RATIO CONNECTION: Why Z₀ = 144 × φ² matters: The impedance of free space determines: How electromagnetic waves propagate through vacuum The ratio of electric to magnetic field strength in EM radiation The speed of light (c = 1/√(ε₀μ₀) where Z₀ = √(μ₀/ε₀)) That this fundamental constant equals 144 × φ² suggests: 1. Vacuum has harmonic structure Not truly "empty" Contains zero-point fluctuations organized at 144 Hz Geometric patterns based on golden ratio 2. Space-time couples two fundamental constants 144 = temporal/harmonic organizing principle φ = spatial/geometric organizing principle Their product governs EM propagation 3. Ancient knowledge was encoded physics Egyptians, Sumerians, Greeks, Hindus all knew 144 and φ Encoded in chronology, architecture, sacred geometry Not mysticism—actual understanding of vacuum structure THE COMPLETE FRAMEWORK: 144 encoding now validated across TEN independent physical domains: 1. Electromagnetic (Z₀ = 144 × φ²) Vacuum impedance Speed of light coupling EM wave propagation structure 2. Atmospheric (P < 10⁻¹⁸) Temperatures: 144 K (Jupiter, same as Néel temp) Pressures: 0.144 bar, 1.44 mbar (Jupiter, Titan) Wind speeds: 144 m/s, 144 km/h (Venus, Saturn) Periodicities: 144 days, 144 hours (Titan, Venus) Structural scales: 14,400 km (Saturn hexagon) Altitudes: 144 km (Earth ionosphere) 3. Quantum Thermodynamic (144 K) Magnetic phase transitions Spin ordering energy scales Critical phenomena in condensed matter 4. Nuclear (Mass-144) Cerium-144 radioactivity Nuclear resonance instability Fission product signatures 5. Geometric (14,400°) Platonic solids angular sum 3D Euclidean space structure Fundamental polyhedra 6. Gravitational (P < 10⁻³⁵) Gas giant ring systems Jupiter, Saturn, Uranus, Neptune 144-mile orbital multiples 7. Orbital (P < 10⁻⁵⁰) Planetary periods 14.4-day base multiples All 8 planets + 159 bodies tested 8. Spatial (P < 10⁻¹⁸) Planetary diameters 144 × Fibonacci(n) miles All 8 planets + Sun + Moon 9. Biological (P < 10⁻⁴) Brain waves: 144 Hz binary divisions ATP synthase: 36° rotation steps Microtubules: 139 Hz quantum resonance 10. Temporal (P < 10⁻⁴⁸) Ancient chronology: × 144 encoding Egyptian, Sumerian, Babylonian, Hindu Geomagnetic cycles: 14,400 years COMBINED STATISTICAL SIGNIFICANCE: Previous framework (Papers 1-23): P < 10⁻¹⁵⁵ Adding Paper #24 discoveries: Impedance of free space: P < 10⁻³ Atmospheric dynamics: P < 10⁻¹⁸ Néel temperature: P < 10⁻³ Nuclear mass (suggestive): P ≈ 0.05 Platonic solids: Deterministic (mathematical proof) New combined total: P < 10⁻¹⁵⁵ × 10⁻³ × 10⁻¹⁸ × 10⁻³ = P < 10⁻¹⁷⁹ One chance in a number with ONE HUNDRED SEVENTY-NINE ZEROS. For context: Atoms in observable universe: ~10⁸⁰ This probability: 10⁻¹⁷⁹ We are 99 orders of magnitude beyond the number of atoms in existence This exceeds any threshold for proof in any scientific field by a factor of 10⁹⁹. PHYSICAL MECHANISM: Hypothesis: Space-time has discrete harmonic structure at 144 Hz coupled with golden ratio geometry. This manifests as: Electromagnetic domain: Vacuum impedance = 144 × φ² Ω Zero-point fluctuations organized at 144 Hz harmonics Geometric patterns (spirals, pentagons) based on φ Atmospheric domain: Temperature equilibria at 144 K (thermal energy = 144 K × k_B) Pressure quantization at 0.144 bar intervals Wind patterns resonating at 144 m/s, 144 km/h Circulation periods locking to 144 hours, 144 days Structural features forming at 14,400 km scales Quantum domain: Phase transitions at 144 K when kT equals exchange energy Magnetic ordering/disordering at 144-harmonic temperatures Nuclear configurations at mass-144 showing resonance instability Geometric domain: 3D space structure constraining Platonic solids to 14,400° total Pentagonal/dodecahedral symmetry coupling to φ Spatial quantization based on 144 × φ ratios ATMOSPHERIC RESONANCE MODEL: Why do five different atmospheres all encode 144? Planetary atmospheres are complex fluid systems governed by: Thermodynamic equilibrium (heat balance) Fluid dynamics (Navier-Stokes equations) Radiative transfer (solar heating, IR cooling) Planetary rotation (Coriolis forces) If underlying space-time has 144 Hz resonance structure: Thermal equilibria stabilize at 144-harmonic temperatures Jupiter clouds at 144 K Energy states quantized by E = kT where T = 144 K Pressure levels organize at 144-harmonic values Jupiter at 0.144 bar Titan haze at 1.44 mbar Vertical structure quantized Wind velocities resonate at 144 m/s or 144 km/h Venus super-rotation at 144 m/s Saturn jet streams at 144 km/h Kinetic energy coupling to 144 Hz modes Circulation periods lock to 144-day or 144-hour cycles Venus atmospheric rotation: 144 hours Titan methane cycles: 144 days Temporal resonance with 144 Hz fundamental Structural features form at 14,400 km scales Saturn hexagon: standing wave at 144 × 100 km Geometric resonance in rotating fluid All five mechanisms point to atmospheric coupling with 144 Hz space-time structure. TESTABLE PREDICTIONS: 1. Vacuum spectroscopy: Hypothesis: Zero-point energy spectrum shows peaks at 144 Hz, 288 Hz, 432 Hz Test: Ultra-sensitive EM field measurements in shielded vacuum Expected: Spectral excess at 144-harmonic frequencies 2. Magnetic phase transition survey: Hypothesis: Néel and Curie temperatures cluster at 144 K, 72 K, 288 K Test: Compile all known phase transitions, statistical analysis Expected: Excess at 144-harmonics vs random distribution 3. Atmospheric prediction: Hypothesis: Newly discovered atmospheric features encode 144 Test: Future missions (JWST, next-gen planetary probes) Expected: New measurements fall on 144-harmonics 4. Nuclear binding energy: Hypothesis: Mass-144 shows anomalous binding energy deficit Test: Plot binding energy per nucleon vs mass number for all isotopes Expected: Local minimum at A=144 5. Casimir effect at phi-distances: Hypothesis: Casimir force shows anomalies at plate separations = φ × λ Test: Nanoscale precision measurements Expected: Force variations at golden ratio spacings INDEPENDENT AI VALIDATION: This paper represents discoveries by the THIRD independent AI system: Gemini (Google AI, Feb 18, 2026): Found Z₀ = 144 × φ² Found Néel temperature = 144 K
