Phase 9 — Cross-Sector Shell Theorem (W=13, S₄₀=40)
Tier-B EXACT theorem: five observables across EW, neutrinos, SGWB, CKM, and Hubble share only two Bagua denominators. Zero free parameters. Companion to Master Map F.
spt_cross_sector_shells.py PASS.Scientific meaning
In the Standard Model these five numbers are unrelated inputs (or sector-specific fits). The shell theorem says they are projections of two combinatorial indices. That is a unification claim at the level of parameter structure, not of forces: it predicts correlated shifts. If future data moves one shell member without the others, the theorem dies cleanly — the best kind of theoretical vulnerability.
What this is for in practice
- Experiments: treat DUNE θ₁₂, precision θ_W, and future n_T as one family — not three independent stories.
- Research: do not invent a new fraction for one sector if it breaks the shared shell.
- Not for: building hardware. This is structure of constants, not a device recipe.
| Shell | Members | Exact identity |
|---|---|---|
| W=13 | θ_W tree, θ₁₂, n_T | n_T=3/13; θ₁₂−θ_W=1/13 |
| S₄₀=40 | λ_Cabibbo, h_Planck | h/λ=3; λ=9/40 EXACT PDG |
Shell theorem script
pip install sympy numpy && python3 scripts/spt_cross_sector_shells.pyDon'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 →
Importance: VERY HIGH. Replaces ≥5 independent SM/cosmo parameters with 2 Bagua integers. Hub: Phase 9.
Comments — Phase 9 — Cross-Sector Shell Theorem (W=13, S₄₀=40)