Plain-language guides to every paper — no prior mathematics required. Filter by theme below.

For a thematic overview of the non-associative work (division algebra ladder, Freudenthal-Tits magic square, 731-ISA), see The Non-Associative Frontier.

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Table of contents

• 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