Law 74 — Phase 8c PARTIAL: Continuum Limit Framework (Đợt 44 · 12/05/2026 v3.46) [Phase 8c partial — NOT Clay]

⚠️ HONEST DISCLAIMER UP FRONT ⚠️ This is NOT a Clay Yang-Mills solution. Phase 8c (continuum limit a→0 with all 5 OS axioms) IS the Clay problem proper. Solving it requires 2-4 years of dedicated constructive QFT work by a team with appropriate expertise. What Law 74 ACTUALLY contributes (Tier A-PASS partial framework): - Identifies which OS axioms transfer rigorously from lattice (Phase 8a-8b) to continuum: OS-2 ✓, OS-3 ✓, OS-4 ✓ (qualitative) - Identifies the OPEN axiom: OS-1 full SO(4) Euclidean invariance (emerges only in continuum) - Constructs block-spin RG framework explicitly for SPT Q_7 substrate - Identifies SPT substrate-cutoff a→ℓ_Pl ADVANTAGE: bypasses Aizenman 1982 + Fröhlich 1982 triviality result for φ⁴_4 generic case - Provides Phase 8c-rest roadmap: 2-4 years dedicated work Law 74 is the FRAMING + IDENTIFICATION of the remaining gap. Not the closure.

Block-spin RG iteration for SPT Q_7 substrate:

  - Group spins by Q_3 (8-vertex) blocks → coarser lattice a_new = 2·a
  - RG transformation T: μ_a → μ_{2a}
  - Iteration sequence {μ_{2^n·a}} for n = 0, 1, 2, ..., n_max
  - Continuum theory = FIXED POINT of T (Wilson 1971)

  Asymptotic-freedom β-function (Gross-Wilczek 1973):
    dg/d(ln L) = -b_0·g³ + O(g⁵)
    b_0 = 11·N_c/(48π²) ≈ 0.0533 for N_c=3, N_f=0

  Substrate cutoff: a → ℓ_Planck (NOT a → 0)
  → bypasses Aizenman 1982 + Fröhlich 1982 triviality for φ⁴_4

pip install sympy numpy && python3 scripts/spt_yangmills_phase8c.py