Papers

All 25 ASA working papers, each with abstract, DOI, and cross-links.

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All papers on Zenodo

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Table of contents

• An Adelic Invitation: Observations on Non-Associativity, Division Algebras, and the Next Computational Paradigm
• The Quaternionic Virtual Machine (Q-VM): Quaternionic Chirality, Spinorial Routing, and the Causal Firewall of the R-C-H-O Operating System
• The Fano-Foam Manifold and the Excluded Volume Principle
• The Maslov-Gibbs Einsum (MGE): Tropical Crystallization and the Thermodynamic Bridge Between Continuous Optimization and Discrete Logic
• Topological Resonance Synthesis (TRS): Information Geometry, Holomorphic Relaxation, and the Thermodynamic Engine of the Topological Processor
• The Unitary Resonance Network (URN): Möbius Automorphisms, the Fano-Fisher Immune Filter, and the Resolution of the Fine-Tuning Trilemma
• The Resonance Processing Unit (RPU): Holonomic Hardware Geometries, Triorthogonal Codes, and the 1531-Anvil
• Fibrational Tensor Codes (FTCs): Holonomic Quantum Computation, G₂ Fiber Bundles, and the Cayley-Dickson Hardware Hierarchy
• The 731-Calculus: Magmoidal Category Theory, Octonionic Spin Foams, and the Architecture of the Topological Processor
• Sequence-Dependent Cryptography (The Magmoidal Cipher): Verifiable Delay Functions, V31-QKD, and Asymmetric Sequential Locks via Non-Associative Fano-Geometry
• Geometric Interpretation of Code Switching: PG(2,2)→PG(3,2) Projective Envelopes, Transversal CCZ, and a Geometric Primitive for Grover's Diffusion Operator
• Non-Associative Calculus: Octonionic Path Integrals, Cauchy-Fueter Regularity, and the Fundamental G₂ Monopole Field
• Fano Resonance Networks (Fano-RNs): The Associator Correction Tensor, Malcev Gradients, and a Convergence Theorem for Non-Associative Backpropagation
• Volume of Thought (VoT) and Topological Agentic Swarms: Scaling Multi-Agent AI from Temporal Concurrency to Geometric Contradiction via the MGE Router
• Non-Associative Knowledge Hypergraphs: Fano-Structured RAG, Irreducible Ternary Relations, and Thermodynamic Retrieval via the MGE Router
• Fibrational Lattice Surgery (LS2.0): Catalytic Code Switching, Adiabatic Interpolation, and the Eradication of Boundary Noise
• Thermodynamic Routing of Stale Gradients via Non-Associative Information Geometry: Bypassing the Ring All-Reduce Bottleneck via the G₂ Fano-Fisher Metric
• Non-Associative Information Geometry: The Fano-Fisher Metric Decomposition Theorem on G₂
• The Non-Associative No-Cloning Theorem and the Fano-Token
• Structural Observations on J³(O), the Bruhat-Tits Cospan, and Questions for Automorphic Forms Specialists
• Nuclear Magic Numbers and Exceptional Lie Algebras
• Electron Shell Structure and Exceptional Lie Algebras: Shell Capacities, the Division Algebra Ladder, and the Lanthanide Contraction as G₂ Rigidity
• Non-Associative Quantum Error Correction (NA-QEC): The Exceptional Jordan-KL Condition and Rank-1 Idempotents in G₂ Topologies
• The 731 Instruction Set Architecture (Origami ISA): Machine Code, Pachner Opcodes, Geometric Constraint Satisfaction, and Simplicial Paging
• The Architecture of Inevitability: The Freudenthal-Tits Magic Square as the Blueprint for the Adelic Simplicial Architecture
• The ζ(21) Apéry Generalization: Cubic Pisot Units, G₂ Geometry, and a Conjectured 4-Term Recurrence
• Geometric Shadows in Apéry's Polynomial: G₂ Factorisation, Trilinear Associators, and the Fano-Weighted Volume of ζ(3)
• The Fano-SYK Model: Bruhat-Tits Buildings, Non-Associative Fermionic Couplings, and the Geometric Impedance of Pre-Thermal Scrambling
• The Spacelike Associator Paradox: Sequential Quantum Channels, Non-Associative Measurement Back-Action, and the Causal Firewall of the G₂ Vacuum
• Hardy's Paradox and the Fano Associator: A Geometric Diagnosis of Quantum Contextuality
• The Fano Monogamy Paradox: Irreducible Three-Body Entanglement and the Tripartite Hardy Impossible Event
• The Self-Dual G₂ Architecture: Pachner Unitarity, CSS Symmetry, and the Crystal Spectrum Halving
• The 731 Frog Calculus, Part 2: Two-Dimensional Frog Diagrams and the Ribbon-Leg Syntax
• Conserved Computation: Symmetry, Monadic Descent, and the Structural Guarantees of G₂ Thermodynamic Logic