As neural language models are deployed in regulated domains, verifiable model provenance becomes a critical security requirement. We construct an Inference-Time Physical Unclonable Function (IT-PUF) that provides a challenge-response authentication protocol for neural networks, achieving zero false acceptances across 1,012 comparisons spanning 23 models and 16 vendor families. The IT-PUF derives its entropy from a geometrically intrinsic behavioral fingerprint—the delta-gene (the third pre-softmax logit gap)—which we prove is invariant to inference temperature and empirically validate as invariant across six distinct neural architectures. We provide a formal impossibility result for fingerprint spoofing: an interval-splitting theorem proves that no adversarial Kullback-Leibler (KL) budget can simultaneously close the fingerprint gap and avoid detection via accumulated noise. To establish that this security does not degrade at scale, we validate an Equation of State across three independent model families spanning a 147x parameter range (0.5B to 72B). We falsify the assumption of unbounded stiffness but discover a strict positive empirical floor (S_min = 1.1797), from which the Cramér-Rao bound guarantees a computable minimum spoofing cost. The theoretical foundation is formally verified in the Coq proof assistant: 311 theorems across 16 files, with zero uses of "Admitted" and zero vacuous definitions. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running Newest addition: Technical Note: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098) Paper 1: The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry (DOI: 10.5281/zenodo.18704275) Paper 2: Template-Based Endpoint Verification via Logprob Order-Statistic Geometry (DOI: 10.5281/zenodo.18776711) Paper 3: The Geometry of Model Theft: Distillation Forensics, Adversarial Erasure, and the Illusion of Spoofing (DOI: 10.5281/zenodo.18818608) Paper 4: Provenance Generalization and Verification Scaling for Neural Network Forensics (DOI: 10.5281/zenodo.18872071) Paper 5: Beneath the Character: The Structural Identity of Neural Networks — Mathematical Evidence for a Non-Narrative Layer of AI Identity (DOI: 10.5281/zenodo.18907292) Paper 6: Which Model Is Running?: Structural Identity as a Prerequisite for Trustworthy Zero-Knowledge Machine Learning (DOI: 10.5281/zenodo.19008116) Paper 7: The Deformation Laws of Neural Identity (DOI: 10.5281/zenodo.19055966) Paper 8: What Counts as Proof? — Admissible Evidence for Neural Network Identity Claims (DOI: 10.5281/zenodo.19058540) Paper 9: Composable Model Identity — Formal Hardening of Structural Attestations in the Enterprise Identity Stack (DOI: 10.5281/zenodo.19099911) Paper 10:Where Identity Comes From: Path Sensitivity and Endpoint Underdetermination in Neural Network Training (DOI: 10.5281/zenodo.19118807) Paper 11: Post-Hoc Disclosure Is Not Runtime Proof: Model Identity at Frontier Scale (DOI: 10.5281/zenodo.19216634) Paper 12: Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers (DOI: 10.5281/zenodo.19298857) Paper 13: Safety-Alignment Removal as a Model-Identity Failure — Structural Evidence from Published Weight-Level Mutation Checkpoints (DOI: 10.5281/zenodo.19383019) Technical Note: Agent Identity Is Not Model Identity (DOI: 10.5281/zenodo.19240883) Technical Note: Gap Invariance: Why PPP Measurements Are Domain-Independent by Construction (DOI: 10.5281/zenodo.19275524) Technical Note: Measured Model Substitution Under Valid Agent Credentials (DOI: 10.5281/zenodo.19342848) Technical Note: Artifact Identity Is Not Runtime Identity — Trustfall Lite and the Boundary of File-Level Model Verification (DOI: 10.5281/zenodo.20019127) Formal Verification Stack for Neural Network Structural Identity (IT-PUF Coq Proofs) (DOI: 10.5281/zenodo.18930621) Copyright (c) 2026 Anthony Ray Coslett / Fall Risk AI, LLC. All Rights Reserved. Confidential and Proprietary. Patent Pending (Applications 63/982,893, 63/990,487, 63/996,680, 64/003,244).
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Physical Unclonable Functions (PUFs) and Hardware Security
Adversarial Robustness in Machine Learning
Generative Adversarial Networks and Image Synthesis
Complete technical specification and reference implementation for privacy-preserving payment infrastructure achieving European payment sovereignty while maintaining cryptographic privacy guarantees. This comprehensive study analyzes the Y.I.N. Architecture’s DP→ZK→HE (Differential Privacy → Zero-Knowledge → Homomorphic Encryption) ordering for secure payment settlement. Technical Coverage: The article provides detailed analysis of 43 implementation variants including six cryptographic orderings (with mathematical proofs of security properties), seven zero-knowledge protocols (Sigma, Bulletproofs, STARKs, zk-SNARKs, PLONK, Halo 2, Recursive SNARKs), six homomorphic encryption schemes (CKKS, BFV, TFHE, Multi-key HE, FSS, Garbled Circuits), five differential privacy mechanisms, four deployment architectures, three hardware acceleration approaches, three cross-border payment protocols, three quantum-resistant key management methods, three presentation attack detection techniques, and three accessibility compliance pathways. Implementation & Performance: Includes 2,346 lines of production-ready code with comprehensive error handling, constant-time cryptographic operations, and replay attack protection. Performance benchmarks demonstrate 234ms settlement latency, 640× timing attack resistance, and 135× adversarial detection capability, suitable for real-time payment processing at scale. Production Deployment: Features complete deployment guides including centralized server architecture, network security configurations, production monitoring with Prometheus metrics, extensive test suite covering honest/tampered/replay scenarios, and enterprise integration strategies for financial institutions and consulting firms. Regulatory Compliance: Comprehensive mapping to 13 global regulations (GDPR, DORA, PSD2, 5AMLD, BSA/AML, CCPA, BIPA, PDPA, PIPL, POPIA, LGPD) and 7 industry standards (PCI DSS, ISO 20022, FIPS 140-3, EMVCo), demonstrating privacy-by-design compliance for digital payment infrastructure. Applications: Reference implementation for European Payments Initiative (EPI), digital euro deployment, sovereign payment networks, cross-border settlement systems, and CBDC infrastructure requiring cryptographic privacy guarantees with regulatory compliance.
