Chapter 6: Sector Witness Bundles, Vacua, and Normalizers

The abstract 4+1 sector decomposition of the relevant chapter is now equipped with its concrete operational machinery. Each sector receives a witness bundle (the typed evidence that certifies membership), a vacuum (the canonical minimiser of the sector’s defect functional), and a normaliser (the NF-coded bounded pipeline that computes coherence verdicts). Two shadow families—the VM/ZFC-PA shadow and the epistemic/pragmatic shadow—are introduced. The Rigidity Corollary guarantees each sector’s internal consistency. The Shadow Soundness Lemma proves that each shadow is sound with respect to its sector.