τ-EM Wave Equation

The τ-EM wave equation (`IV.T47`) is the τ-categorical theorem that, in the source-free Lorenz gauge, the τ-Maxwell system reduces to □ A^μ = 0, with plane-wave solutions propagating at speed c = L·H. It is the structural origin of light propagation; light's speed is fixed by the cascade product of the lattice spacing L and the Hubble-like parameter H, not by experimental fitting.

Categorical invariant. In source-free Lorenz gauge: □ A^μ = 0 on the τ-EM gauge bundle; plane-wave solutions propagate at c = L·H.

Primary registry anchor: IV.T47

Supporting items: IV.T44, IV.T259

1. I.K0 — Universe Postulate
2. IV.T44 — Complete τ-Maxwell System — dF = 0, d⋆F = ⋆J
3. IV.T259 — Wave Equation from τ-Maxwell — derivation in arbitrary gauge
4. IV.T47 — τ-EM Wave Equation — source-free Lorenz gauge: □ A^μ = 0, c = L·H

Lean modules referenced: TauLib.BookIV.Electroweak.TauMaxwell

Calibration anchor: PG-P01-neutron

Calibration chain:

1. Lorenz-gauge fixing on the EM gauge bundle
2. c = L · H from the τ-cascade (lattice × Hubble parameter)
3. SI bridge: c → 299 792 458 m·s⁻¹ via the τ-second and τ-metre cascade

Manuscript reference: manuscript-sources/book-04/part03/ch28-electroweak-synthesis.tex

Status: Formalized

Module: TauLib.BookIV.Electroweak.TauMaxwell

Lean kind: theorem

Lean symbol: Tau.BookIV.Electroweak.EmWaveEquation

Related glossary entries

• PG-L03-tau-maxwell-system τ-Maxwell System (Complete)
• PG-U01-tau-second τ-Second