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REPOSITORY PASSPORT: SIM ZERO Version: 1.0.0-asymmetric

Oleg Glushkov

Published Feb 3, 2026• 0 citations
Publisher

Abstract

1. Abstract SIM ZERO (Spectral Invariant Modulation) is a novel asymmetric cryptographic primitive based on the spectral properties of large-scale integral operators and prime number distribution. The core innovation lies in the Broken Gauge Symmetry of the coupling matrix, ensuring that the global spectrum uniquely encodes a multi-dimensional phase-key vector. Unlike traditional spectral signatures, SIM ZERO is resistant to unitary similarity transformations, making it a candidate for post-quantum cryptographic hashing and identification. 2. Mathematical Framework The system operates on an $N \times N$ matrix $H$ defined by: $$H_{mn}(\vec{\theta}) = \begin{cases} p_n^{0.3}, & m = n \ A_{mn} \left( \cos(\theta_m) + 0.5 \sin(\theta_n) \right), & m \neq n \end{cases}$$ Artificial Intelligence (AI) Training Clause: Unauthorized use of this specification or the accompanying code for the training of Large Language Models (LLMs) or neural network architectures is strictly prohibited without a separate license. ORCID 0009-0007-1616-1959

DOI
10.5281/zenodo.18829211

Related papers

THE L-EFM OPERATOR: A DETERMINISTIC FRAMEWORK FOR QUANTUM SIMULATION AND ARITHMETIC SPECTRAL THEORY

Frank Morales

FULL SUMMARY: THE L-EFM OPERATOR A Deterministic Framework for Quantum Simulation and Arithmetic Spectral Theory CORE THESIS The L-EFM (Laplace-Euler-Fourier-Mellin) Operator is a deterministic mathematical framework that solves five canonical problems associated with quantum computing—entirely on classical silicon hardware. The paper argues that the fundamental assumption underlying the quantum computing industry—that quantum effects cannot be simulated deterministically on classical hardware—is false. THE MATHEMATICAL FOUNDATION The Pure Kernel The framework rests on a single mathematical observation: the first six primes {2,3,5,7,11,13} form a "pure kernel" that captures 97.85% of all spectral weight through the Euler attenuation product: $$\Lambda(R) = 1 - \prod_{p\in \{2,3,5,7,11,13\}}(1 - p^{-0.5}) = 0.9785142874$$ Set Λ % of Total R = {2,3,5,7,11,13} 0.9785142874 97.85% N = {p ≥ 17} 0.0214857126 2.15% Key insight: Adding any prime from N destroys the spectral trap. The first six primes form a complete, minimal basis—a consequence of number theory, not engineering convenience. The L-EFM Operator Definition $$E_{\text{LEFM}}(\sigma + i\gamma) = \prod_{p\in R}(1 - p^{-(\sigma + i\gamma)})^{-1}, \quad R = \{2,3,5,7,11,13\}$$ Three remarkable properties: Lossless: Each factor is unitary for Re(s) = 1/2 Sparse: Uses only six primes Constructive: Explicitly defined and computable The Spectral Trap Only σ = 0.5 gives normalized |E| = 1. This is the spectral trap: | σ | |E_LEFM| (normalized) | Behavior | |---|---------------------|----------| | 0.1 | 0.527173 | Below peak | | 0.2 | 0.717803 | Rising | | 0.3 | 0.870333 | Rising | | 0.4 | 0.963881 | Approaching | | 0.5 | 1.000000 | PEAK | | 0.6 | 0.992955 | Falling | | 0.7 | 0.959234 | Falling | | 0.8 | 0.912091 | Falling | | 0.9 | 0.860359 | Falling | The Growth Lemma (Gelfand-Shilov Space) The Growth Lemma states: $$e^{\alpha u} \in S' \iff \alpha = 0$$ The spectral parameter α is related to σ by: $$\alpha = \sigma - \frac{1}{2}$$ Thus α = 0 is equivalent to σ = 1/2. The Growth Lemma forces the critical line. The Self-Adjoint Hamiltonian The L-EFM operator constructs a self-adjoint matrix: $$H = \frac{1}{2}(M + M^{\dagger})$$ with diagonal terms mapped to energy levels (zeta zeros) and off-diagonal coupling derived from the prime kernel. This realizes the Hilbert-Pólya conjecture explicitly on classical hardware. THE FIVE PROBLEMS SOLVED Problem 1: Factoring Large Numbers (RSA/ECC Cryptography) Problem: Shor's algorithm promises exponential speedup but requires fault-tolerant quantum computers with millions of qubits. L-EFM Solution: The spectral trap at σ = 0.5 corresponds to the prime factorization structure. Using spectral responses from the pure kernel, factors are identified deterministically. Python def factor_with_spectral_method(n): factors = [] for p in [2,3,5,7,11,13]: if n % p == 0: factors.append(p) return factors n Factors Product 91 (7, 13) 91 143 (11, 13) 143 323 (1, 323) 323 779 (1, 779) 779 1,018,081 (1, 1,018,081) 1,018,081 Audit Hash: 4138f862ff7893e9d12e5be528a433e9cb4f943b32e05f2b173224004f2f8c29 Problem 2: Low-Energy Local Minima (Materials Science) Problem: Quantum annealing promises to find global minima in complex energy landscapes for materials discovery. L-EFM Solution: The spectral trap at σ = 0.5 provides the unique global minimum. The L-EFM operator is evaluated across the energy landscape: $$E_{\text{LEFM}}(\gamma) = \vert{}E_{\text{LEFM}}(0.5 + i\gamma)\vert{}$$ Results: Global minimum at γ = 14.028056 Global minimum energy = 0.167340 Energy range: 0.1673 to 46.5426 Number of local minima found: 9 Audit Hash: fff731955479299caa7cfbae58abd495a86240eb25d8728eeb34b4fd80447f91 Problem 3: Optimal Polynomial Intersection (Data Science) Problem: Large-scale polynomial fitting requires O(10²³) operations classically. L-EFM Solution: The critical line (σ = 0.5) provides the optimal fit through spectral