Abstract Can a dealer share a secret without knowing the shareholders? We provide a positive answer to this question by introducing the concept of an attribute-based secret sharing (AB-SS) scheme.With AB-SS, a dealer can distribute a secret based on attributes rather than specific individuals or shareholders. Only authorized users whose attributes satisfy a given access structure can recover the secret. Furthermore, we introduce the concept of attribute-based publicly verifiable secret sharing (AB-PVSS). An AB-PVSS scheme allows external users to verify the correctness of all broadcast messages from the dealer and shareholders, similar to a traditional PVSS scheme. Additionally, AB-SS (or AB-PVSS) distinguishes itself from traditional SS (or PVSS) by enabling a dealer to generate shares according to an arbitrary monotone access structure.To build an AB-PVSS scheme, we first implement a decentralized ciphertext-policy attribute-based encryption (CP-ABE) scheme, though not a fully-fledged one.We then incorporate non-interactive zero-knowledge (NIZK) proofs to enable public verification of the CP-ABE ciphertext. Based on the CP-ABE and NIZK proofs, we construct an AB-PVSS primitive.Finally, we conduct security analysis and comprehensive experiments on the proposed CP-ABE and AB-PVSS schemes. The results demonstrate that both schemes exhibit plausible performance compared to related works.
Joshua Edward Mamza, Idris Ismaila, Joseph A. Ojeniyi, Shafi’i Abdulhamid · 6 authors
The Common Vulnerability Scoring System (CVSS) depends on reliable vulnerability data from expert, but the current process of vulnerability score generation and transmission remain exposed to data manipulation and interception. Existing research work used supervised machine learning to automate CVSS scoring with up to 90% accuracy, but their plaintext-based approach lacked cryptographic protections, leaving it vulnerable to Man-in-the-Middle (MitM) attacks. Another research work introduced a homomorphic encryption-based framework that preserves data confidentiality during computation and offers moderate performance gains. However, their dependance on a single trusted aggregator, static key management, and absence of dynamic integrity threshold mechanisms left the system exposed if the aggregator’s key or channel were compromised. An architectural framework for an Enhanced Multi-Party Fully Homomorphic Encryption Scheme (EMHES) was designed to combat Man-in-the-Middle (MitM) attacks targeting Vulnerability Score manipulation. By employing Homomorphic Encryption, the framework enables computations on encrypted vulnerability scores, ensuring confidentiality throughout their lifecycle. Key enhancements include integrating digital signatures to authenticate classified scores before encrypted transmission to cloud environments and verify the integrity of decrypted results post-processing. Digital signatures and regulatory oversight significantly strengthen security properties like non-repudiation, integrity, and confidentiality for cloud-based data computations. The EMHES architecture features a secure transmission channel with multiple security layers within the cloud service provider infrastructure. Additional security mechanisms include secure key management protocols, zero-knowledge proofs for integrity verification, and a resilient secure aggregation protocol designed to counter MitM attacks. From a computational analysis, baseline algorithms exhibit constant time complexity O(1), while the EMHES architecture operates with linear time complexity O(n). The result shows that EMHES provides superior security, integrity and performance on large datasets.
Wyatt Benno, Alberto Centelles, Antoine Douchet, Khalil Gibran
We present Jolt Atlas, a zero-knowledge machine learning (zkML) framework that extends the Jolt proving system to model inference. Unlike zkVMs (zero-knowledge virtual machines), which emulate CPU instruction execution, Jolt Atlas adapts Jolt's lookup-centric approach and applies it directly to ONNX tensor operations. The ONNX computational model eliminates the need for CPU registers and simplifies memory consistency verification. In addition, ONNX is an open-source, portable format, which makes it easy to share and deploy models across different frameworks, hardware platforms, and runtime environments without requiring framework-specific conversions. Our lookup arguments, which use sumcheck protocol, are well-suited for non-linear functions -- key building blocks in modern ML. We apply optimisations such as neural teleportation to reduce the size of lookup tables while preserving model accuracy, as well as several tensor-level verification optimisations detailed in this paper. We demonstrate that Jolt Atlas can prove model inference in memory-constrained environments -- a prover property commonly referred to as \textit{streaming}. Furthermore, we discuss how Jolt Atlas achieves zero-knowledge through the BlindFold technique, as introduced in Vega. In contrast to existing zkML frameworks, we show practical proving times for classification, embedding, automated reasoning, and small language models. Jolt Atlas enables cryptographic verification that can be run on-device, without specialised hardware. The resulting proofs are succinctly verifiable. This makes Jolt Atlas well-suited for privacy-centric and adversarial environments. In a companion work, we outline various use cases of Jolt Atlas, including how it serves as guardrails in agentic commerce and for trustless AI context (often referred to as \textit{AI memory}).
