Pillar 7

Pillar 7 — Lorentz emergence

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

Lorentz invariance as IR fixed-point of BCC-channel anisotropic (Reading H) flow; light-cone emerges below condensate scale.

Status semantics

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

Conditional on:

• H_textbook-SM-gauge-axioms: DISCHARGED at textbook level per Math422 §5 recursive closure. Ward identities (Peskin Ch.7+19); SO(10) per-generation consistency (Slansky 1981); Witten SU(2) global anomaly (Witten 1982 + Atiyah-Patodi-Singer); Lorentz IR fixed-point (Polchinski 1984 standard RG). Math47/48/49 family + Math143 substantive cascade located.
• H_Reading-H-BCC-channel-axiom: TECT-specific axiom (C1-wide; shared with Pillar 8). Same axiom as Pillar 8 final conditional content; cross-pillar axiom sharing, not a new axiom. T7 promotion blocked at meta-level (Path A uniqueness derivation or Path B axiom acceptance; both outside Pillar 7 scope).

Key Math notes

• Math422-Master-Pillar7-Complete-Proof-Archive
• Math47
• Math48
• Math49-rigorous-v2
• Math49b-rigorous-v3
• Math49c-rigorous-v2
• Math143-B5-anomaly-Ward
• Math06
• Math07
• Math388-RG4-FRW-vs-Periodic-Lattice
• Math422

Open questions

See Open-questions for active items tagged with P7. GitHub Issues with the same label provide discussion threads: issues with P7 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.