To Become a Stone with Six Birds: A Physics is A Theory

Physics theories are often treated as separate “models” (quantum vs. classical vs. fluids vs. gravity), even though in practice they are frequently used as scale-dependent closures: we retain a coarse description, complete what is discarded, and then evolve. This repository contains a follow-up instantiation of the Six‑Birds framework, showing how several familiar physics layers can be expressed with the same dictionary—lens (what is retained), completion (how missing information is filled in), closure/packaging (the induced projection family), audit monotonicity (data processing), and route mismatch (noncommutation between evolve-then-close and close-then-evolve).

The accompanying paper, To Become a Stone with Six Birds: A Physics is A Theory, provides four reproducible instantiations: (i) quantum→classical as dephasing closure, with numerical regression checks of quantum relative-entropy data processing and a controlled unitary-vs-closure commutator; (ii) kinetic→fluids via a discrete BGK-like model with moment lens and local-equilibrium completion, including coherence trends and explicit failure regimes; (iii) filtering/LES on viscous Burgers, where filter∘evolve ≠ evolve∘filter and the mismatch yields the canonical subgrid rewrite term; and (iv) a nonlinear averaging/backreaction toy illustrating that average then evolve ≠ evolve then average under heterogeneity, also expressed in explicit (Q/U/E) operator form.

The repo emphasizes checkability and reuse: all figures and tables are generated deterministically from scripts, a one-command build reproduces the PDF, and a small Lean4/mathlib backbone certifies key algebraic facts about finite-state lenses and closures (section ⇒ idempotence, factorization ⇒ commutation, total-variation contraction, and definability counting). These materials are intended as a reproducible “closure ledger” for comparing multi-scale theories, not as derivations of continuum limits or claims about the foundations of quantum-to-classical transition.