Pillar 1

Pillar 1 — Mass m*

Tier: T6 — PROVED CONDITIONAL
Epistemic category: C1 — Core emergence (TECT-internal, rigorously derived)
Last sync: 2026-06-05

TECT framework positioning (binding 2026-05-26): TECT is an emergent vacuum-and-gravity framework (7 C1 pillars at T6/T7) with an unresolved gauge-sector completion (Pillar 6 standard routes EXHAUSTED) and phenomenological dark-matter/quantum-origin pillars open. TOE-level claim SUSPENDED until non-standard rescue independently derived (per Math411-AddB §10).

Statement

Brazovskii spectral gap $m^{*2}$ as analytic eigenvalue of the fluctuation operator on the BCC fluctuation channel within the Brazovskii fluctuation-stabilised disordered vacuum (Reading H).

Status semantics

This pillar is currently classified at tier T6 (PROVED CONDITIONAL) per the canonical TOE-FACT-SHEET.

Conditional on:

• Brazovskii uniqueness (Math66)
• BCC fluctuation channel (Math1-v2) [post-Math401: reformulated under Reading H — channel, not ground state]
• Math415 (2026-05-27, A-Round 1 of C1 closure programme): Pillar 1 hypothesis set H_1^RH = {H_{1,1}^uniq (Math66 reformulated under Reading H — unique cosmologically-isotropy-compatible TRUE-local-min stable channel), H_{1,2}^channel (Math1-v2 reformulated — channel non-degeneracy at |q|=q* with r_R=+0.4193>0)}; T6 PROVED CONDITIONAL retained; T7 promotion path Math415-AddA queued (isotropy-redundancy proof). Verified Math415_pillar1_pillar2_audit.py 6/6 self-test asserts PASS.

Key Math notes

• Math37
• Math82

Open questions

See Open-questions for active items tagged with P1. GitHub Issues with the same label provide discussion threads: issues with P1 label.

Source of truth

Canonical pillar tier: Codes/config/pillar_status.json (raw). Per-pillar narrative: Docs/status/TOE-FACT-SHEET.md Stage-1 scorecard (raw). Updates propagate through the cascade pipeline (CLAUDE.md §18) — do not edit this wiki page directly.