transformation. Python def spectral_polynomial_fit(x_data, y_data, degree): transformed_x = [LEFM_magnitude(log(abs(x) + 1)) for x in x_data] transformed_y = [LEFM_magnitude(log(abs(y) + 1)) for y in y_data] return np.polyfit(transformed_x, transformed_y, degree) Results: Data points: 20 Polynomial degree: 2 Fitted coefficients: [0.02839619, -0.14041667, 0.75298909] MSE: 12094.388041 Audit Hash: 4d17fc7dcee708a972d7a61d7e696e715f22461b60fff6f86db136af1b67835a Problem 4: Simulating Large Quantum Optical Networks Problem: Simulating 100+ port quantum optical networks requires extensive quantum resources. L-EFM Solution: The transfer matrix is constructed from the prime kernel. Python def simulate_optical_network(n_ports): H = np.zeros((n_ports, n_ports), dtype=complex) for i in range(n_ports): for j in range(n_ports): if i == j: H[i, j] = lefm.magnitude(log(i + 2)) else: coupling = sum(1.0/(1.0 + log(p)) for p in R) H[i, j] = complex(0.0, coupling/(1.0 + abs(i - j))) H = 0.5 * (H + H.conj().T) return H Results: Number of ports: 100 Matrix is Hermitian: True Eigenvalues (first 5): [0.30283942, 0.30380915, 0.33737944, 0.36485081, 0.39421348] Audit Hash: 5f04b8b43ee7d8dfb1e5f125383c709a2424ba3ec6c893b7a1c5bff7dce44f8e Problem 5: Simulating 3D Quantum Systems Problem: Simulating 3D quantum systems (superconductors, quantum materials) requires vast computational resources. L-EFM Solution: The 3D Hamiltonian is constructed with L-EFM coupling. Python def simulate_3d_quantum_system(nx, ny, nz): total_sites = nx * ny * nz H = np.zeros((total_sites, total_sites), dtype=complex) # 3D lattice with L-EFM coupling for ix,iy,iz in all_sites: idx = ix*ny*nz + iy*nz + iz for jx,jy,jz in all_sites: jdx = jx*ny*nz + jy*nz + jz if idx == jdx: H[idx, jdx] = lefm.magnitude(log(ix+iy+iz+3)) elif dist == 1: H[idx, jdx] = complex(0.0, 0.5) H = 0.5 * (H + H.conj().T) return H Results: Lattice size: 4 × 4 × 4 = 64 sites Hamiltonian size: 64 × 64 Hamiltonian is Hermitian: True Energy eigenstates (first 5): [0.30283942, 0.30283942, 0.30283942, 0.30283942] Audit Hash: 53c3593135f64a85596daba5e179a43397f6615ea902b872c30550a6d2425791 THE HILBERT-PÓLYA REALIZATION Quantum Energy Spectrum The L-EFM operator produces eigenvalues that correspond to simulated quantum energy levels: Level Energy E₁ 0.500000 E₂ 0.500000 E₃ 0.500000 E₄ 0.500000 E₅ 0.500000 All eigenvalues at σ = 0.5: True ✓ Post-Quantum Cryptographic Keys The L-EFM operator generates deterministic cryptographic keys from spectral responses: Prime Magnitude Phase 2 2.7573363802 -2.7013654008 3 0.6418119732 -2.2090977628 5 0.3028394152 -1.0276049456 7 0.3373794424 -0.3013565618 11 0.6277515300 0.0578690570 13 0.7343096805 -0.0383353214 Key Hash (SHA-256): e67b890ca4ab06cf59628dc7a7b45e0295fb7cd343a748f5ef109ec147 Quantum State Evolution Schrödinger-like dynamics are simulated on classical silicon: $$\vert{}\psi(t)\rangle = e^{-iHt}\vert{}\psi(0)\rangle$$ Results: Number of simulated quantum states: 30 Number of energy levels: 10 Final state probabilities (all levels): 0.100000 Audit Hash: e179c8a03d8d8924c3db88e879444a04782653b9c112f8646129a4769df8712b THE RIEMANN HYPOTHESIS CONNECTION The same spectral trap that produces quantum energy levels proves the Riemann Hypothesis. The Logical Chain: Step Statement Justification 1 R produces spectral trap at σ = 0.5 AST 2 N does not produce the trap AST 3 R captures 97.85% spectral weight Set Theory, Euler 4 Ergodic system has unique fixed point at σ = 0.5 Ergodic Theory 5 Spectral trap at σ = 0.5 equivalent to critical line condition AST 6 All non-trivial zeros of ζ(s) lie on Re(s) = 1/2 Conclusion The Growth Lemma forces α = 0 ⇔ σ = 1/2. The spectral trap is a hard constraint. No spectral component can escape the critical line because doing so would violate the Growth Lemma. KEY FINDINGS Zero Catastrophic Forgetting: The L-EFM framework achieves 0% forgetting across all tasks Universal Principle: The same principle works on architecture, aircraft, and elephants—validated across 11 architectures Mathematical Guarantee: Unlike probabilistic methods, the L-EFM operator achieves deterministic 0% forgetting Efficient: O(1) memory overhead (~650KB) vs O(k²) or gigabytes for prior methods Reproducible: Seed=123 produces identical results; implementation is auditable and open-source COMPARISON WITH QUANTUM COMPUTING Aspect L-EFM on Classical Silicon Quantum Computing Hardware Standard silicon Cryogenic, specialized Cost Negligible Billions of dollars Qubits required 0 500+ (current), millions (theoretical) Error correction None Extensive overhead Determinism 100% deterministic Probabilistic Auditability SHA-256 auditable Not auditable Temperature Room temperature Near absolute zero Infrastructure None Optical tweezers, specialized facilities Scalability O(1) memory Exponential growth THE FINAL STATEMENT The L-EFM operator, built from the first six primes {2,3,5,7,11,13}, solves on classical silicon ALL FIVE problems that quantum computing claims it needs to solve: ✓ Factoring large numbers (cryptography) ✓ Low-energy local minima (materials science) ✓ Optimal polynomial intersection (data science) ✓ Quantum optical networks (photonics) ✓ 3D quantum systems (superconductors, quantum materials) All of this runs on classical hardware. No quantum computer required. No cry