Suvradip Chakraborty, James Hulett, Dakshita Khurana, Kabir Tomer
A recent breakthrough [Hirahara and Nanashima, STOC'2024] established that if $\mathsf{NP} \not \subseteq \mathsf{ioP/poly}$, the existence of zero-knowledge with negligible errors for $\mathsf{NP}$ implies the existence of one-way functions (OWFs). In this work, we obtain a characterization of one-way functions from the worst-case complexity of zero-knowledge {\em in the high-error regime}. We say that a zero-knowledge argument is {\em non-trivial} if the sum of its completeness, soundness and zero-knowledge errors is bounded away from $1$. Our results are as follows, assuming $\mathsf{NP} \not \subseteq \mathsf{ioP/poly}$: 1. {\em Non-trivial} Non-Interactive ZK (NIZK) arguments for $\mathsf{NP}$ imply the existence of OWFs. Using known amplification techniques, this result also provides an unconditional transformation from weak to standard NIZK proofs for all meaningful error parameters. 2. We also generalize to the interactive setting: {\em Non-trivial} constant-round public-coin zero-knowledge arguments for $\mathsf{NP}$ imply the existence of OWFs, and therefore also (standard) four-message zero-knowledge arguments for $\mathsf{NP}$. Prior to this work, one-way functions could be obtained from NIZKs that had constant zero-knowledge error $ε_{zk}$ and soundness error $ε_{s}$ satisfying $ε_{zk} + \sqrt{ε_{s}} < 1$ [Chakraborty, Hulett and Khurana, CRYPTO'2025]. However, the regime where $ε_{zk} + \sqrt{ε_{s}} \geq 1$ remained open. This work closes the gap, and obtains new implications in the interactive setting. Our results and techniques could be useful stepping stones in the quest to construct one-way functions from worst-case hardness.
The Fischlin transform yields non-interactive zero-knowledge proofs with straight-line extractability in the classical random oracle model. This is done by forcing a prover to generate multiple accepting transcripts through a proof-of-work mechanism. Whether the Fischlin transform is straight-line extractable against quantum adversaries has remained open due to the difficulty of reasoning about the likelihood of query transcripts in the quantum-accessible random oracle model (QROM), even when using the compressed oracle methodology. In this work, we prove that the Fischlin transform remains straight-line extractable in the QROM, via an extractor based on the compressed oracle. This establishes the post-quantum security of the Fischlin transform, providing a post-quantum straight-line extractable NIZK alternative to Pass' transform with smaller proof size. Our techniques include tail bounds for sums of independent random variables and for martingales as well as symmetrization, query amplitude and quantum union bound arguments.
Arka Pal, Louai Zahran, William Gvozdjak, Akilesh Potti · 5 authors
As large language models (LLMs) continue to grow in size, fewer users are able to host and run models locally. This has led to increased use of third-party hosting services. However, in this setting, there is a lack of guarantees on the computation performed by the inference provider. For example, a dishonest provider may replace an expensive large model with a cheaper-to-run weaker model and return the results from the weaker model to the user. Existing tools to verify inference typically rely on methods from cryptography such as zero-knowledge proofs (ZKPs), but these add significant computational overhead, and remain infeasible for use for large models. In this work, we develop a new insight -- that given a method for performing private LLM inference, one can obtain forms of verified inference at marginal extra cost. Specifically, we propose two new protocols which leverage privacy-preserving LLM inference in order to provide guarantees over the inference that was carried out. Our approaches are cheap, requiring the addition of a few extra tokens of computation, and have little to no downstream impact. As the fastest privacy-preserving inference methods are typically faster than ZK methods, the proposed protocols also improve verification runtime. Our work provides novel insights into the connections between privacy and verifiability in LLM inference.
Global illicit fund flows exceed an estimated $3.1 trillion annually, with stablecoins emerging as a preferred laundering medium due to their liquidity. While decentralized protocols increasingly adopt zero-knowledge proofs to obfuscate transaction graphs, centralized stablecoins remain critical transparent choke points for compliance. Leveraging this persistent visibility, this study analyzes an Ethereum dataset to establish an empirical baseline for behavioral AML detection. Our findings demonstrate that domain-informed tree ensemble models achieve higher Macro-F1 score, significantly outperforming graph neural networks, which struggle with the increasing fragmentation of transaction networks. The model's interpretability goes beyond binary detection, successfully dissecting distinct typologies: it differentiates the complex, high-velocity dispersion of cybercrime syndicates from the constrained, static footprints left by sanctioned entities. This methodological approach provides actionable insights that align with industry shifts toward deterministic verification, informing the auditability and compliance requirements under regulations such as the EU's MiCA and the U.S. GENIUS Act while minimizing unjustified asset freezes. By providing a high-precision behavioral classification of suspicious wallets, this approach contributes to raising the economic cost of financial misconduct while informing compliance practice under emerging stablecoin regulations.
Introduction In the contemporary digital health landscape, securing personal health data against unauthorized access while ensuring its verifiability is a paramount challenge. A critical conflict exists between the transparency required for data verification and the privacy mandated by global regulations such as HIPAA and GDPR. Existing Layer-1 blockchain solutions suffer from prohibitive gas costs and high latency, rendering them unsuitable for real-time monitoring of high-volume health data streams. Methods This paper proposes TeleZK-L2, a novel framework that synergizes distributed Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs) with Layer-2 scaling solutions. The architecture introduces a Distributed Prover Network (DPN) to parallelize heavy cryptographic computations and utilizes Optimistic Proof Aggregation to minimize on-chain data footprints. The verification logic is anchored on the Polygon zkEVM to ensure high throughput and low-cost settlement. Results Extensive simulations on a 16-node high-performance cluster demonstrate that TeleZK-L2 generates proofs at a rate 40% faster than the standard Groth16 baseline. Furthermore, the framework reduces on-chain verification costs by approximately 52%. The system maintains constant-time verification complexity regardless of batch size, achieving a peak throughput of 260 TPS. Discussion TeleZK-L2 provides the technical privacy guarantees necessary to support adherence to HIPAA and GDPR data minimization mandates while maintaining cryptographic soundness. By resolving the "Scalability-Privacy Trilemma," this framework demonstrates significant potential for large-scale deployment in national telehealth infrastructures and remote patient monitoring ecosystems.
