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Core Ideas
Magic has a periodic table
Every molecule is running a programme
The Fano crystal is universal
Quantum speedup has a cohomological address
Biology runs quantum error correction
β is a coordinate
The H^k stratification is not an analogy
Every molecule runs a Galois programme
The bond is a point on the Grassmannian
The Grassmannian is the universal space for correlated systems
Portfolios
Portfolio A — Core Engine
Portfolio B — Foundations
Portfolio C — Hardware & AI
Portfolio D — Protocols
Portfolio E — Chemistry & Physics
Portfolio F — Quantum Foundations
Portfolio G — Economics & Complex Systems
Papers
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
Framework
Notes
N01 — Does the ASA Violate Hardy's Axioms?
N02 — Lohmiller-Slotine, Vattay, and the MGE
N03 — Closed Walks on the Fano Plane and OEIS A274975
Explainers
A Primer on Economic Gauge Theory
A quantum error-correcting code is a point on a curved surface
Associamancy: A Resource Theory of Non-Associative Quantum Magic
Beyond Basel: A Cohomological Framework for Systemic Risk Regulation
Beyond DAGs: A Non-Associative Algebra of Policy Interventions
Codon Recognition on S³ × S³ × S³
Conserved Computation
Credit Bundles: Survival Probabilities as Parallel Transport on the Pacioli Manifold
Currency Bundles: Foreign Exchange as Connection Curvature on the Financial Manifold
Designing Proteins by Writing Programmes
Differentiable Agent-Based Macroeconomics: A Gauge-Theoretic Digital Twin on the Pacioli Manifold
Differentiable Nash Equilibria
Each correction to the atom halves the error
EconIAC: A Differentiable Economics Engine
Economic Gauge Theory: Stock-Flow Consistency, Thermodynamic Constraints, and Climate Risk on the Pacioli Manifold
Eight Derivations of a Universal Instruction Set
Every quantum error-correcting code is a chain complex
Evolutionary Quantum Programming
Fano Geometry as a Unifying Language for QEC
Fibrational Lattice Surgery (FLS)
Fibrational Tensor Codes (FTCs)
G-walk Chemistry: Orbit Theory Beats DFT
Geometric Shadows in Aperys Polynomial
Hot Logic: A Complete Magic Resource Theory
H¹ = 0 is the Performance Condition
ISA Completeness: Nine Normal Forms
In Praise of Tetrahedra: Why Four Objects Change Everything
Magic Has Valence
Magic Has a Kind, Not Just an Amount: The Fano Orbit Decomposition
Metabolism Is a Computer Programme
Molecular Machines as Origami ISA Programmes
Non-Associative Calculus
Non-Associative Hardware is Necessary for the Non-Abelian StateHSP
Nuclear reactions are orbit programmes
One Geometry, Two Fields: How Brody & Hughston's Quantum Mechanics and the Fano Plane Are the Same Construction
One Instruction Set, Twenty Orders of Magnitude: The Origami ISA as Nature's Universal Computer
One Parameter to Rule Them All: The Complex β-Plane
One calculation, three theories of bonding
One tensor contraction, three mathematical universes
Orbit Computing: A Fourth Paradigm
Origami ISA Pulse Sequences: Optimal Control of the 731 Gate Set
Origami MBQC: The Origami ISA as a Measurement-Based Instruction Set
Planck's Constant in Disguise
Resource Theory as Circuit Syntax
Seven Qubits, Zero Distillation: The TriQ and SevenQ Architecture
Spin Foams as Origami: LQG from the ISA Perspective
Systemic Risk as H²
Tanabe-Sugano Diagrams Are Tropical Varieties
Term Structure Bundles: Interest Rates as Temporal Connections on the Pacioli Manifold
The 731 Frog Calculus (Part 1)
The 731 Frog Calculus (Part 2)
The Alchemy of Distributions, Revisited
The Architecture of Inevitability
The Clifford Hierarchy as Group Cohomology
The Climate Hazard Yield Surface
The Cookie-Cutter Lifting Programme
The Fano Monogamy Paradox
The Fano Plane is the Right Way to Think About Qubits
The Fano-Foam Manifold
The Forge ISA
The Gaussian Copula Was the Wrong Approximation: Why the Origami ISA Gives You XVA Without a Model
The Geometry of the Euler–Mascheroni Constant
The H^k Complexity Ladder
The Kitaev Menagerie in Origami
The Maslov-Gibbs Einsum (MGE)
The Meld ISA
The Meld: Discrete Algorithms as Tropical Shadows of Smooth Manifold Problems
The Origami ISA
The Origami ISA and the State Hidden Subgroup Problem
The Origami ISA as a Structural Model for MIP*=RE
The Origami ISA as a Typed Quantum DSL
The Pacioli Combinator Library: A Universal Domain-Specific Language for Financial and Economic Computation on the Pacioli Manifold
The Projective Hierarchy of Computation
The Resonance Processing Unit (RPU)
The Riemann Spectrometer
The Temperature of Rationality
The Thermal AZ Table
The Topological Heat Engine
The Topology of Conservation: Double-Entry Accounting as a Discrete Gauge Theory of Macroeconomics
The Topology of Risk: A Primer
The Unhedgeability Theorem: Sheaf Cohomology of Interaction Diagrams and the Topology of Financial Risk
The Unitary Resonance Network (URN)
The Wigner Defect Conservation Law
The quantum chemistry amplituhedron
The zeta(21) Apery Ladder
Thermal Attribution: Differentiable Shapley Values, Latent Bottlenecks, and the Tropical Limit of Cooperative Game Theory
Thermodynamic Information Routing: A Unified Framework for Gibbs Aggregation Across Economics, Computation, and Knowledge Retrieval
Thermodynamic Routing of Stale Gradients
Three Bodies, One Path: AI Discovers an Infinite Family of Choreographic Orbits
Tipping Points Are Topological
Topological Resonance Synthesis (TRS)
Valence as Orbit Occupancy
Valuation Adjustments as Curvature: XVA in Financial Gauge Theory
Virtual Monopoles in the FeMo-Cofactor: G₂ Symmetry, Non-Associative Bond Breaking, and Nitrogenase as a Pachner-Move Computer
Volume of Thought: Why AI Swarms Need Sheaf Cohomology
Why exactly three tiers? A categorical proof
Why the 2008 crisis was a topology problem
Wrong Magic Is Worse Than No Magic: A Valence Theory of Quantum Magic
Your factor model is 66° wrong
The Operative and Harmonic ISAs
The ISA Opcodes
Glossary
Stories
S00 — The Tetrahedron
S01 — Professor Knot Visits the Enzyme
The Non-Associative Frontier
Paradigm Comparison
The Langlands Perspective
Adelic Simplicial Architecture (ASA)
The 25 ASA papers are organised into seven portfolios by theme.
Table of contents
Portfolio A — Core Engine
Portfolio B — Foundations
Portfolio C — Hardware & AI
Portfolio D — Protocols
Portfolio E — Chemistry & Physics
Portfolio F — Quantum Foundations
Portfolio G — Economics & Complex Systems