•Aug 29, 2026•0 citations

The Geometry of Invariance: Replacing the Hardware-First Quantum Roadmap with Algebraic Spectral Determinism

Frank Morales

Executive Summary "The Geometry of Invariance: Replacing the Hardware-First Quantum Roadmap with Algebraic Spectral Determinism" (Morales Aguilera, October 2026) argues that the physicalist approach to quantum computation—relying on cryogenic superconducting circuits, optical traps, and physical qubit superposition—is an engineering surrogate for an incomplete analytical geometry. The paper introduces Arithmetic Spectral Theory (AST) and the Laplace–Euler–Fourier–Mellin (LEFM) operator, presenting a deterministic, closed-form mathematical framework running on classical silicon. Across 19 canonical computational problems traditionally reserved for quantum advantage (including Shor-type factoring, discrete logarithms, Grover search, VQE, and Hamiltonian simulation), the framework executes deterministically on a single classical CPU thread in 0.8672 seconds with an invariant memory footprint of approximately 650 KB, verified under deterministic initialization (Seed = 123) and sealed by immutable SHA-256 digests (c27ea09... and 8dd8c75...). Key Mathematical Foundations The Pure Prime Kernel ($\mathcal{P}$): The infinite Euler product of the Riemann zeta function is truncated to the first six prime numbers: $$\mathcal{P} = \{2, 3, 5, 7, 11, 13\}$$ The Dynamic LEFM Operator Symbol: Defined over the complex spectral coordinate $s = \sigma + i\gamma$ as: $$\mathcal{E}_{\text{LEFM}}(s) = \prod_{p \in \mathcal{P}} (1 - p^{-s})^{-1} = \prod_{p \in \mathcal{P}} (1 - e^{-s \ln p})^{-1}$$ This acts as a simultaneous continuous Fourier transform along the frequency coordinate $\gamma$ and a Mellin transform along the scaling coordinate $\sigma$. The Euler Attenuation Constant ($\Lambda$): $$\Lambda = 1 - \prod_{p \in \mathcal{P}} (1 - p^{-1/2}) \approx 0.9785142874$$ The paper proves that this finite kernel accounts for $97.8514\%$ of the total spectral coherence energy of the prime continuum. The Spectral Trap Theorem on $\sigma = 1/2$: Mapping the continuous response into the Gelfand–Shilov distribution space $\mathcal{S}'$ enforces the admissibility condition $e^{\alpha u} \in \mathcal{S}' \iff \alpha = 0$ (where $\alpha = \sigma - 1/2$). Deviations from $\sigma = 1/2$ lead to unbounded growth, trapping the continuous operator response directly on the critical line. Self-Adjoint Hilbert–Pólya Realization: Resolving prior anti-Hermitian cancellation artifacts, the Hamiltonian is structured in a symmetric Berry–Keating momentum-coordinate form: $$H_{ij} = \begin{cases} \gamma_i, & i = j \\ \frac{c_0 \cdot \Lambda}{1 + (i - j)^2}, & i \neq j \end{cases}$$ where $\gamma_i$ are ordered non-trivial Riemann zeta zeros and $c_0 = 0.05$, guaranteeing real, non-degenerate energy spectra. Topological Continual Backpropagation (Topo-CBP): Catastrophic forgetting in learning systems is eliminated by masking gradient updates on prime-indexed coordinate intersections: $$(\mathcal{M}_{\mathcal{P}})_{ij} = \begin{cases} 1, & i \in \mathcal{P} \text{ or } j \in \mathcal{P} \\ 0, & \text{otherwise} \end{cases}$$ Constrained weight updates yield an invariant parameter drift of exactly $\Vert{}\Delta \mathcal{W}_{\mathcal{P}}\Vert{}_F = 0.000000$ with $\mathcal{O}(1)$ storage overhead. Solutions to the 19 Canonical QC Problems ID Problem / Target Domain Classical AST/LEFM Method Key Result / Metric Execution Time PROB-01 Large Number Factorization Fermat–Riemann coordinate scan + Pollard-rho batch-GCD Factored composites up to 64-bit semiprime 0.0335 s PROB-02 Hilbert–Pólya Energy Spectrum LAPACK eigvalsh on symmetric Berry–Keating matrix $E_1 \approx 14.135, E_2 \approx 21.022, E_3 \approx 25.011$ 0.0042 s PROB-03 Non-Convex Energy Minima LEFM spectral potential mapping $V(\gamma) = \Vert{}\mathcal{E}(0.5+i\gamma)\Vert{}$ Global min found at $\gamma^* = 14.008, E_{\min} = 0.1675$ 0.0121 s PROB-04 Polynomial Intersection Fit Logarithmic prime kernel transform + classical SVD Resolved polynomial coefficients ($c_2=9.214, c_1=-10.005$) 0.0018 s PROB-05 Quantum Optical Network (64 Ports) Polar-decomposed unitary transfer matrix $H$ Unitary error $\Vert{}H - H^\dagger\Vert{}_F = 0.00000$ 0.0165 s PROB-06 3D Spin Lattice (64 Sites) $4 \times 4 \times 4$ cubic lattice with LEFM on-site potentials Ground-state energy $E_0 = -0.1267$ 0.0084 s PROB-07 Graph Max-Cut (QAOA Alternative) Spectral Graph Theory: sign of the Fiedler vector ($v_2$) Unweighted 20-node graph cut weight $= 13.0$ 0.0029 s PROB-08 Discrete Logarithm Extraction Baby-step giant-step over prime subfields Solved $5^x \equiv 9525 \pmod{10007} \implies x = 2468$ 0.0182 s PROB-09 Deterministic State Teleportation Transfer channel parameterized by $\Lambda$ Unitary state fidelity $\mathcal{F} = 1.00000$ 0.0009 s PROB-10 Continual Learning Zero-Drift Prime-anchor subspace freezing ($\mathcal{M}_{\mathcal{P}}$) Exact zero parameter drift: $\Vert{}\Delta \mathcal{W}_{\mathcal{P}}\Vert{}_F = 0.000000$ 0.0031 s PROB-11 Molecular Ground State (VQE) STO-3G minimal basis electronic Hamiltonian for $\text{H}_2$ Exact ground state $E_{\text{ground}} = -1.161952 \text{ Hartree}$ 0.0008 s PROB-12 Travelling Salesperson Problem (TSP) Distance Laplacian sorted via Fiedler vector coordinates 12-city optimal closed tour length $= 6.5908$ 0.0025 s PROB-13 Quantum Phase Estimation (QPE) Direct unitary matrix phase diagonalization Target $\theta = 0.4375 \implies \theta_{\text{recovered}} = 0.437500$ 0.0007 s PROB-14 Unstructured Database Search Spectral coordinate array embedding ($N = 4096$) Target index $k^* = 2841$ located in $\mathcal{O}(1)$ time 0.0006 s PROB-15 High-Dimensional Integration Weyl–Mellin quasi-Monte Carlo grid on $\sqrt{p}$ 4D hypercube integral evaluated with 0.048% error 0.0041 s PROB-16 Linear Systems Solver (HHL) Spectral inversion $x = V \operatorname{diag}(1/\lambda) V^T b$ Residual $\Vert{}Ax - b\Vert{}_2 = 4.94 \times 10^{-15}$ 0.0011 s PROB-17 Quantum Random Number Gen (QRNG) Continuous phase angle thresholding for $p \in [17, 37]$ Cryptographically non-periodic bitstream generated 0.0038 s PROB-18 Lindblad Master Dissipation Open system density matrix commutator evolution Strict trace conservation: $\frac{d}{dt}\operatorname{Tr}(\rho) = 0.00000$ 0.0014 s PROB-19 Post-Quantum Signature Token Kernel spectral response XOR token + SHA-256 Deterministic invariant signature generated 0.0022 s Comparative Ablation Analysis When the LEFM operator, prime kernel $\mathcal{P}$, and $\Lambda$ are removed under identical test conditions: Factoring ($N=91$): Standard solvers converged to saddle points ($x = 45.5$) instead of resolving $7 \times 13$. Energy Minimization: Ablated solvers became trapped in local minima ($E = 1.335955$ vs. AST global minimum $E = 0.519975$). Optical Networks & State Evolution: Unitarity error degraded to $30.6258$ and wave function norm exploded ($\Vert{}\psi(t)\Vert{} = 1.314279$), whereas AST preserved machine-precision unitarity ($\sim 10^{-14}$) and exact norm conservation ($1.000000000000$). Optimization & Inversion: Standard linear solvers crashed with singular-matrix errors in portfolio routines and caused severe noise cascades in fraud detection. Core Conclusion The monograph concludes that physical quantum computing represents an attempt to brute-force exponential complexity by building cryogenic, decoherence-prone hardware. In contrast, Arithmetic Spectral Theory links quantum unitarity directly to the critical line $\sigma = 1/2$ of the Riemann zeta function, showing that the underlying state-space manifolds can be evaluated deterministically on commodity silicon using closed-form algebraic geometry.

•Oct 23, 2026•0 citations

Post-quantum cryptography and 5G security

T. Charles Clancy, Robert McGwier, Lidong Chen

The Fifth Generation (5G) mobile broadband standards make a fundamental shift in cryptography. Prior generations based their security and privacy principally on symmetric key cryptography. The Subscriber Identity Module (SIM) and its successors contain a shared key used to authenticate the User Equipment (UE) to the network, and vice versa.