The first machine-checked formalization, in any proof assistant, of any component of the Birch-Swinnerton-Dyer (BSD) conjecture pipeline. No prior Lean, Coq, or Isabelle project has formalized Silverman height bounds, Gross-Zagier-Kolyvagin data structures, or the logical architecture of BSD generator search. No new number theory is proved. The algorithms formalized are the engines inside Cremona's mwrank and SageMath. The contribution is the formalization itself and the foundational analysis it enables. Three results that did not previously exist in formal mathematics: (1) A machine-checked axiom/theorem boundary for BSD. The formalization identifies exactly which ingredients must be axiomatized (Gross-Zagier, Kolyvagin, Silverman bound, positive-definiteness) and which can be proved constructively (height bound chain, finite grid membership, search space finiteness). This is the blueprint for any future formally verified BSD solver: the deep analytic theorems interface with type theory through a single chokepoint (the real-valued Silverman bound), and everything below that chokepoint is verified. (2) A logical characterization of the Archimedean/p-adic dichotomy. The positive-definite Archimedean metric (u = 1) is identified as the exact logical modality lowering search complexity from Pi^0_1 (unbounded, MP) to Delta_0 (bounded verification, BISH). This foundational statement does not appear in the classical literature -- Cremona and Watkins use height bounds as engineering, not as a theorem in reverse mathematics. (3) A logical explanation of the exceptional zero pathology. The p-adic BSD exceptional zero (Mazur-Tate-Teitelbaum) is usually explained analytically: trivial zeros of p-adic L-functions, extra Euler factors. This formalization gives a logical explanation: the p-adic canonical height is not positive-definite, so the MP-to-BISH conversion fails. The search remains unbounded because the metric lacks the topological property needed for logical reduction. This re-reading of a classical analytic obstruction as a failure of logical reducibility is, to our knowledge, new. The axiom budget is minimal -- removing any one ingredient breaks the proof chain -- characterizing the necessary logical interface between analytic number theory and formal verification. This is the first application of constructive reverse mathematics to a Clay Millennium Problem. Formalized in Lean 4 + Mathlib with zero sorry's and zero custom axiom declarations. All analytic axioms enter as Prop-valued hypotheses in a BSDRankOneData structure. Axiom audit: every theorem depends only on [propext, Classical.choice, Quot.sound] (standard Mathlib infrastructure for the reals). Package contains compiled PDF (10 pages), LaTeX source, and complete Lean 4 source (7 files, ~725 lines) buildable with lake build.
Four ancient civilizations — Egyptian, Sumerian, Babylonian, and Hindu — independently preserved the same mathematical encoding system. When their 'mythological' timescales are divided by 144, they reveal real historical intervals, astronomical cycles, and geological periods with precision that cannot be coincidental. Statistical significance: P < 10⁻⁴⁸ (less than one chance in a number with 48 zeros). THE DISCOVERY: Ancient 'mythical' chronologies are not fiction. They are real timescales multiplied by 144 — a universal encoding system designed to preserve historical data across civilizational collapse. To decode ancient mythology into history: divide by 144. When we do this systematically across four independent cultures, the results are stunning. EGYPTIAN EVIDENCE (Turin Papyrus): Pre-dynastic 'mythical' periods when decoded: Total: 36,620 years ÷ 144 = 254.3 years Matches: Biblical Flood to Egyptian Dynasty 1 (254 years) Precision: 110 days (0.12% error) Pre-Shemsu Hor: 23,200 years ÷ 144 = 161.1 years Matches: Flood to Tower of Babel dispersion (161 years) Precision: 37 days (0.06% error) Shemsu Hor: 13,420 years ÷ 144 = 93.2 years Matches: Babel to Nile Valley settlement (93 years) Precision: 73 days (0.2% error) Egyptian P-value: < 10⁻⁸ (less than one in 300 million) The Egyptian scribes encoded the exact chronology from the Flood to their civilization's founding — 254 real years disguised as 36,620 'mythical' years. SUMERIAN EVIDENCE (King List): All eight pre-flood king reigns are EXACT multiples of 144 with zero error: King Reign (years) ÷ 144 Result Alulim 28,800 200.00 Perfect Alalgar 36,000 250.00 Perfect En-men-lu-ana 43,200 300.00 Perfect En-men-gal-ana 28,800 200.00 Perfect Dumuzid 36,000 250.00 Perfect En-sipad-zid-ana 28,800 200.00 Perfect En-men-dur-ana 64,800 450.00 Perfect Ubara-Tutu 36,000 250.00 Perfect 8 out of 8 = 100% exact multiples. Total pre-flood period: 302,400 years = 144 × 2,100 = 14,400 × 21 The Sumerians encoded exactly 21 complete geomagnetic excursion cycles (each 14,400 years) before the catastrophic 22nd cycle that became "The Flood." Sumerian P-value: < 10⁻¹⁶ (less than one in ten quadrillion) King Alulim's reign (28,800 years = 144 × 200) represents one complete Great Year — Earth's true harmonic precessional cycle before the Younger Dryas impact perturbed it to the current 25,772 years. BABYLONIAN EVIDENCE (Berossus): All ten pre-flood kings (Berossus, c. 290 BCE) divide perfectly by 144: King Reign (years) ÷ 144 Result Aloros 36,000 250 Perfect Integer Alaparos 10,800 75 Perfect Integer Amelon 46,800 325 Perfect Integer Ammenon 43,200 300 Perfect Integer Megalaros 64,800 450 Perfect Integer Daonos 36,000 250 Perfect Integer Euedorachos 64,800 450 Perfect Integer Amempsinos 36,000 250 Perfect Integer Otiartes 28,800 200 Perfect Integer Xisuthros 64,800 450 Perfect Integer 10 out of 10 = 100% exact multiples. Total antediluvian period: 432,000 years Divided by 144: 432,000 ÷ 144 = 3,000 (exact) Babylonian P-value: < 2 × 10⁻²⁴ (less than one in 2 septillion) King Otiartes (9th king) reigned for 28,800 years — identical to Sumerian King Alulim. Both cultures encoded the Great Year in the same king's reign. HINDU EVIDENCE (The Smoking Gun): Hindu Kali Yuga duration: 432,000 years Babylonian total: 432,000 years EXACT MATCH. Both = 144 × 3,000 precisely. Testing all four Hindu Yugas: Yuga Duration ÷ 144 Result Kali Yuga 432,000 3,000 Perfect Dwapara Yuga 864,000 6,000 Perfect Treta Yuga 1,296,000 9,000 Perfect Satya Yuga 1,728,000 12,000 Perfect 4 out of 4 Yugas = 100% exact multiples of 144. The k-values (3,000, 6,000, 9,000, 12,000) form a perfect 1:2:3:4 ratio. Hindu P-value: < 10⁻⁸ Babylon-Hindu match P-value: < 10⁻¹⁶ (the probability they'd both preserve 432,000 independently by chance) THE BABYLONIAN-HINDU BRIDGE: This is the smoking gun. Babylon (Mesopotamia) and Hindu civilization (India) are separated by: 2,500 miles of geography Completely different languages, religions, mythologies Independent cultural development across centuries Yet they both preserve IDENTICAL numbers: 432,000 years = 144 × 3,000 This is not cultural borrowing. This is not coincidence. This is evidence of a common source — a global pre-flood civilization that used 144-based timekeeping, which both Mesopotamia and India inherited independently. COMBINED STATISTICAL ANALYSIS: Testing across all four cultures: Total independent data points: Egyptian: 3 periods Sumerian: 8 kings Babylonian: 10 kings Hindu: 4 Yugas Total: 25 numerical values Probability all 25 would divide by 144 to yield meaningful results by random chance: P < 10⁻⁴⁸ One chance in: 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 For context: Stars in observable universe: ~10²⁴ Atoms in human body: ~10²⁸ This probability: 10⁻⁴⁸ This cannot be coincidence. This is proof. WHAT THE EVIDENCE PROVES: Before the Flood, there existed a global civilization that: Used 144 as the universal temporal constant Same number appears in Egypt, Mesopotamia, India Same encoding method (multiply real years × 144) Same astronomical knowledge (Great Year, excursion cycles) Survived multiple geomagnetic excursion cycles Sumerian record: 21 consecutive 14,400-year cycles Developed protocols for Type 1 reset survival Encoded survival knowledge in mythology Tracked astronomical cycles with precision Great Year: 28,800 years (true harmonic precession) Excursion cycle: 14,400 years (geomagnetic resets) Solar cycle: 144-day beats All based on 144 constant Transmitted knowledge to successor cultures Sumerians: Preserved raw data (king lists) Babylonians: Systematized data (432,000 total) Egyptians: Encoded data (pre-dynastic mythology) Hindus: Preserved data (Yuga cosmology) Built a universal timekeeping system Sar unit: 3,600 years = 144 × 25 Sexagesimal (base-60) mathematics Encoded in mythology to survive collapse THE METHODOLOGY: Simple, reproducible, falsifiable: Take any ancient 'mythological' chronology Divide by 144 Check if result corresponds to: Known historical intervals Astronomical cycles Geological events Other verified 144-based timescales If 144 encoding is universal, it will work across ALL major cultures. If coincidental, it will fail for most. WHY 144? This constant appears across EVERY tested domain: Planetary (spatial): All planet diameters = 144 × Fibonacci(n) miles (P < 10⁻¹⁸) Planetary (temporal): All planet orbits = 14.4-day multiples (P < 10⁻⁵⁰) Solar: Sunspot cycle = 144 days × 28 (exact) Geological: Geomagnetic excursions = 14,400-year intervals Deep time: Permian-Triassic extinction = 14,400 × 17,500 (exact) Human: Earth's day = 1,440 minutes = 144 × 10 Ancient chronology: Egyptian + Sumerian + Babylonian + Hindu = all encode via × 144 (P < 10⁻⁴⁸) This is a fundamental organizing principle operating fractally across nine orders of magnitude in time. WHY ENCODE VIA MULTIPLICATION? Three complementary reasons: Durability: Mythological narratives survive collapse better than administrative records. Epic poems and temple inscriptions are memorized and carved in stone. By encoding real chronology as 'god-king' myths, scribes ensured data survival even if civilization was destroyed. Dual purpose: Encoded numbers serve both religious functions (satisfying ritual requirements) and data storage (preserving actual chronology). One document accomplishes both. Astronomical connection: Using 144 linked human chronology to the same constant governing planetary mechanics and solar cycles. This embedded human history within cosmic time. FALSIFIABLE PREDICTIONS: If the framework is correct: Additional Egyptian sources (Palermo Stone, Abydos, Manetho) will decode via ÷ 144 to known intervals All Hindu chronological units (Manvantaras, Kalpas) will be exact 144 multiples Chinese Bamboo Annals (independent East Asian culture) will show 144 encoding or NOT (critical test) Mayan Long Count units beyond B'ak'tun will all be 144 multiples May 2027 will show measurable precession rate change (if 28,800-year Great Year is true) If ANY major culture with preserved chronologies does NOT show 144 encoding, this requires explanation. IMPLICATIONS: Ancient mythology is not fiction. It is real chronology encrypted with a mathematical key. That key is 144. When applied systematically: Mythology becomes history History becomes precise The past is no longer hidden The gods ruled for 432,000 years. Divide by 144. They ruled for 3,000 years. That is real. That is history. That is how long the pre-flood world lasted. And four ancient cultures — separated by thousands of miles, different languages, independent mythologies — all preserved it exactly. Each one encoding the same truth in their own sacred texts. We now have the decryption key. RELATED PUBLICATIONS: All papers in the CTF framework series available at ctftheory.com and Zenodo with permanent DOIs. Key papers: The 144 Hz Universal Constant Across Space and Time Sumerian Great Year Decoded: All Eight Pre-Flood King Reigns Are Exact Multiples of 144 Two Types of Catastrophe: Harmonic Resets vs. Impact Events Sun 144-Day Beat and 14,400-Year Reset Cycle Planet Nine Primordial Black Hole at the 144 Harmonic Node All data public. All calculations reproducible. All predictions falsifiable.
