Law 24 — B + L conservation from yao parity (Đợt 2 · 10/05/2026 v3.3)

Baryon number B and lepton number L separately conserved at every SM vertex. Forbidden process p → e⁺π⁰ violates ΔB = ΔL = ±1 ⇒ EXACTLY forbidden by yao-mod-6 (Law 19). Proton stable: τ_p > 1.6×10³⁴ yr (Super-K). At high T, sphalerons can flip B and L but ΔB = ΔL — B−L is the truly exact combination.

Created 05/14/2026, 01:28 GMT+7Updated 05/14/2026, 01:28 GMT+7

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🪨 Law 24 (B + L · Tier-B EXACT): Yao-mod-6 + U(1)_Y (Law 19) force B and L separate conservation. Proton stable τ_p > 1.6×10³⁴ yr (Super-K). At high T, sphalerons flip B and L equally → B − L exactly conserved.

§1 Cách verify hoạt động (5 bước)

Step 1 — Yao count assignment

Each SM fermion gets (B, L) based on yao composition: quarks → B = 1/3, leptons → L = 1.

Step 2 — U(1) symmetries

SPT Action invariant under ψ_quark → e^{iα/3}ψ and ψ_lepton → e^{iβ}ψ separately ⇒ Noether → B, L conserved.

Step 3 — Vertex check

β-decay n → p + e⁻ + ν̄_e: ΔB = 0, ΔL = 0 ✓. μ-decay, π-decay, Z⁰-decay all ΔB = ΔL = 0.

Step 4 — Proton stability

p → e⁺ + π⁰ violates ΔB = −1, ΔL = +1 (yao-mod-6 forbids). Super-K bound: τ_p > 1.6×10³⁴ yr.

Step 5 — Sphaleron preserves B−L

At T > T_EW, sphalerons flip B and L but ΔB = ΔL. B − L exact ⇒ enables electroweak baryogenesis.

§2 Dẫn chứng SymPy

SymPy verify — download for offline testSYMPY ✓

Reproduce B + L conservation with SymPy

Symbolic vertex enumeration + B − L invariance under sphalerons. ~155 LOC.

scripts/spt_baryon_lepton.py

spt_baryon_lepton.py — verifies ΔB = ΔL = 0 at all SM vertices + p stable

155 LOCDownload

Reproduce in 30 seconds

pip install sympy numpy && python3 scripts/spt_baryon_lepton.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.

§3 Độ chính xác

📊 Δ ≡ 0 EXACT at all SM vertices. τ_p > 1.6×10³⁴ yr Super-K confirmed. Tier-B.

§4 So sánh với học thuyết hiện đại

SM (1970s): B and L are accidental symmetries, hold only in the renormalisable Lagrangian. GUT (SU(5)): predicts proton decay τ_p ~ 10³⁰ yr — ruled out by Super-K. SPT: FORCES B + L from yao-mod-6 — proton stable AUTOMATICALLY.

§5 Tầm quan trọng

🌟 HIGH — Proton stability is a 50+ year puzzle: GUT predicted decay was ruled out; SM treats B, L as accidents. SPT explains stability from Bagua structure.

§6 Falsifiable claim

📣 SPT claim: τ_p = ∞ (proton stable). Falsifier: any confirmed proton-decay event at future detectors (Hyper-K, DUNE).

§7 Kết luận

✅ B and L are forced conservations from yao-mod-6 — not accidents, not GUT-allowed decay. Proton is stable as a structural consequence.