The ISA Family

All named ISAs share the same five opcodes (LABEL 🏷️ / ORBIT 🔄 / TWIST 🌀 / BIND 💎 / FLIP 👁️) — they differ only in the value of the inverse temperature β and the arithmetic they run over.

ISA	β location	In one phrase	Paper
Origami	all β (umbrella)	Five-opcode open standard; tropical at β→∞, quantum at β=it	631
Forge	0 < β < ∞ (real Gibbs)	Free-energy routing; MGE soft threshold; snap at β*	419
Meld	β = it (imaginary)	Complex amplitudes; full quantum mechanics	454
Raven	β ≈ β* (physiological)	Biological proofreading; enzyme catalysis; kinetic QEC	Raven
Motive	abstract parent	Five primitive opcodes; ERASE = second law	Motive
Hum	β = it/ℏ (QFT)	QFT vacuum; EMIT opcode; amplituhedron as ORBIT	620
Pentagon	coherence theorem	Monoidal coherence; five sides = five opcodes	622
Rising Sea	full ℂ_β plane	Every ISA as a fibre over the β-plane	621

Full opcode reference: The ISA Opcodes · β-plane geometry: Forge & Meld · Non-associative frontier (BIND at 𝕆-rung): 731-ISA

Paper Index

630+ papers published to the Thermyon Zenodo community (2024–).

The tables below cover landmark and foundational papers. For the full list browse Zenodo directly.

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Foundations (Portfolio A–B)

#	Title	DOI
000	An Adelic Invitation	19977475
201	The Maslov-Gibbs Einsum (MGE)	17981393
202	Topological Resonance Synthesis (TRS)	19858021
258	The Origami ISA (731-ISA)	19916429
370	The Origami ISA as Nature’s Universal Computer	20543454
393	Projective Geometry as the Mother Tongue of QM	20634729
420	The H^k Complexity Ladder	20773526
443	Planck’s Constant in Disguise	20752384
454	The Meld ISA	20773563
455	Eight Derivations of a Universal Instruction Set	20774076
543	The Complex β-Plane	21245459
631	Origami: An Open ISA for Quantum-Classical Systems	21428853

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Quantum Hardware & AI (Portfolio C)

#	Title	DOI
199	The Quaternionic Virtual Machine (Q-VM)	20060303
205	The Resonance Processing Unit (RPU)	19743800
217	Fibrational Lattice Surgery	19922441
303	Pacioli Combinator Library (PCL)	20262070
310	In Praise of Qudits	20269991
385	SQU TriQ and SevenQ: Standard Registers	20581486
598	Orbit Processing Unit (OPU)	21360838
604	Trapped-Ion OPU	21360907
606	Schubert Halt Condition	21373481
607	Diagrammatic QEC as ISA	21372999

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Quantum Foundations (Portfolio F)

#	Title	DOI
268	The Spacelike Associator Paradox	20058013
357	Interactive Verification without Trust (MIP* = RE)	20541989
361	Fano Orbit Decomposition of Magic	20541583
366	A Valence Theory of Quantum Magic	20541665
469	ISA Completeness	21219698
470	Hot Logic	21219700
595	Weyl Chamber Homology	21309088
596	Weyl–DFT Accelerator	21373469
597	In Praise of Soft Thresholds	21373469
602	Hecke–Weyl Routing	21372929

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Chemistry & Biology (Portfolio D–E)

#	Title	DOI
324	The Decoding Engine (Ribosome)	20400652
325	The Topological Heat Engine (FMO)	20400638
487	Valence as Orbit Occupancy	21219722
488	G-walk Chemistry	21219720
490	G-walk Protein Design	21219724
510	Kinetic Proofreading as QEC	21345099
515	Protein Folding ISA	21345099
603	G-Step CO₂ Fixation	21373477

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Finance & Economics (Portfolio G)

#	Title	DOI
291	Pacioli Homology	20234853
299	XVA as Gauge Curvature	20257724
316	EconIAC / MONIAC	20315689
397	Systemic Risk as H²	20642908
478	H^k Pricing	21158959
542	Incentive Geometry	21219738
549	Ergodicity Economics ISA	21249153

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Grand Challenges

#	Title	DOI
240	Structural Observations on J³(𝕆)	19824028
245	Nuclear Magic Numbers and Exceptional Lie Algebras	19960385
265	The ζ(21) Apéry Generalisation	20029647
553	Apéry ISA	21250670
608	ISA Self-Reference Tower	21373483

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Machine-readable index: _data/papers.csv

The ISA Family

All named ISAs share the same five opcodes (LABEL 🏷️ / ORBIT 🔄 / TWIST 🌀 / BIND 💎 / FLIP 👁️) — they differ only in the value of the inverse temperature β and the arithmetic they run over.

ISA	β location	In one phrase	Paper
Origami	all β (umbrella)	Five-opcode open standard; tropical at β→∞, quantum at β=it	631
Forge	0 < β < ∞ (real Gibbs)	Free-energy routing; MGE soft threshold; snap at β*	419
Meld	β = it (imaginary)	Complex amplitudes; full quantum mechanics	454
Raven	β ≈ β* (physiological)	Biological proofreading; enzyme catalysis; kinetic QEC	Raven
Motive	abstract parent	Five primitive opcodes; ERASE = second law	Motive
Hum	β = it/ℏ (QFT)	QFT vacuum; EMIT opcode; amplituhedron as ORBIT	620
Pentagon	coherence theorem	Monoidal coherence; five sides = five opcodes	622
Rising Sea	full ℂ_β plane	Every ISA as a fibre over the β-plane	621

Full opcode reference: The ISA Opcodes · β-plane geometry: Forge & Meld · Non-associative frontier (BIND at 𝕆-rung): 731-ISA

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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
• Grassmannian Compression