Pillar 3

Pillar 3 — One-loop renormalisation

Tier: T5 — CLOSED@1-LOOP
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

One-loop fixed-point convergence of the TECT Lagrangian under Wilson-cycle RGE.

Status semantics

This pillar is currently classified at tier T5 (CLOSED@1-LOOP) per the canonical TOE-FACT-SHEET.

Conditional on:

• 1-loop matching (Math200-AddC §2)
• Math416 (2026-05-27, A-Round 2 of C1 closure programme): Pillar 3 T5@1-loop honest label retained; Reading H compatibility CONFIRMED via Math110-AddH dependence on Pillar 2 (verified Reading H compatible per Math415). T5 → T6 promotion paths queued: Math416-AddA (Math200-AddC §2 ℏ_TECT 2-loop extension, ~5-10 hours, HIGHEST priority) + Math416-AddB (Math41 emergent-graviton 2-loop renormalisation via Math400-AddE-AddA methodology, ~8-12 hours); T5 → T7 unconditional requires Math416-AddC (Wetterich exact-RG asymptotic-safety, long-tail). Verified Math416_pillar3_2loop_audit.py 6/6 self-test asserts PASS.

Key Math notes

• Math200-AddC
• Math163

Open questions

See Open-questions for active items tagged with P3. GitHub Issues with the same label provide discussion threads: issues with P3 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.