thermion

Core engine for the Adelic Simplicial Architecture.

Every symmetry. Every scale. Exact.

Thermion is the Rep(G) rewriting engine at the heart of the Adelic Simplicial Architecture (ASA). It provides five opcodes — FLIP, FLOP, SPLIT, SPLAT, TWIST — that form a universal, exact, compositional language for any computation in the representation theory of compact groups.

Every result is a sympy expression. No floats, no rounding, no guessing.

from thermion import flop, flip

# The 6j symbol — the single most important object in Rep(G)
flop(0, 1, 1, 1, 1, 1)
# → -1/3  (exact rational)

# FLIP;FLOP: the Pandya theorem, X(3872)→J/ψγ, CO₂ Q-branch, FMO η
# — all the same two opcodes, across nuclear/QCD/molecular/biological scales
flip(1) * flop(0, 1, 1, 1, 1, 1)
# → -1/3

The five opcodes

The five opcodes are the Pachner moves of the 3-simplex — the elementary rewriting rules for triangulated 3-manifolds (Regge 1961, Ponzano-Regge 1968, Mac Lane 1963, Turaev-Viro 1992):

The Pentagon identity — five FLOPs compose to the identity — is Mac Lane's coherence theorem for monoidal categories. It is also the Pachner 2→3 move identity and the Biedenhahn-Elliott identity of nuclear spectroscopy.

Where the same opcodes appear

Same opcodes. Every scale. The Origami ISA is the FFT of representation theory.

The Gibbs ensemble

The thermodynamic core — the partition function, Gibbs weights, and free energy — is in thermion.core.ensemble (requires thermion[numerics]):

from thermion.core.ensemble import gibbs_weights, partition_function

# The FMO light-harvesting efficiency (Paper 325, x356b)
# η = 1 - SPLAT(β_cold) / SPLAT(β_hot) = 0.1825

The Fano geometry

The Fano plane PG(2,2) — incidence structure of the seven imaginary octonion units, backbone of the 731-ISA (Paper 258):

from thermion.core.fano import are_collinear, broken_fano_edges

are_collinear(1, 2, 4)   # True — on the first Fano line
are_collinear(1, 2, 3)   # False — not a Fano line

Installation

pip install thermion                 # core opcodes only (sympy)
pip install thermion[numerics]       # + numpy, scipy (Gibbs ensemble)
pip install thermion[jax]            # + jax (differentiable routing)

Applications built on thermion

Papers

All open access on Zenodo:

License

MIT. Author: Ian R. C. Buckley — ian.r.c.buckley@gmail.com