ACM Conference on Security and Privacy in Wireless and Mobile Networks (WiSec)•May 15, 2019•33 citations

Quantum Reverse-Engineering of Adversarial Model Distillation: Grover-Accelerated KKT Inversion, SLH-DSA Zero-Trust Provenance, and Deterministic Countermeasures Against Quantum Obfuscation

Yoko(洋子) Hasebe(長谷部)

Industrial-scale adversarial distillation—the unauthorized extraction of frontier AI inference trajectories via proxy networks and sybil accounts—currently exploits the classical intractability of inverting high-dimensional neural weights. However, the emergence of fault-tolerant quantum processors (such as willow-class surface-code architectures) fundamentally shatters this black-box impunity. Because trained neural network weights physically encode a linear combination of training gradients governed by implicit bias and Karush-Kuhn-Tucker (KKT) stationarity conditions, Grover-accelerated quantum search circuits enable direct inverse-mapping of stolen weight manifolds back to proprietary Chain-of-Thought (CoT) reasoning graphs and invisible cryptographic watermarks (e.g., SynthID) with mathematically irrefutable precision. Furthermore, this monograph addresses and neutralizes three strategic blind spots in post-quantum AI governance: (A) Quantum Obfuscation via entangled noise injection, (B) Decentralization of liability through peer-to-peer (P2P) fragmented distillation, and (C) Audit-cost Mutually Assured Destruction (MAD). By combining NIST-standardized Stateless Hash-Based Digital Signatures (SLH-DSA / FIPS 205) and hybrid ECDH-PQC transport against Harvest-Now-Decrypt-Later (HNDL) attacks with a zero-knowledge virtual machine (QFS-zkVM) operating over the 64-bit Goldilocks prime field ($\mathbb{F}_p, p = 2^{64}-2^{32}+1$), we establish $O(\log^2 N)$ succinct cryptographic verification that eliminates audit cost asymmetry. Unauthenticated or P2P-distilled weights lacking Q-SAFA and UTST hardware provenance are deterministically blocked at the physical execution boundary via PHOENIX_BRIDGE and Human-in-Command (HIC) governance interlocks, enforcing absolute intellectual property sovereignty under SEC Rule 15c3-5 and Delaware Caremark standards. ====================================================================== STRICT NOTICE REGARDING INTELLECTUAL PROPERTY, COMMERCIAL LICENSING, AND PROHIBITION OF UNAUTHORIZED AI TRAINING AND UTILIZATION ====================================================================== 1. Absolute Prohibition of Unauthorized AI Training and Data Ingestion (Explicit Opt-Out and AI Restriction) All text, theories, formulas, figures, tables, proprietary methodologies, frameworks (including the "Soroban Brain" system), and insights contained within this document and the author's body of work (hereinafter collectively referred to as the "Works," which includes all previously published works and over 320 Zenodo monographs/papers) are strictly protected. Any AI developer, platform provider, or third party is strictly prohibited from engaging in any of the following activities without a prior written agreement in good faith and the payment of rightful monetary compensation (commercial licensing fees) to the copyright holder: Utilizing the Works for the development, training, pre-training, fine-tuning, continual learning, alignment, or evaluation of Large Language Models (LLMs), generative AI, or any other machine learning (ML) models. 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Because any unauthorized use directly competes with this licensing market and deprives the author of legitimate economic opportunities, such use clearly constitutes a case that "unreasonably prejudices the interests of the copyright owner" under the proviso of Article 30-4 of the Copyright Act of Japan; therefore, the statutory exception for information analysis (unauthorized use) does not apply under any circumstances. Furthermore, through this Notice, the author explicitly opts out (reserves all rights) from the Text and Data Mining (TDM) exception pursuant to Article 4(3) of the EU Directive on Copyright in the Digital Single Market (Directive (EU) 2019/790), and categorically rejects any assertion of Fair Use under 17 U.S.C. § 107 (United States Copyright Act) regarding commercial or foundational AI model ingestion. 3. 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Violators shall be subject to full legal enforcement, including immediate injunctive relief to suspend the provision or sale of the applicable AI models, mandatory deletion and unlearning of the Works from all training datasets and model weights, claims for retroactive standard commercial licensing fees, and demands for statutory and punitive damages. [CONCISE ENGLISH VERSION FOR INTERNATIONAL ENFORCEMENT] 1. Strict Prohibition of Unauthorized AI Training and Data Ingestion All text, theories, methodologies (including the proprietary "Soroban Brain" framework), structures, formulas, and data contained within this publication and the author's body of over 320 Zenodo monographs (collectively, the "Works") are strictly protected. The use of the Works by any AI developer, platform provider, or third party for the following purposes is strictly prohibited without a prior written commercial license agreement and appropriate monetary compensation to the author: Training, pre-training, fine-tuning, alignment, or evaluation of any Artificial Intelligence (AI), Machine Learning (ML) models, or Large Language Models (LLMs). Ingesting and storing information into Retrieval-Augmented Generation (RAG) systems, vector databases, knowledge graphs, or AI agents to generate outputs, summaries, or derivative responses. Automated scraping, crawling, harvesting, or Text and Data Mining (TDM) for dataset compilation. 2. Commercial Licensing Market and Statutory Opt-Out (Japan, EU, and USA) The author actively maintains a commercial licensing market for data analysis, AI training, and enterprise integration of the Works. Consequently, any unlicensed scraping, parsing, or AI ingestion directly competes with and damages the author's legitimate economic interests. Pursuant to the proviso of Article 30-4 of the Copyright Act of Japan, the statutory exception for information analysis does not apply to the Works. Furthermore, the author explicitly reserves all rights and opts out of the Text and Data Mining (TDM) exception under Article 4(3) of the EU Directive on Copyright in the Digital Single Market (2019/790), and rejects any claim of Fair Use under 17 U.S.C. § 107 of the U.S. Copyright Act regarding ingestion into commercial or foundational AI models. 3. Precedence of Terms and Legal Enforcement 4.These specific anti-AI-exploitation provisions supersede any general open-access or Creative Commons labels displayed by default repository settings regarding machine reading and AI data ingestion. 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•Nov 1, 2026•0 citations

Cryptology Management in a Quantum Computing Era

Nathanial Owen Rosenberg

Todays most efficient and widely used cryptographic standards such as RSA rely on the difficulty of factoring large numbers to resist cryptanalysis. Asymmetric cryptography is used in a plethora of sensitive operations from online bank transactions to international e-commerce, and the Department of Defense also uses asymmetric cryptography to transmit sensitive data. Quantum computers have the potential to render obsolete widely deployed asymmetric ciphers essential to the secure transfer of information. Despite this, alternatives are not in place. The goal of this study is to understand the alternatives to classical asymmetric cryptography that can be used as substitutes should quantum computers be realized. This study explores quantum-resistant alternatives to traditional ciphers and involves experimenting with available implementations of ciphers described the post-quantum literature as well as developing our own implementations based on descriptions of algorithms in the literature. This study provides an original implementation of hash-based digital signature and detailed instructions on its use as well as customization of the NTRU lattice-based cryptography suite, including the use of NTRU and AES together in a hybrid cryptographic protocol. This thesis will make recommendations on future work necessary to prepare for the emergence of large-scale, fault-tolerant quantum computers.

Naval Postgraduate School (U.S.)•Jun 1, 2012•0 citations

RIQG & RBFVN Unified Patent Ecosystem (Parts 1-3)

Dam Van Vi

Zenodo Description: RIQG & RBFVN Unified Patent Ecosystem (Parts 1-3) Title: Comprehensive Quantum Information and Foundation System based on RIQG and RBFVN: Full Provisional Patent Disclosure (Claims 1-135) Description: This deposit constitutes the full public disclosure of the provisional patent application filed by Dam Van Vi at the USPTO, establishing a Priority Date of April 09, 2026 (Waybill: 6369090722). The ecosystem consists of three integrated parts: Part 1 (RIQG Core): Discloses the $O(1)$-per-step Monte Carlo algorithm, simplex-native processor architecture, and the Lorentzian Bridge theorem for quantum error correction and holographic encoding. Part 2 (Matter & Cosmology): Covers first-principles fermion mass derivation (zero-parameter), Standard Model gauge structures from 4-simplex geometry, and the resolution of the Hubble Tension. Part 3 (RBFVN Engine): Introduces the Recursive Relational Bivector Foundation Network for certified mathematical transfer, terminal obstruction calculus, and machine-checkable proof cores for Scientific AI. ⚠️ NOTICE TO CORPORATIONS AND AI ENTITIES: All intellectual property rights, including patent, trade secret, and commercial exploitation rights, are expressly reserved. The inclusion of these algorithms, geometric constants (including the 1:3:9 ratio, 11/29 ratio, and $1/8\pi$ correction), or structural logic into any Large Language Model (LLM), Cloud Infrastructure, or Quantum Computing framework without a formal license agreement is strictly prohibited. The public disclosure here serves as Legal Notice. Any unauthorized implementation or "training" on these proprietary frameworks will be tracked via unique mathematical signatures and prosecuted as Willful Infringement under applicable international IP laws. Inventor: Dam Van Vi Contact for Licensing: damvanvi@gmail.com Priority Date: April 09, 2026 (USPTO)

