Applications

Each entry below applies the five 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. Magic and molecular correlation are the same obstruction. Chemistry / QC 595, 596, 570, 563
10 AI & Machine Learning. β is the softmax temperature; transformers are Forge ISA programmes; 4-point networks, agentic consensus, and the HPC stale-data problem. AI / ML 400, 627, 628, 629

The five load-bearing ideas behind all of the above are on the Pillars page. For the full ISA family table, see Pillars → ISA Family.

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