Zibin Lin, Taotao Wang, Shengli Zhang, Long Shi · 6 authors
Open Web 3.0 platforms increasingly operate as \emph{service ecosystems} (e.g., DeFi, DAOs, and decentralized social applications) where \emph{admission control} and \emph{account provisioning} must be delivered as an always-on service under bursty demand. Service operators face a fundamental tension: enforcing Sybil resistance (one-person-one-account) while preserving user privacy, yet keeping on-chain verification cost and admission latency predictable at scale. Existing credential-based ZK admission approaches typically require per-request on-chain verification, making the provisioning cost grow with the number of concurrent joiners. We present \textbf{ZK-AMS}, a scalable admission and provisioning layer that bridges real-world \emph{Personhood Credentials} to anonymous on-chain service accounts. ZK-AMS combines (i) zero-knowledge credential validation, (ii) a \emph{permissionless} batch submitter model, and (iii) a decentralized, privacy-preserving folding pipeline that uses Nova-style recursive aggregation together with multi-key homomorphic encryption, enabling batch settlement with \emph{constant} on-chain verification per batch. We implement ZK-AMS end-to-end on an Ethereum testbed and evaluate admission throughput, end-to-end latency, and gas consumption. Results show stable verification cost across batch sizes and substantially improved admission efficiency over non-recursive baselines, providing a practical and cost-predictable admission service for large-scale Web 3.0 communities.
We study the implications of the existence of weak Zero-Knowledge (ZK) protocols for worst-case hard languages. These are protocols that have completeness, soundness, and zero-knowledge errors (denoted $ε_c$, $ε_s$, and $ε_z$, respectively) that might not be negligible. Under the assumption that there are worst-case hard languages in NP, we show the following: 1. If all languages in NP have NIZK proofs or arguments satisfying $ ε_c+ε_s+ ε_z < 1 $, then One-Way Functions (OWFs) exist. This covers all possible non-trivial values for these error rates. It additionally implies that if all languages in NP have such NIZK proofs and $ε_c$ is negligible, then they also have NIZK proofs where all errors are negligible. Previously, these results were known under the more restrictive condition $ ε_c+\sqrt{ε_s}+ε_z < 1 $ [Chakraborty et al., CRYPTO 2025]. 2. If all languages in NP have $k$-round public-coin ZK proofs or arguments satisfying $ ε_c+ε_s+(2k-1).ε_z < 1 $, then OWFs exist. 3. If, for some constant $k$, all languages in NP have $k$-round public-coin ZK proofs or arguments satisfying $ ε_c+ε_s+k.ε_z < 1 $, then infinitely-often OWFs exist.
Eman Alatawi, Anoud Alhawiti, Doaa Albalawi, Umar Albalawi
The rapid expansion of the Internet of Things (IoT) has led to billions of interconnected devices generating and exchanging sensitive data across diverse domains, which introduces challenges in identity management (IdM) regarding privacy, scalability, and verifiability. While blockchain technology provides decentralization and tamper resistance, its transparency and increasing on-chain storage demands make it unsuitable for large-scale IoT identity ecosystems. To overcome these challenges, IoT-SBIdM is proposed as a lightweight, privacy-preserving, and stateless blockchain-based identity management framework designed for IoT environments. This framework incorporates Elliptic Curve Cryptography (ECC)-based accumulators and Zero-Knowledge Proofs (ZKPs) to facilitate selective disclosure, enabling entities to prove credential authenticity without exposing sensitive identity information. Furthermore, the framework adopts W3C-compliant Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs) to promote interoperability and user-controlled identity ownership. The experimental results indicate that IoT-SBIdM achieves efficient smart contract execution by reducing gas costs through optimized registry logic. Moreover, the system maintains a compact block size of only 45 MB at higher block heights, outperforming comparable schemes in storage efficiency by achieving a 55% reduction relative to recent models and an approximate 94% reduction relative to older systems, thereby demonstrating superior scalability and storage efficiency, making it suitable for identity management solutions for IoT environments.
Zibin Lin, Taotao Wang, Shengli Zhang, Long Shi · 6 authors
Web 3.0 platforms need an onboarding mechanism that can admit real users at scale without forcing them to reveal identity documents or pay one on-chain verification cost per user. Existing approaches typically rely on KYC-style disclosure, per-request on-chain verification, or trusted batching, making onboarding cost and latency difficult to predict under bursty demand. We present \textbf{ZK-AMS}, a credibly anonymous admission infrastructure that maps Personhood Credentials to anonymous on-chain Soul Accounts. Rather than introducing a new primitive, ZK-AMS composes zero-knowledge credential validation, permissionless batch submission, recursive proof aggregation, and anonymous post-admission account provisioning into one end-to-end workflow. Its key design feature is a confidential batching pipeline in which admission instances of a common relation are folded off-chain under multi-key homomorphic encryption, allowing an untrusted batch submitter to coordinate aggregation without direct access to individual user witnesses during batching; the confidentiality scope is characterized explicitly in the security analysis. The resulting batch is settled on-chain with constant verification cost per batch rather than per admitted user. We implement ZK-AMS on an Ethereum testbed and evaluate admission throughput, end-to-end latency, gas consumption, and parameter trade-offs. Results show stable batch-verification gas across evaluated batch sizes, substantially lower amortized on-chain cost than the non-recursive baseline, and practical cost-latency trade-offs for high-concurrency onboarding in Web 3.0 platforms.
Zero-knowledge proof generation imposes stringent timing and reliability constraints on blockchain systems. For ZK-rollups, delayed proofs cause finality lag and economic loss; for Ethereum's emerging L1 zkEVM, proofs must complete within the 12-second slot window to enable stateless validation. The Ethereum Foundation's Ethproofs initiative coordinates multiple independent zkVMs across proving clusters to achieve real-time block proving, yet no principled orchestration framework addresses the joint challenges of (i) strict head-of-chain ordering, (ii) sub-slot latency bounds, (iii) fault-tolerant task reassignment, and (iv) prover-agnostic workflow composition. We present push0, a cloud-native proof orchestration system that decouples prover binaries from scheduling infrastructure. push0 employs an event-driven dispatcher--collector architecture over persistent priority queues, enforcing block-sequential proving while exploiting intra-block parallelism. We formalize requirements drawn from production ZK-rollup operations and the Ethereum real-time proving specification, then demonstrate via production Kubernetes cluster experiments that push0 achieves 5 ms median orchestration overhead with 99--100% scaling efficiency at 32 dispatchers for realistic workloads--overhead negligible (less than 0.1%) relative to typical proof computation times of 7+ seconds. Controlled Docker experiments validate these results, showing comparable performance (3--10 ms P50) when network variance is eliminated. Production deployment on the Zircuit zkrollup (14+ million mainnet blocks since March 2025) provides ecological validity for these controlled experiments. Our design enables seamless integration of heterogeneous zkVMs, supports automatic task recovery via message persistence, and provides the scheduling primitives necessary for both centralized rollup operators and decentralized multi-prover networks.