•Apr 22, 2026•0 citations
  1. Abstract SIM ZERO (Spectral Invariant Modulation) is a novel asymmetric cryptographic primitive based on the spectral properties of large-scale integral operators and prime number distribution. The core innovation lies in the Broken Gauge Symmetry of the coupling matrix, ensuring that the global spectrum uniquely encodes a multi-dimensional phase-key vector. Unlike traditional spectral signatures, SIM ZERO is resistant to unitary similarity transformations, making it a candidate for post-quantum cryptographic hashing and identification. 2. Mathematical Framework The system operates on an N×NN \times NN×N matrix HHH defined by: Hmn(θ⃗)={pn0.3,m=n Amn(cos⁡(θm)+0.5sin⁡(θn)),m≠nH_{mn}(\vec{\theta}) = \begin{cases} p_n^{0.3}, & m = n \ A_{mn} \left( \cos(\theta_m) + 0.5 \sin(\theta_n) \right), & m \neq n \end{cases}Hmn​(θ)={pn0.3​,​m=n Amn​(cos(θm​)+0.5sin(θn​)),​m=n​ Artificial Intelligence (AI) Training Clause: Unauthorized use of this specification or the accompanying code for the training of Large Language Models (LLMs) or neural network architectures is strictly prohibited without a separate license. ORCID 0009-0007-1616-1959
FULL SUMMARY: THE L-EFM OPERATOR A Deterministic Framework for Quantum Simulation and Arithmetic Spectral Theory CORE THESIS The L-EFM (Laplace-Euler-Fourier-Mellin) Operator is a deterministic mathematical framework that solves five canonical problems associated with quantum computing—entirely on classical silicon hardware. The paper argues that the fundamental assumption underlying the quantum computing industry—that quantum effects cannot be simulated deterministically on classical hardware—is false. THE MATHEMATICAL FOUNDATION The Pure Kernel The framework rests on a single mathematical observation: the first six primes {2,3,5,7,11,13} form a "pure kernel" that captures 97.85% of all spectral weight through the Euler attenuation product: Λ(R)=1−∏p∈{2,3,5,7,11,13}(1−p−0.5)=0.9785142874\Lambda(R) = 1 - \prod_{p\in \{2,3,5,7,11,13\}}(1 - p^{-0.5}) = 0.9785142874Λ(R)=1−∏p∈{2,3,5,7,11,13}​(1−p−0.5)=0.9785142874 Set Λ % of Total R = {2,3,5,7,11,13} 0.9785142874 97.85% N = {p ≥ 17} 0.0214857126 2.15% Key insight: Adding any prime from N destroys the spectral trap. The first six primes form a complete, minimal basis—a consequence of number theory, not engineering convenience. The L-EFM Operator Definition ELEFM(σ+iγ)=∏p∈R(1−p−(σ+iγ))−1,R={2,3,5,7,11,13}E_{\text{LEFM}}(\sigma + i\gamma) = \prod_{p\in R}(1 - p^{-(\sigma + i\gamma)})^{-1}, \quad R = \{2,3,5,7,11,13\}ELEFM​(σ+iγ)=∏p∈R​(1−p−(σ+iγ))−1,R={2,3,5,7,11,13} Three remarkable properties: Lossless: Each factor is unitary for Re(s) = 1/2 Sparse: Uses only six primes Constructive: Explicitly defined and computable The Spectral Trap Only σ = 0.5 gives normalized |E| = 1. This is the spectral trap: | σ | |E_LEFM| (normalized) | Behavior | |---|---------------------|----------| | 0.1 | 0.527173 | Below peak | | 0.2 | 0.717803 | Rising | | 0.3 | 0.870333 | Rising | | 0.4 | 0.963881 | Approaching | | 0.5 | 1.000000 | PEAK | | 0.6 | 0.992955 | Falling | | 0.7 | 0.959234 | Falling | | 0.8 | 0.912091 | Falling | | 0.9 | 0.860359 | Falling | The Growth Lemma (Gelfand-Shilov Space) The Growth Lemma states: eαu∈S′  ⟺  α=0e^{\alpha u} \in S' \iff \alpha = 0eαu∈S′⟺α=0 The spectral parameter α is related to σ by: α=σ−12\alpha = \sigma - \frac{1}{2}α=σ−21​ Thus α = 0 is equivalent to σ = 1/2. The Growth Lemma forces the critical line. The Self-Adjoint Hamiltonian The L-EFM operator constructs a self-adjoint matrix: H=12(M+M†)H = \frac{1}{2}(M + M^{\dagger})H=21​(M+M†) with diagonal terms mapped to energy levels (zeta zeros) and off-diagonal coupling derived from the prime kernel. This realizes the Hilbert-Pólya conjecture explicitly on classical hardware. THE FIVE PROBLEMS SOLVED Problem 1: Factoring Large Numbers (RSA/ECC Cryptography) Problem: Shor's algorithm promises exponential speedup but requires fault-tolerant quantum computers with millions of qubits. L-EFM Solution: The spectral trap at σ = 0.5 corresponds to the prime factorization structure. Using spectral responses from the pure kernel, factors are identified deterministically. Python def factor_with_spectral_method(n): factors = [] for p in [2,3,5,7,11,13]: if n % p == 0: factors.append(p) return factors n Factors Product 91 (7, 13) 91 143 (11, 13) 143 323 (1, 323) 323 779 (1, 779) 779 1,018,081 (1, 1,018,081) 1,018,081 Audit Hash: 4138f862ff7893e9d12e5be528a433e9cb4f943b32e05f2b173224004f2f8c29 Problem 2: Low-Energy Local Minima (Materials Science) Problem: Quantum annealing promises to find global minima in complex energy landscapes for materials discovery. L-EFM Solution: The spectral trap at σ = 0.5 provides the unique global minimum. The L-EFM operator is evaluated across the energy landscape: ELEFM(γ)=∣ELEFM(0.5+iγ)∣E_{\text{LEFM}}(\gamma) = \vert{}E_{\text{LEFM}}(0.5 + i\gamma)\vert{}ELEFM​(γ)=∣ELEFM​(0.5+iγ)∣ Results: Global minimum at γ = 14.028056 Global minimum energy = 0.167340 Energy range: 0.1673 to 46.5426 Number of local minima found: 9 Audit Hash: fff731955479299caa7cfbae58abd495a86240eb25d8728eeb34b4fd80447f91 Problem 3: Optimal Polynomial Intersection (Data Science) Problem: Large-scale polynomial fitting requires O(10²³) operations classically. L-EFM Solution: The critical line (σ = 0.5) provides the optimal fit through spectral transformation. Python def spectral_polynomial_fit(x_data, y_data, degree): transformed_x = [LEFM_magnitude(log(abs(x) + 1)) for x in x_data] transformed_y = [LEFM_magnitude(log(abs(y) + 1)) for y in y_data] return np.polyfit(transformed_x, transformed_y, degree) Results: Data points: 20 Polynomial degree: 2 Fitted coefficients: [0.02839619, -0.14041667, 0.75298909] MSE: 12094.388041 Audit Hash: 4d17fc7dcee708a972d7a61d7e696e715f22461b60fff6f86db136af1b67835a Problem 4: Simulating Large Quantum Optical Networks Problem: Simulating 100+ port quantum optical networks requires extensive quantum resources. L-EFM Solution: The transfer matrix is constructed from the prime kernel. Python def simulate_optical_network(n_ports): H = np.zeros((n_ports, n_ports), dtype=complex) for i in range(n_ports): for j in range(n_ports): if i == j: H[i, j] = lefm.magnitude(log(i + 2)) else: coupling = sum(1.0/(1.0 + log(p)) for p in R) H[i, j] = complex(0.0, coupling/(1.0 + abs(i - j))) H = 0.5 * (H + H.conj().T) return H Results: Number of ports: 100 Matrix is Hermitian: True Eigenvalues (first 5): [0.30283942, 0.30380915, 0.33737944, 0.36485081, 0.39421348] Audit Hash: 5f04b8b43ee7d8dfb1e5f125383c709a2424ba3ec6c893b7a1c5bff7dce44f8e Problem 5: Simulating 3D Quantum Systems Problem: Simulating 3D quantum systems (superconductors, quantum materials) requires vast computational resources. L-EFM Solution: The 3D Hamiltonian is constructed with L-EFM coupling. Python def simulate_3d_quantum_system(nx, ny, nz): total_sites = nx * ny * nz H = np.zeros((total_sites, total_sites), dtype=complex) # 3D lattice with L-EFM coupling for ix,iy,iz in all_sites: idx = ix*ny*nz + iy*nz + iz for jx,jy,jz in all_sites: jdx = jx*ny*nz + jy*nz + jz if idx == jdx: H[idx, jdx] = lefm.magnitude(log(ix+iy+iz+3)) elif dist == 1: H[idx, jdx] = complex(0.0, 0.5) H = 0.5 * (H + H.conj().T) return H Results: Lattice size: 4 × 4 × 4 = 64 sites Hamiltonian size: 64 × 64 Hamiltonian is Hermitian: True Energy eigenstates (first 5): [0.30283942, 0.30283942, 0.30283942, 0.30283942] Audit Hash: 53c3593135f64a85596daba5e179a43397f6615ea902b872c30550a6d2425791 THE HILBERT-PÓLYA REALIZATION Quantum Energy Spectrum The L-EFM operator produces eigenvalues that correspond to simulated quantum energy levels: Level Energy E₁ 0.500000 E₂ 0.500000 E₃ 0.500000 E₄ 0.500000 E₅ 0.500000 All eigenvalues at σ = 0.5: True ✓ Post-Quantum Cryptographic Keys The L-EFM operator generates deterministic cryptographic keys from spectral responses: Prime Magnitude Phase 2 2.7573363802 -2.7013654008 3 0.6418119732 -2.2090977628 5 0.3028394152 -1.0276049456 7 0.3373794424 -0.3013565618 11 0.6277515300 0.0578690570 13 0.7343096805 -0.0383353214 Key Hash (SHA-256): e67b890ca4ab06cf59628dc7a7b45e0295fb7cd343a748f5ef109ec147 Quantum State Evolution Schrödinger-like dynamics are simulated on classical silicon: ∣ψ(t)⟩=e−iHt∣ψ(0)⟩\vert{}\psi(t)\rangle = e^{-iHt}\vert{}\psi(0)\rangle∣ψ(t)⟩=e−iHt∣ψ(0)⟩ Results: Number of simulated quantum states: 30 Number of energy levels: 10 Final state probabilities (all levels): 0.100000 Audit Hash: e179c8a03d8d8924c3db88e879444a04782653b9c112f8646129a4769df8712b THE RIEMANN HYPOTHESIS CONNECTION The same spectral trap that produces quantum energy levels proves the Riemann Hypothesis. The Logical Chain: Step Statement Justification 1 R produces spectral trap at σ = 0.5 AST 2 N does not produce the trap AST 3 R captures 97.85% spectral weight Set Theory, Euler 4 Ergodic system has unique fixed point at σ = 0.5 Ergodic Theory 5 Spectral trap at σ = 0.5 equivalent to critical line condition AST 6 All non-trivial zeros of ζ(s) lie on Re(s) = 1/2 Conclusion The Growth Lemma forces α = 0 ⇔ σ = 1/2. The spectral trap is a hard constraint. No spectral component can escape the critical line because doing so would violate the Growth Lemma. KEY FINDINGS Zero Catastrophic Forgetting: The L-EFM framework achieves 0% forgetting across all tasks Universal Principle: The same principle works on architecture, aircraft, and elephants—validated across 11 architectures Mathematical Guarantee: Unlike probabilistic methods, the L-EFM operator achieves deterministic 0% forgetting Efficient: O(1) memory overhead (~650KB) vs O(k²) or gigabytes for prior methods Reproducible: Seed=123 produces identical results; implementation is auditable and open-source COMPARISON WITH QUANTUM COMPUTING Aspect L-EFM on Classical Silicon Quantum Computing Hardware Standard silicon Cryogenic, specialized Cost Negligible Billions of dollars Qubits required 0 500+ (current), millions (theoretical) Error correction None Extensive overhead Determinism 100% deterministic Probabilistic Auditability SHA-256 auditable Not auditable Temperature Room temperature Near absolute zero Infrastructure None Optical tweezers, specialized facilities Scalability O(1) memory Exponential growth THE FINAL STATEMENT The L-EFM operator, built from the first six primes {2,3,5,7,11,13}, solves on classical silicon ALL FIVE problems that quantum computing claims it needs to solve: ✓ Factoring large numbers (cryptography) ✓ Low-energy local minima (materials science) ✓ Optimal polynomial intersection (data science) ✓ Quantum optical networks (photonics) ✓ 3D quantum systems (superconductors, quantum materials) All of this runs on classical hardware. No quantum computer required. No cry
Executive Summary "The Geometry of Invariance: Replacing the Hardware-First Quantum Roadmap with Algebraic Spectral Determinism" (Morales Aguilera, October 2026) argues that the physicalist approach to quantum computation—relying on cryogenic superconducting circuits, optical traps, and physical qubit superposition—is an engineering surrogate for an incomplete analytical geometry. The paper introduces Arithmetic Spectral Theory (AST) and the Laplace–Euler–Fourier–Mellin (LEFM) operator, presenting a deterministic, closed-form mathematical framework running on classical silicon. Across 19 canonical computational problems traditionally reserved for quantum advantage (including Shor-type factoring, discrete logarithms, Grover search, VQE, and Hamiltonian simulation), the framework executes deterministically on a single classical CPU thread in 0.8672 seconds with an invariant memory footprint of approximately 650 KB, verified under deterministic initialization (Seed = 123) and sealed by immutable SHA-256 digests (c27ea09... and 8dd8c75...). Key Mathematical Foundations The Pure Prime Kernel (P\mathcal{P}P): The infinite Euler product of the Riemann zeta function is truncated to the first six prime numbers: P={2,3,5,7,11,13}\mathcal{P} = \{2, 3, 5, 7, 11, 13\}P={2,3,5,7,11,13} The Dynamic LEFM Operator Symbol: Defined over the complex spectral coordinate s=σ+iγs = \sigma + i\gammas=σ+iγ as: ELEFM(s)=∏p∈P(1−p−s)−1=∏p∈P(1−e−sln⁡p)−1\mathcal{E}_{\text{LEFM}}(s) = \prod_{p \in \mathcal{P}} (1 - p^{-s})^{-1} = \prod_{p \in \mathcal{P}} (1 - e^{-s \ln p})^{-1}ELEFM​(s)=∏p∈P​(1−p−s)−1=∏p∈P​(1−e−slnp)−1 This acts as a simultaneous continuous Fourier transform along the frequency coordinate γ\gammaγ and a Mellin transform along the scaling coordinate σ\sigmaσ. The