Theory
The load-bearing mathematics — β, cohomology, exceptional points, Grassmannians — that the framework is built from.
| Page | What it covers |
|---|---|
| Diagrammatic Chemistry | Which parts of chemistry are combinatorial, and which need a Hamiltonian |
| Thermodynamic Computing | Extropic’s probabilistic hardware and gate language: what it is, why it is not quantum, and what it leaves open |
| Why Formalise Chemistry? | What a proof assistant buys you when the mathematics is combinatorial — and what it does not |
| Why Hot Logic? | Boolean logic is zero-temperature; every LLM runs at finite β; the unification via the β-plane |
| β: The Universal Temperature | β interpolates classical → statistical → quantum; Maslov dequantisation; tropical arithmetic |
| Disagreement | JSD = H(mean) − mean(H); why pooled beliefs cannot distinguish confident disagreement from shared ignorance |
| The β-plane | The full complex-β plane; Forge (real β), Meld (β = it), Raven (complex β) |
| PT Symmetry & Exceptional Points | Exceptional points as tier boundaries; PiTch number; 38-fold way; HPU substrates |
| The Non-Associative Frontier | Division algebra ladder; octonions; G₂; 731-ISA |
Table of contents
- Why Hot Logic?
- β: The Universal Temperature
- The β-plane
- PT Symmetry & Exceptional Points
- The Non-Associative Frontier
- Knots, Spiders & the ISA
- Pachner Moves and Quantum Symbols
- Diagrammatic Chemistry
- Thermodynamic Computing
- Why Formalise Chemistry?
- Lean for F# and OCaml Programmers
- Disagreement (JSD)