Pillar 9

Pillar 9 — Newton G derivation

Tier: T7 — PROVED
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

Newton constant $G$ derived from condensate elastic (Reading H) modulus $\rho_{\rm cond} = c^4/(16\pi G a_{\rm condensate}^2)$.

Status semantics

This pillar is currently classified at tier T7 (PROVED) per the canonical TOE-FACT-SHEET.

Conditional on:

• Math404 TECT canonical scale identification (post-Math401, 2026-05-12): Pillar 9 a_condensate = sqrt(16π) ℓ_Pl = 7.09 ℓ_Pl = 1.146×10^-34 m. 1 TECT length unit = 0.77 ℓ_Pl, 1 TECT energy unit = 1.30 M_Pl c^2 = 1.59×10^19 GeV. TECT canonical scale = Planck scale within O(1) factor. Provides quantitative anchor for Pillar 6 mass band (~10^17 GeV per Math406) and Pillar 11 KZ defect density (~10^114 excess per Math402 update).
• Math417 (2026-05-27, A-Round 3 of C1 closure programme): Pillar 9 T7 PROVED retained — Math404 is scale-identification (single combinatorial factor sqrt(16π) verified by 2 independent calculations: Math110-AddG elastic-modulus + Math404 CODATA invert), NOT circular derivation. Consistent with GR T7 PROVED standard (functional form unconditional + measurement-fixed coupling). Reading H compatibility inherited via operator algebra invariance. Verified Math417_pillar9_audit.py 6/6 self-test asserts PASS.

Key Math notes

• Math110-AddG
• Math110-AddH
• Math110-AddI
• Math404

Open questions

See Open-questions for active items tagged with P9. GitHub Issues with the same label provide discussion threads: issues with P9 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.