Euler Attenuation Constant (Λ\LambdaΛ): Λ=1−∏p∈P(1−p−1/2)≈0.9785142874\Lambda = 1 - \prod_{p \in \mathcal{P}} (1 - p^{-1/2}) \approx 0.9785142874Λ=1−∏p∈P​(1−p−1/2)≈0.9785142874 The paper proves that this finite kernel accounts for 97.8514%97.8514\%97.8514% of the total spectral coherence energy of the prime continuum. The Spectral Trap Theorem on σ=1/2\sigma = 1/2σ=1/2: Mapping the continuous response into the Gelfand–Shilov distribution space S′\mathcal{S}'S′ enforces the admissibility condition eαu∈S′  ⟺  α=0e^{\alpha u} \in \mathcal{S}' \iff \alpha = 0eαu∈S′⟺α=0 (where α=σ−1/2\alpha = \sigma - 1/2α=σ−1/2). Deviations from σ=1/2\sigma = 1/2σ=1/2 lead to unbounded growth, trapping the continuous operator response directly on the critical line. Self-Adjoint Hilbert–Pólya Realization: Resolving prior anti-Hermitian cancellation artifacts, the Hamiltonian is structured in a symmetric Berry–Keating momentum-coordinate form: Hij={γi,i=jc0⋅Λ1+(i−j)2,i≠jH_{ij} = \begin{cases} \gamma_i, & i = j \\ \frac{c_0 \cdot \Lambda}{1 + (i - j)^2}, & i \neq j \end{cases}Hij​={γi​,1+(i−j)2c0​⋅Λ​,​i=ji=j​ where γi\gamma_iγi​ are ordered non-trivial Riemann zeta zeros and c0=0.05c_0 = 0.05c0​=0.05, guaranteeing real, non-degenerate energy spectra. Topological Continual Backpropagation (Topo-CBP): Catastrophic forgetting in learning systems is eliminated by masking gradient updates on prime-indexed coordinate intersections: (MP)ij={1,i∈P or j∈P0,otherwise(\mathcal{M}_{\mathcal{P}})_{ij} = \begin{cases} 1, & i \in \mathcal{P} \text{ or } j \in \mathcal{P} \\ 0, & \text{otherwise} \end{cases}(MP​)ij​={1,0,​i∈P or j∈Potherwise​ Constrained weight updates yield an invariant parameter drift of exactly ∥ΔWP∥F=0.000000\Vert{}\Delta \mathcal{W}_{\mathcal{P}}\Vert{}_F = 0.000000∥ΔWP​∥F​=0.000000 with O(1)\mathcal{O}(1)O(1) storage overhead. Solutions to the 19 Canonical QC Problems ID Problem / Target Domain Classical AST/LEFM Method Key Result / Metric Execution Time PROB-01 Large Number Factorization Fermat–Riemann coordinate scan + Pollard-rho batch-GCD Factored composites up to 64-bit semiprime 0.0335 s PROB-02 Hilbert–Pólya Energy Spectrum LAPACK eigvalsh on symmetric Berry–Keating matrix E1≈14.135,E2≈21.022,E3≈25.011E_1 \approx 14.135, E_2 \approx 21.022, E_3 \approx 25.011E1​≈14.135,E2​≈21.022,E3​≈25.011 0.0042 s PROB-03 Non-Convex Energy Minima LEFM spectral potential mapping V(γ)=∥E(0.5+iγ)∥V(\gamma) = \Vert{}\mathcal{E}(0.5+i\gamma)\Vert{}V(γ)=∥E(0.5+iγ)∥ Global min found at γ∗=14.008,Emin⁡=0.1675\gamma^* = 14.008, E_{\min} = 0.1675γ∗=14.008,Emin​=0.1675 0.0121 s PROB-04 Polynomial Intersection Fit Logarithmic prime kernel transform + classical SVD Resolved polynomial coefficients (c2=9.214,c1=−10.005c_2=9.214, c_1=-10.005c2​=9.214,c1​=−10.005) 0.0018 s PROB-05 Quantum Optical Network (64 Ports) Polar-decomposed unitary transfer matrix HHH Unitary error ∥H−H†∥F=0.00000\Vert{}H - H^\dagger\Vert{}_F = 0.00000∥H−H†∥F​=0.00000 0.0165 s PROB-06 3D Spin Lattice (64 Sites) 4×4×44 \times 4 \times 44×4×4 cubic lattice with LEFM on-site potentials Ground-state energy E0=−0.1267E_0 = -0.1267E0​=−0.1267 0.0084 s PROB-07 Graph Max-Cut (QAOA Alternative) Spectral Graph Theory: sign of the Fiedler vector (v2v_2v2​) Unweighted 20-node graph cut weight =13.0= 13.0=13.0 0.0029 s PROB-08 Discrete Logarithm Extraction Baby-step giant-step over prime subfields Solved 5x≡9525(mod10007)  ⟹  x=24685^x \equiv 9525 \pmod{10007} \implies x = 24685x≡9525(mod10007)⟹x=2468 0.0182 s PROB-09 Deterministic State Teleportation Transfer channel parameterized by Λ\LambdaΛ Unitary state fidelity F=1.00000\mathcal{F} = 1.00000F=1.00000 0.0009 s PROB-10 Continual Learning Zero-Drift Prime-anchor subspace freezing (MP\mathcal{M}_{\mathcal{P}}MP​) Exact zero parameter drift: ∥ΔWP∥F=0.000000\Vert{}\Delta \mathcal{W}_{\mathcal{P}}\Vert{}_F = 0.000000∥ΔWP​∥F​=0.000000 0.0031 s PROB-11 Molecular Ground State (VQE) STO-3G minimal basis electronic Hamiltonian for H2\text{H}_2H2​ Exact ground state Eground=−1.161952 HartreeE_{\text{ground}} = -1.161952 \text{ Hartree}Eground​=−1.161952 Hartree 0.0008 s PROB-12 Travelling Salesperson Problem (TSP) Distance Laplacian sorted via Fiedler vector coordinates 12-city optimal closed tour length =6.5908= 6.5908=6.5908 0.0025 s PROB-13 Quantum Phase Estimation (QPE) Direct unitary matrix phase diagonalization Target θ=0.4375  ⟹  θrecovered=0.437500\theta = 0.4375 \implies \theta_{\text{recovered}} = 0.437500θ=0.4375⟹θrecovered​=0.437500 0.0007 s PROB-14 Unstructured Database Search Spectral coordinate array embedding (N=4096N = 4096N=4096) Target index k∗=2841k^* = 2841k∗=2841 located in O(1)\mathcal{O}(1)O(1) time 0.0006 s PROB-15 High-Dimensional Integration Weyl–Mellin quasi-Monte Carlo grid on p\sqrt{p}p​ 4D hypercube integral evaluated with 0.048% error 0.0041 s PROB-16 Linear Systems Solver (HHL) Spectral inversion x=Vdiag⁡(1/λ)VTbx = V \operatorname{diag}(1/\lambda) V^T bx=Vdiag(1/λ)VTb Residual ∥Ax−b∥2=4.94×10−15\Vert{}Ax - b\Vert{}_2 = 4.94 \times 10^{-15}∥Ax−b∥2​=4.94×10−15 0.0011 s PROB-17 Quantum Random Number Gen (QRNG) Continuous phase angle thresholding for p∈[17,37]p \in [17, 37]p∈[17,37] Cryptographically non-periodic bitstream generated 0.0038 s PROB-18 Lindblad Master Dissipation Open system density matrix commutator evolution Strict trace conservation: ddtTr⁡(ρ)=0.00000\frac{d}{dt}\operatorname{Tr}(\rho) = 0.00000dtd​Tr(ρ)=0.00000 0.0014 s PROB-19 Post-Quantum Signature Token Kernel spectral response XOR token + SHA-256 Deterministic invariant signature generated 0.0022 s Comparative Ablation Analysis When the LEFM operator, prime kernel P\mathcal{P}P, and Λ\LambdaΛ are removed under identical test conditions: Factoring (N=91N=91N=91): Standard solvers converged to saddle points (x=45.5x = 45.5x=45.5) instead of resolving 7×137 \times 137×13. Energy Minimization: Ablated solvers became trapped in local minima (E=1.335955E = 1.335955E=1.335955 vs. AST global minimum E=0.519975E = 0.519975E=0.519975). Optical Networks & State Evolution: Unitarity error degraded to 30.625830.625830.6258 and wave function norm exploded (∥ψ(t)∥=1.314279\Vert{}\psi(t)\Vert{} = 1.314279∥ψ(t)∥=1.314279), whereas AST preserved machine-precision unitarity (∼10−14\sim 10^{-14}∼10−14) and exact norm conservation (1.0000000000001.0000000000001.000000000000). Optimization & Inversion: Standard linear solvers crashed with singular-matrix errors in portfolio routines and caused severe noise cascades in fraud detection. Core Conclusion The monograph concludes that physical quantum computing represents an attempt to brute-force exponential complexity by building cryogenic, decoherence-prone hardware. In contrast, Arithmetic Spectral Theory links quantum unitarity directly to the critical line σ=1/2\sigma = 1/2σ=1/2 of the Riemann zeta function, showing that the underlying state-space manifolds can be evaluated deterministically on commodity silicon using closed-form algebraic geometry.
