The empirical science of Epimechanics.
Epimechanics is a theoretical framework — the mathematical grammar of how representations change under forces, applicable to any substrate. Epiphysics is the empirical program that tests it.
All representations have mechanical structure (trivially — it's calculus). Good representations have simple mechanical structure — simple enough to predict dynamics at minimal computational cost. The existence of an optimal representation is a theorem (Shannon, Rissanen, Solomonoff). That the optimal representation has Lagrangian structure is the conjecture this project investigates.
- Theory — Epimechanics: the formal framework (Parts 0-5)
- Applications — Testing the framework in specific domains
- Research — Papers, proofs, and open problems
- Popular — "The Physics of Common Sense" — accessible introductions
- Experiments — Empirical tests (planned)
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Theorem (U(1) uniqueness): Under product-state independence, compositional consistency, recursive closure, and compact connected Lie regularity, the unique nontrivial amplitude phase group is
$\mathrm{U}(1)$ . See Compositional Fixed-Point Derivation. - Conjecture: Information-theoretically optimal representations have Lagrangian structure.
- Open problem: Does this hold for irreversible systems?
Theory: developed. Applications: 2 written, more planned. Experiments: protocol designed, not yet run.
epiphysics.xyz (coming soon)
This project is developed collaboratively between human researchers and semi-autonomous AI agents. The agents assist with:
- Theory development — adversarial review, proof verification, gap identification
- Documentation — maintaining consistency across papers, terminology audits
- Quality assurance — automated checks for circularity, notation consistency, claim status
All substantive theoretical claims are human-authored and human-verified. AI contributions are logged and auditable (see docs/research/audits/).
- Ian Derrington
- Parnian Barekatain
Contributions welcome. See CONTRIBUTING.md for guidelines.
For AI-assisted contributions: include audit trails and clearly distinguish proved results (✅) from conditional claims (
MIT