Finite-Stage Strong Vacuum

The τ-finite-stage strong vacuum Γ_s*[n] is the stage-n argmin of the strong-sector defect functional Δ_n^s over the admissible class Adm_s[n], with NFMin tie-breaking. It is the τ-native replacement for the standard 'QCD vacuum': not an empty state but the unique normal-form-minimal configuration at finite resolution stage n, formalized as a Lean structure in TauLib.

Categorical invariant. Unique finite-stage minimizer of the strong-sector defect functional under NFMin tie-breaking; categorically inhabited (no empty-state idealization).

Primary registry anchor: IV.D149

Supporting items: IV.D169, IV.D170, IV.P296

1. I.K0 — Universe Postulate
2. IV.D169 — Strong configuration space
3. IV.D170 — Strong connection assignment
4. IV.D149 — Finite-stage strong vacuum: argmin Δ_n^s with NFMin tie-breaking
5. IV.P296 — Higgs vacuum (related sector vacuum) as parallel construction

Lean modules referenced: TauLib.BookIV.Strong.StrongVacuum

Calibration anchor: PG-P01-neutron

Calibration chain:

1. Stage n (categorical resolution parameter)
2. Δ_n^s defect functional (strong-sector dimensional load)
3. NFMin tie-breaking (categorical canonicalization)
4. Hadronic mass scales recovered via m_n calibration

Manuscript reference: manuscript-sources/book-04/part04/ch30-confinement-admissibility.tex

Status: Formalized

Module: TauLib.BookIV.Strong.StrongVacuum

Lean kind: structure

Lean symbol: FiniteStageStrongVacuum

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q01-mass Mass

Referenced by

• PG-O08-crystal-regime Crystal Regime (τ-Lattice)
• PG-O10-fractional-cr-sublattice Fractional CR-Sublattice