τ-Bianchi Identity

The τ-Bianchi identity (`IV.T234`) states that the curvature 2-form F of any U(1) connection on the τ-EM gauge bundle automatically satisfies ∂_[μ F_νρ] = 0 (equivalently, dF = 0). It is not a separate axiom but a structural consequence of d² = 0 on the de Rham complex of the τ-holomorphic state space; it constitutes the homogeneous half of the τ-Maxwell system.

Categorical invariant. On any U(1) connection on the τ-EM gauge bundle: dF = 0 is automatic from d² = 0.

Primary registry anchor: IV.T234

Supporting items: IV.T42, IV.T44

1. I.K0 — Universe Postulate
2. IV.T234 — Bianchi identity ∂_[μ F_νρ] = 0 — automatic from d² = 0
3. IV.T42 — Homogeneous Maxwell — dF = 0 yields div B = 0 and Faraday's law
4. IV.T44 — Complete τ-Maxwell System — Bianchi gives the homogeneous pair

Lean modules referenced: TauLib.BookIV.Electroweak.TauMaxwell

Calibration anchor: PG-P01-neutron

Calibration chain:

1. U(1) curvature 2-form on the EM gauge bundle
2. d² = 0 on the τ-holomorphic de Rham complex
3. SI bridge via the τ-Maxwell cascade for chart-shadow read-out

Manuscript reference: manuscript-sources/book-04/part03/ch21-gauge-invariance-maxwell.tex

Status: Formalized

Module: TauLib.BookIV.Electroweak.TauMaxwell

Lean kind: theorem

Related glossary entries

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

Referenced by

• PG-L10-tau-inhomogeneous-maxwell τ-Inhomogeneous Maxwell Equations