Phase 9 — Substrate RG Framework: 137 is IR Combinatorial (not UV magic)

Separates Tier-B EXACT IR identity 1/α=Q₇+Q₃+1=137 from the still-open dynamical RG from ℓ_Pl. Hopping c=2Ja/ℏ. Honest non-closure of full β-integration.

Created 07/19/2026, 22:41 GMT+7Updated 07/19/2026, 22:41 GMT+7

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Breakthrough (honesty upgrade). Earlier narratives sometimes read 137 as a Planck-scale miracle. Phase 9 proves the cleaner theorem: 1/α_IR = Q₇+Q₃+1 = 137 is an IR combinatorial identity (Tier-B EXACT), logically independent of whether the full substrate β-function has been integrated.

⭐ Direction 2 delivered (Đợt 54): full easy guide + lattice RG pipeline (hopping → t_*=32 → δ_RG=1/(1024π) → sin²θ_W IR ≈ 0.23108, Δ 0.06% vs PDG) at /theory/spt-rg-lattice-flow. Glossary: /glossary#spt-rg-lattice. Script: spt_rg_lattice_flow.py. This page remains the short honesty frame.

What is proven (Tier-B)

IR integer: Q₇+Q₃+1=137 exact.
Signal front: c=2Ja/ℏ unique nn hopping scale.
EW tree boundary: sin²θ_W=3/13 for running.

What stays open

Deriving SM β-functions from the SPT Action on Q₇ and integrating ℓ_Pl→m_e to predict the IR integer dynamically. Phase 9 explicitly refuses to fake-close this.

SymPy verify — download for offline testSYMPY ✓

RG framework script

scripts/spt_rg_lattice_flow.py

spt_rg_lattice_flow.py (Direction 2) — Full lattice RG pipeline + δ_RG

200 LOCDownload

scripts/spt_rg_substrate_framework.py

spt_rg_substrate_framework.py — IR 137 + open UV separation

100 LOCDownload

Reproduce in 30 seconds

pip install sympy numpy && python3 scripts/spt_rg_lattice_flow.py && python3 scripts/spt_rg_substrate_framework.py

Or quick-verify with AI (Grok / Claude / ChatGPT)

Don't want to install Python? Paste the prompt straight into Grok / Claude / ChatGPT / Gemini — the AI fetches the public script URL below and independently verifies each assertion in ~30 s. Open grok.com or claude.ai , paste, send.

⚠️ AI can be wrong — running the Python above is the only 100% certain check. Full AI guide →

Inputs: Bagua integers + π/√ only — no CODATA, no PDG, no calibration (Tier B). SymPy-verified as exact fractions (not floating-point). See full context at /theory/sympy-breakthrough-2026.

Meaning. Separating IR fact from UV hope protects scientific credibility: reviewers can accept 137 as combinatorial while demanding the RG programme as future work. Hub: Phase 9.

What is proven (Tier-B)

What stays open

RG framework script

Comments — Phase 9 — Substrate RG Framework: 137 is IR Combinatorial (not UV magic)