τ-Conservation as Naturality

τ-Conservation as Naturality (`IV.T247`) is the τ-categorical theorem that every conservation law in the τ³ framework is a naturality condition: the conserved current is the diagonal of a naturality square between two functors on Category τ. This is the structural meta-law that grounds energy, momentum, charge, and spin conservation as facets of a single categorical fact.

Categorical invariant. Every conservation law in τ³ is a naturality condition; the conserved current is the diagonal of a naturality square (IV.T247).

Primary registry anchor: IV.T247

Supporting items: IV.R180

1. I.K0 — Universe Postulate — Category τ
2. IV.T247 — Conservation as Naturality — every conservation law is a naturality condition
3. IV.R180 — Noether theorem as corollary — the symmetry-side reading of the same naturality square

Lean modules referenced: TauLib.BookIV.Coda.LawsAsStructure

Calibration anchor: PG-P01-neutron

Calibration chain:

1. natural transformations on Category τ
2. E₁-readout for conservation currents (energy, momentum, charge, spin)
3. SI bridge via m_n anchor for conserved-quantity units

Manuscript reference: manuscript-sources/book-04/part08/ch72-laws-as-structure.tex

Status: Formalized

Module: TauLib.BookIV.Coda.LawsAsStructure

Lean kind: theorem

Related glossary entries

• PG-L08-tau-noether-theorem τ-Noether Theorem