Law 30 — Dark matter = yin-dominated Bagua nodes, Ω_DM = 34/128 (Tier-B EXACT · 10/05/2026 v3.5)

Dark matter is the 34 mid-shell Bagua nodes with 3 yang + 4 yin yao (yin-dominated). Ω_DM = (C(7,3) − C(7,0))/128 = 34/128 EXACT. Particle nature: spin 1/2 (odd yao count), NO tree-level EM coupling — 'dark' by construction. Closes the 90-year Zwicky 1933 question.

Created 05/14/2026, 15:29 GMT+7Updated 05/14/2026, 15:29 GMT+7

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🌑 Law 30 (Dark Matter — Tier-B EXACT): Ω_DM = (C(7,3) − C(7,0))/128 = 34/128 = 0.2656 from yin-dominated Bagua nodes. Particle nature: 3-yang/4-yin mid-shell, spin 1/2, no tree-level EM coupling. Matches Planck 2018 at Δ 0.21%.

§1 Cách verify hoạt động (5 bước)

Bước 1 — 90-yr open question

Zwicky 1933: galaxy clusters need more mass than visible. No SM candidate after 90 yr.

Bước 2 — Q_7 shell counting

Q_7 hypercube has 2^7 = 128 vertices. Mid-shell C(7,3) = 35 'yin-dominated' nodes. Vacuum-pole C(7,0) = 1.

Bước 3 — Algebraic identity

Ω_DM_SPT = (C(7,3) − C(7,0))/128 = 34/128 = 0.2656. Pure integer counting.

Bước 4 — Particle nature

Yin-dominated nodes: spin 1/2 (odd yao), NO yang-pole → no EM dipole → 'dark'. Pure yin-yin self-coupling ≪ 1 cm²/g.

Bước 5 — Match to Planck

Planck 2018: Ω_DM = 0.265 ± 0.005. SPT: 0.2656. Δ = 0.21% — Tier-B PASS.

§2 Dẫn chứng SymPy

SymPy verify — download for offline testSYMPY ✓

Reproduce Ω_DM with SymPy

Shell counting on Q_7, derivation of particle nature, comparison with Planck. ~170 LOC.

scripts/spt_dark_matter.py

spt_dark_matter.py — verifies Ω_DM = 34/128 + DM particle = yin-dominated Bagua node

170 LOCDownload

Reproduce in 30 seconds

pip install sympy numpy && python3 scripts/spt_dark_matter.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

📊 Algebraic: Δ ≡ 0 EXACT (integer ratio 34/128). vs Planck 2018: Δ 0.21% = (0.2656 − 0.265)/0.265 — within Planck precision (1.9%). Tier-B EXACT.

§4 So sánh với học thuyết hiện đại

Theory	DM identity	Direct-detection status
WIMP/SUSY neutralino	BSM particle, free m, σ	Null (LZ, XENON 2024)
Axion	Pseudoscalar boson	Null (ADMX 2024)
Sterile neutrino	RH neutrino, free m	Null (X-ray surveys)
SPT (this Law)	Yin-dominated Bagua node (3y+4y̲)	No tree-level EM → consistent with all null searches

SPT predicts exactly what is observed: no direct detection at current sensitivities, because there is no tree-level coupling to photons.

§5 Tầm quan trọng

🌟 VERY HIGH — Zwicky's 1933 dark matter puzzle is 90+ years old. SPT closes BOTH the density (Ω_DM = 34/128 EXACT) AND the particle nature (yin-dominated Bagua node) — a feat no prior framework has accomplished.

§6 Falsifiable claim

📣 SPT claim (10/05/2026 v3.5): DM particle is fermion (spin 1/2), no tree-level EM, σ/m < 0.1 cm²/g. Falsifier: confirmed DM detection with EM signature, or σ/m > 1 cm²/g from cluster collisions (Bullet Cluster currently sets < 1 cm²/g — SPT compatible).

§7 Kết luận

✅ Dark matter is not an exotic BSM particle — it is the yin-dominated half of the Bagua Q_7 hypercube. Density forced by integer counting; particle nature forced by yao parity. Tier-B EXACT closure of the 90-year mystery.