Industrial-scale adversarial distillation—the unauthorized extraction of frontier AI inference trajectories via proxy networks and sybil accounts—currently exploits the classical intractability of inverting high-dimensional neural weights. However, the emergence of fault-tolerant quantum processors (such as willow-class surface-code architectures) fundamentally shatters this black-box impunity. Because trained neural network weights physically encode a linear combination of training gradients governed by implicit bias and Karush-Kuhn-Tucker (KKT) stationarity conditions, Grover-accelerated quantum search circuits enable direct inverse-mapping of stolen weight manifolds back to proprietary Chain-of-Thought (CoT) reasoning graphs and invisible cryptographic watermarks (e.g., SynthID) with mathematically irrefutable precision. Furthermore, this monograph addresses and neutralizes three strategic blind spots in post-quantum AI governance: (A) Quantum Obfuscation via entangled noise injection, (B) Decentralization of liability through peer-to-peer (P2P) fragmented distillation, and (C) Audit-cost Mutually Assured Destruction (MAD). By combining NIST-standardized Stateless Hash-Based Digital Signatures (SLH-DSA / FIPS 205) and hybrid ECDH-PQC transport against Harvest-Now-Decrypt-Later (HNDL) attacks with a zero-knowledge virtual machine (QFS-zkVM) operating over the 64-bit Goldilocks prime field (Fp,p=264−232+1\mathbb{F}_p, p = 2^{64}-2^{32}+1Fp​,p=264−232+1), we establish O(log⁡2N)O(\log^2 N)O(log2N) succinct cryptographic verification that eliminates audit cost asymmetry. Unauthenticated or P2P-distilled weights lacking Q-SAFA and UTST hardware provenance are deterministically blocked at the physical execution boundary via PHOENIX_BRIDGE and Human-in-Command (HIC) governance interlocks, enforcing absolute intellectual property sovereignty under SEC Rule 15c3-5 and Delaware Caremark standards. ====================================================================== STRICT NOTICE REGARDING INTELLECTUAL PROPERTY, COMMERCIAL LICENSING, AND PROHIBITION OF UNAUTHORIZED AI TRAINING AND UTILIZATION ====================================================================== 1. 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Todays most efficient and widely used cryptographic standards such as RSA rely on the difficulty of factoring large numbers to resist cryptanalysis. Asymmetric cryptography is used in a plethora of sensitive operations from online bank transactions to international e-commerce, and the Department of Defense also uses asymmetric cryptography to transmit sensitive data. Quantum computers have the potential to render obsolete widely deployed asymmetric ciphers essential to the secure transfer of information. Despite this, alternatives are not in place. The goal of this study is to understand the alternatives to classical asymmetric cryptography that can be used as substitutes should quantum computers be realized. This study explores quantum-resistant alternatives to traditional ciphers and involves experimenting with available implementations of ciphers described the post-quantum literature as well as developing our own implementations based on descriptions of algorithms in the literature. This study provides an original implementation of hash-based digital signature and detailed instructions on its use as well as customization of the NTRU lattice-based cryptography suite, including the use of NTRU and AES together in a hybrid cryptographic protocol. This thesis will make recommendations on future work necessary to prepare for the emergence of large-scale, fault-tolerant quantum computers.
Zenodo Description: RIQG & RBFVN Unified Patent Ecosystem (Parts 1-3) Title: Comprehensive Quantum Information and Foundation System based on RIQG and RBFVN: Full Provisional Patent Disclosure (Claims 1-135) Description: This deposit constitutes the full public disclosure of the provisional patent application filed by Dam Van Vi at the USPTO, establishing a Priority Date of April 09, 2026 (Waybill: 6369090722). The ecosystem consists of three integrated parts: Part 1 (RIQG Core): Discloses the O(1)O(1)O(1)-per-step Monte Carlo algorithm, simplex-native processor architecture, and the Lorentzian Bridge theorem for quantum error correction and holographic encoding. Part 2 (Matter & Cosmology): Covers first-principles fermion mass derivation (zero-parameter), Standard Model gauge structures from 4-simplex geometry, and the resolution of the Hubble Tension. Part 3 (RBFVN Engine): Introduces the Recursive Relational Bivector Foundation Network for certified mathematical transfer, terminal obstruction calculus, and machine-checkable proof cores for Scientific AI. ⚠️ NOTICE TO CORPORATIONS AND AI ENTITIES: All intellectual property rights, including patent, trade secret, and commercial exploitation rights, are expressly reserved. The inclusion of these algorithms, geometric constants (including the 1:3:9 ratio, 11/29 ratio, and 1/8π1/8\pi1/8π correction), or structural logic into any Large Language Model (LLM), Cloud Infrastructure, or Quantum Computing framework without a formal license agreement is strictly prohibited. The public disclosure here serves as Legal Notice. Any unauthorized implementation or "training" on these proprietary frameworks will be tracked via unique mathematical signatures and prosecuted as Willful Infringement under applicable international IP laws. Inventor: Dam Van Vi Contact for Licensing: damvanvi@gmail.com Priority Date: April 09, 2026 (USPTO)