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Pillar 4

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Jusang Lee edited this page Jun 5, 2026 · 12 revisions

Pillar 4 — Mass-spectrum closure

Tier: T6 — PROVED CONDITIONAL on Reading H interpretive framework (Math400-AddE Path α + Math400-AddF BCC stable channel)
Epistemic category: C2 — Secondary emergence (TECT-internal, residual gates)
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

SM fermion mass hierarchy as eigenvalues of the Dirac operator on the BCC fluctuation channel within the Brazovskii fluctuation-stabilized disordered phase (Reading H). The vacuum is disordered (Math400-AddE: r_R = +0.4193 self-consistent at canonical mu^2=+0.005, Path α confirmed across full sweep mu^2 in [-1, +0.5]); BCC is the cosmologically-relevant stable fluctuation channel (Math400-AddF: n_neg=0 at canonical, FCC saddle-6 rejected).

Status semantics

This pillar is currently classified at tier T6 (PROVED CONDITIONAL on Reading H interpretive framework (Math400-AddE Path α + Math400-AddF BCC stable channel)) per the canonical TOE-FACT-SHEET.

Conditional on:

  • Reading H interpretive framework: Brazovskii fluctuation-stabilized disordered phase per Math400-AddE one-loop self-consistency at TECT canonical params (Path α confirmed; r_R = +0.4193 at mu^2=+0.005, sextic stabilisation outweighs attractive quartic by factor 1.8).
  • BCC fluctuation channel cosmological-relevance: Math400-AddF N=64 tighter at canonical mu^2=+0.005 confirms BCC n_neg=0 (true local min in snapshot energy landscape), FCC saddle-6 (rejected at canonical), HEX stable but uniaxial (cosmological-isotropy filter rejected per Math400-AddA).
  • Lemma A (Math221-AddC): T6 PROVED CONDITIONAL — Math355 audit-confirmed 2026-05-09 ✓
  • Lemma B (Math220-AddB): T6 PROVED CONDITIONAL — Math277 audit-confirmed 2026-05-01 ✓
  • Lemma E_3' (Math218-AddA): now reformulated under Reading H as Pillar 11 Kibble-Zurek frozen-defect cosmological abundance question (no longer Pillar 4 blocker per Math400-AddF §6 + reading framework reorganization).
  • ADVERSARIAL AUDIT NOTE 2026-05-12 (operator review of Math382): Math382 multi-channel closure has internal k_lock convention inconsistency — formula V_lock ∝ 1/k_lock implies k_lock→0 = perfect locking, but text states k_lock→∞ as "perfect locking limit". Numerical conclusion (exp(-2/k_lock) ≈ 1.6×10^-6 at k_lock=0.15) IS consistent with Math376 v3 convention (k_lock = inverse penalty), but verbal limit-direction in Math382 is wrong. Math407 (correction note) issued. Pillar 4 T6 PROVED CONDITIONAL UNCHANGED at structural level (Math400-AddE one-loop and Math400-AddE-AddA two-loop independent of multi-channel question), but the "Math382 closure" subclaim is weakened from "established" to "consistent-with-corrected-convention".

Key Math notes

Open questions

See Open-questions for active items tagged with P4. GitHub Issues with the same label provide discussion threads: issues with P4 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.

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