Conserved Computation: Symmetry, Monadic Descent, and the Structural Guarantees of G₂ Thermodynamic Logic
| Paper: 286 | Portfolio B — Mathematical Physics |
Abstract
Establishes Noether’s theorem as a categorical adjunction between the Kleisli category of free trajectories and the Eilenberg-Moore category of invariant algebras. The moment map is identified as the counit of this adjunction. $G_2$ self-duality makes this adjunction a self-map, yielding a closed structural guarantee: every computation in the 731 Frog Calculus that respects $G_2$ symmetry automatically conserves a canonical invariant.
Key Results
- Noether adjunction: symmetry group action $\dashv$ conserved quantity extraction, with moment map as counit
- Monadic descent: the Flow/Snap thermodynamic schedule is a descent datum in the Eilenberg-Moore sense
- $G_2$ self-duality: the adjunction folds onto itself — symmetry and conservation are the same object
- Gauge freedom: residual $G_2$ freedom after fixing a Fano line corresponds to the adjunction unit
Zenodo
Related Papers
- Paper 271 — G₂ Self-Duality (algebraic foundation for the self-map claim)
- Paper 207 — Frog Calculus Part 1 (computational framework this paper provides guarantees for)
- Paper 221 — Fano-Fisher (information-geometric context for the moment map)