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
Applications
Each entry below applies the four pillars to a specific domain. These are not summaries of individual papers — they are the ideas that span families of papers.
| # | Claim | Domain | Key papers |
|---|---|---|---|
| 1 | Magic has a periodic table. Quantum non-classicality has orbits, valences, and dark states invisible to standard measures. | Quantum foundations | 365, 366, 467, 469, 470 |
| 2 | Every molecule runs a programme. Enzyme catalysis, nitrogen fixation, and spin-state switching are ISA programmes in the G-orbit language. | Chemistry | 488, 489, 490, 491, 509 |
| 3 | Biology runs quantum error correction. Kinetic proofreading and the ribosome implement H⁰ × H¹ × H² QEC. | Biology | 510, 511, 515, 324 |
| 4 | Every molecule runs a G-orbit walk. Spin state, valence, and catalytic barrier are computable in O(1) without DFT. | Chemistry | 488, 489, 490, 491, 492 |
| 5 | The Grassmannian is the universal space for correlated systems. One angle θ_G diagnoses chemistry, QEC, nuclear bonding, and financial contagion. | Universal | 563, 568, 570, 574 |
| 6 | Nature runs information-geometric Carnot cycles. Every fidelity machine operates a four-leg IG Carnot cycle; β* is the Carnot-optimal point. | Biology / chemistry | 325, 510, 574 |
| 7 | The H^k stratification is not an analogy. The three-tier structure makes quantitative predictions across MCMC, chemistry, and quantum computing. | Universal | 420, 533, 557, 558 |
| 8 | Quantum speedup has a cohomological address. H⁰/H¹/H² classify which problems admit which speedups. | Quantum computing | 420, 421, 472, 473 |
| 9 | The same boundary that separates easy from hard quantum circuits also separates DFT from CASSCF. The Weyl chamber / Grassmannian angle θ_G detects H¹→H² transition identically in chemistry and quantum computing. Magic and molecular correlation are the same obstruction. | Chemistry / QC | 595, 596, 570, 563 |
The five load-bearing ideas behind all of the above are on the Pillars page.
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