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
Computation at finite temperature
Classical logic is the zero-temperature limit — frozen, deterministic, β→∞. Every if statement, every argmax, every hard decision boundary is what you get when you turn the heat all the way down. Thermyon is the framework for what happens when you turn it back up.
Your favourite large language model already runs at finite temperature. Softmax with temperature T is not a trick bolted onto neural networks — it is Gibbs sampling, the same Boltzmann distribution that governs a steam engine, a financial market, and an enzyme active site. Fuzzy has been the new computing paradigm for a while. Thermyon makes the mathematics explicit.
At finite β, probabilistic reasoning becomes Gibbs sampling. At imaginary β = it/ℏ, quantum interference appears — the Wick rotation that connects statistical mechanics to quantum mechanics is just β going complex. Near a critical point β*, biological computation balances exploration against commitment: too cold and the enzyme is frozen in a local minimum, too hot and selectivity vanishes.
The name comes from thermionic emission — the process by which a heated cathode releases electrons, controlled by temperature and the Boltzmann factor e^{−βE}. A vacuum tube computes by managing thermal energy. So does Thermyon. β is the voltage; the five opcodes are the circuit.
Thermyon is built around a five-opcode instruction set — the Origami ISA — that runs at every temperature, over any arithmetic, under any symmetry group. The Maslov–Gibbs Einsum (MGE) makes β a differentiable coordinate: discrete combinatorial models become smooth functions of temperature, and the snap at β* is a genuine phase transition, not a metaphor.
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