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
Author: Ian R. C. Buckley — ORCID 0009-0004-9287-2902
One instruction set. Twenty orders of magnitude. From nuclear spectroscopy to quantum chemistry to systemic financial risk.
Browse all papers on Zenodo ISA reference → View on GitHub
What is Thermyon?
Thermyon is a unified computational framework built around a five-opcode instruction set — the Origami ISA — whose operations correspond exactly to the primitives of Čech cohomology on a sheaf.
The computation works because Lie groups are the natural tape for a generalised Turing machine: the Chladni resonance patterns on the group manifold encode the computational state, and the topology of those nodal lines — their H⁰/H¹/H² structure — is the skeleton of the calculation. The Maslov–Gibbs Einsum (MGE) makes that skeleton differentiable: discrete combinatorial models become smooth functions of a single temperature parameter β.
The five opcodes
| Opcode | Symbol | Role | H^k tier |
|---|---|---|---|
LABEL 🏷️ | ⊢ | Assign a symmetry sector / orbit label | H⁰ |
ORBIT 🔄 | 𝒪 | Enumerate orbits under a group action | H⁰ |
FLIP 👁️ | ⌁ | Sheaf dualisation / time-reversal | H⁰ |
TWIST 🌀 | ∮ | Gauge transformation / phase accumulation | H¹ |
BIND 💎 | ⋈ | Entanglement / correlation / Pachner surgery | H² |
The Pentagon identity (d² = 0) is simultaneously: the HJM no-arbitrage condition · the Biedenharn–Elliott identity for angular momentum recoupling · the MIP* verifier constraint · the H² = 0 stability condition for financial cascades. One equation, four theorems.
The β-deformation
The same five opcodes execute at every value of the inverse temperature β, producing specialised ISAs for each regime:
| ISA | β regime | Arithmetic | Character |
|---|---|---|---|
| Tropical limit | β → ∞ | (max,+) | Classical logic, argmax, discrete optimisation |
| Forge | 0 < β < ∞ (real) | Gibbs / ℝ | Statistical mechanics, soft thresholds, annealing |
| Meld | β = it/ℏ | Unitary / ℂ | Quantum mechanics, interference, Feynman path integral |
| Raven | β ≈ β* | Near-critical | Biological computation, kinetic proofreading, H² QEC |
| Hum | β = it/ℏ (QFT) | (ℂ, EMIT) | Quantum field theory, amplituhedron |
| Origami | all β | Fibred family | Five-opcode open standard; umbrella for all regimes |
Lowering β is quantisation; raising β is the classical limit. Planck’s constant, viscosity, volatility, softmax temperature, and the quantum-group deformation parameter q = e^{iπβ} are all the same object seen from different fields.
β-plane geometry and named ISAs →
Universality table
The same five opcodes appear across twenty orders of magnitude in scale:
| System | H⁰ | H¹ | Pentagon = H² |
|---|---|---|---|
| Nuclear spectroscopy | Selection rules | Racah 6j symbol | Biedenharn–Elliott |
| FMO light harvesting | Site energies | Transfer efficiency η = 0.1828 | Carnot bound |
| Quantum computing | Pauli syndromes | Magic valence | MIP* = RE |
| Three-body orbits | Kepler solutions | Choreographic solutions | KZ equations |
| Interest rates | Bilateral prices | Convexity (HJM drift) | HJM no-arbitrage |
| Systemic risk | Bilateral stress | Triangular contagion | H² = 0 stability |
| Molecular chemistry | Ground-state NOON | Correlation (Weyl c₂) | G-step reaction |
This is not analogy. It is the same theorem — the 6j symbol is H¹ of the relevant representation sheaf — instantiated for different sheaves over different interaction diagrams.
Portfolio map
| Portfolio | Theme | Representative papers |
|---|---|---|
| A — Core Engine | MGE, Origami framework, β-deformation | 201, 202, 443, 454, 543, 631 |
| B — Foundations | Algebra, simplicial topology, category theory | 200, 207, 258, 263, 393, 595 |
| C — Hardware & AI | OPU, RPU, trapped-ion, quantum registers | 199, 205, 598, 604, 606 |
| D — Protocols | QEC, shadow tomography, kinetic proofreading | 488, 490, 510, 515, 555, 607 |
| E — Grand Challenges | Riemann, number theory, molecular design | 240, 265, 487, 553, 554 |
| F — Quantum Foundations | Magic, contextuality, Weyl, homology | 361, 366, 469, 595, 596, 602 |
| G — Finance & Economics | Risk cohomology, XVA, ergodicity | 291, 299, 397, 478, 542, 549 |
Start here
- New to the framework? → In Praise of Soft Thresholds (Paper 597) — accessible introduction — or the Origami ISA manifesto (Paper 631) for the full technical picture
- Quantum computing? → Schubert halt theorem (Paper 606) or Trapped-ion OPU (Paper 604)
- Chemistry? → G-walk CO₂ fixation (Paper 603) or Valence as orbit occupancy (Paper 487)
- Finance? → Systemic risk as H² (Paper 397) or H^k pricing (Paper 478)
- Biology? → Kinetic proofreading as QEC (Paper 510) or Protein folding ISA (Paper 515)
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