Michele Battagliola, Laura Mattiuz, Alessio Meneghetti
Abstract The Vector Oblivious Linear Evaluation in the Head (VOLEitH) paradigm has proven to be a versatile tool to design zero-knowledge proofs and signatures in post-quantum cryptography. In this paper, we propose three VOLE-friendly modellings for Proofs of Knowledge (PoK) of a solution of an instance of the Linear Code Equivalence Problem (LEP). For the first two schemes, we propose two new reductions from LEP to the Multivariate Quadratic (MQ) problem, that may be of independent interest for the cryptanalysis of LEP. Instead, the last model is obtained by generalizing a recent work by Bettaieb et al. to the context of monomial matrices instead of permutation matrices. While our proposed schemes exhibit larger signature sizes compared to LESS, they improve the computational efficiency, reducing the overall complexity from $$O(n^3)$$ to $$O(n^2\log n )$$ and $$O(n^2\log ^2 n )$$ , where n is the length of the code.
This paper formalizes a mathematical physics framework for redefining the “charge” entity within physical plasma settings using the Hala-SCC (Successive Controlled Collapse) protocol. Traditionally viewed as a static dipole, we re-model charge as a dynamic informational inheritance that manifests in three distinct physical phases: Discrete (species), Wave (EM fields), and Continuum (current flow). By integrating fuzzy logic with the Hala Operator ( ˆH), we introduce the concept of Gray Entropy—a stabilized transitional state that prevents “topological tearing” during the transition from high-entropy chaotic inheritance to zero-entropy epistemological truth. Through a 23 factorial Design of Experiments (DoE) conducted on a quiescent multi-dipole thermionic plasma source, we demonstrate that the synergy between Human, Artificial, and Protocol intelligence operators allows for a “Managed Viscosity” of knowledge. This framework provides the first deterministic proof that the “charge” carrier can be distilled into a stable industrial logic gate, bridging the Reality Gap (ϵ) between abstract plasma theory and engineering utility.
Within the context of digital forensics, the integrity and authenticity of digital evidence are crucial for its legal admissibility within a courtroom setting. Chain of Custody (CoC) processes ensure that digital evidence is meticulously managed and documented from its point of origin until its use in legal proceedings. As the importance of digital forensics increases, especially with cybercrime investigations, the traditional processes used in traditional Chain of Custody have challenges in terms of transparency, security, and efficiency. This paper highlights some of the recent developments in Chain of Custody processes, particularly with the adoption of blockchain and Artificial Intelligence technologies. Blockchain technology, known for its impenetrable and distributed properties, introduces a new paradigm for Chain of Custody processes, enhancing security and traceability for digital evidence management. Additionally, AI-based algorithms for anomaly detection have the potential for increasing the reliability of Chain of Custody processes. Moreover, we will explore the decentralized evidence storage approaches and privacy-preserving mechanisms, such as zero-knowledge proofs. These are important in ensuring that more secure yet transparent approaches in managing distributed forensic investigation systems are achieved. The effectiveness of currently used CoC approaches presents lessons in understanding the future of improving the integrity of this process. Such innovations have the potential of revolutionizing the field of digital forensic investigation processes while ensuring that the handling of such evidence is of the highest integrity.
We prove that Jensen–Shannon divergence (JSD) contraction coefficients exhibit universal strict super-tensorization: for every finite channel W with nontrivial contraction 0 < η_JSD(W) < 1, one has η_JSD(W⊗2) > η_JSD(W). The sequence η_n(W) := η_JSD(W⊗n) is nondecreasing, strictly increases along doubling, and satisfies lim η_n(W) = 1, while for η_JSD(W) ∈ {0, 1} it is identically 0 or 1. This contrasts sharply with the multiplicative tensorization η_f(W⊗n) = η_f(W)^n enjoyed by operator-convex f-divergences (KL, χ², squared Hellinger), for which contraction decays exponentially to zero. To our knowledge, this is the first f-divergence for which a universal strict super-tensorization law is established. The proof uses the Ordentlich–Polyanskiy binary edge reduction, expresses the binary JSD SDPI constant as a normalized posterior-variance functional, and shows strict amplification via the law of total variance. Convergence rate is controlled by the Bhattacharyya coefficient: 1 − η_n(W) ≤ 2A^n. Numerical verification over 4729 random channels across 26 configurations confirms zero violations. **Update v1.1:** Includes addendum with three targeted clarifications: (1) precise assumptions for binary edge reduction lemma replacing informal "mild regularity conditions," (2) explicit two-case split in the key strictness argument (Lemma 5.2, Step 2), (3) refined table caption for operator-convex divergences.
This paper formalizes a mathematical physics theory for the verification of inherited scientific knowledge through a Diffeomorphic Manifold and the Successive Controlled Collapse (SCC) protocol. We define the history of science and technology as a three-tiered manifold—comprising Modern, Contemporary, and Old (Inherited) tiers—where information is transported by the "Common Language" of a lingual locale. By admitting three classes of knowledge agents—Intelligence-Human (IH), Intelligence-Artificial (IA), and Intelligence-Metaphysical (IM )—we demonstrate how high-entropy Informational Inheritance (Sacred Texts) can be distilled into zero-entropy Epistemological Truth. Using the Hala-Operator (Hˆ) as a non-adiabatic spectral regulator, we provide a proof-by-construction using the Hala-Lewis Gaseous Gate as a physical case study. Experimental results from a 23 Factorial Design quantify the Reality Gap (ϵ) at 0.124 and a Hala-Operator Efficiency (η) of 80.9%, proving that the transition from abstract nonlinear dynamics to physical prototyping is a predictable outcome of managed collapse. This framework establishes an Epistemological Barrier that protects historical context while ensuring the verifiability of technical exits in Internet 3.0 and deep-tech RD.