Action ↔ Map F — Easy guide: what we proved, what it means

1. One picture: Action and Map F

Think of two layers:

ACTION S  =  “engine + traffic rules of the universe”
             (flip, spin, rotate, phase potential V(φ) on a Bagua lattice)

MAP F     =  “which fractions the dashboard numbers must show”
             (sin²θ_W = 3/13, Cabibbo = 9/40, h = 27/40, …)

Bridge    =  reading the *counting content* of S
             → locks (denominators 13, 40) and teeth (numerators 3,4,9,27)

Action answers: how does nature move? Map F answers: which rational numbers are forced for mixing angles and a few cosmo ratios? They are not the same object — F is a projection of Action structure onto fractions.

2. What is an “axiom” here? (30 seconds)

An axiom is a starting rule we accept so we can prove the rest. Example: “each node has 7 bits; internal bits carry SU(3)×SU(2)×U(1).” From that we derive shell 13 — we do not put 13 in by hand to fit PDG.

• Axiom → starting rules (A0–A5).
• Theorem → forced results (W=13, S₄₀=40, uniqueness).
• Experiment → judge (DUNE, CMB, LZ…).

3. The research journey (simple timeline)

4. The two locks (shells) in plain words

Lock W = 13 (electroweak family)

Imagine the EW “mixing room” has 13 seats: 8 from the Bagua trigram cell + 5 from the hypercharge budget (what is left after 3 weak generators take their place). The weak force uses 3 of those seats →

sin²θ_W (tree) = 3 / 13
sin²θ₁₂ (solar) = 4 / 13   ← next seat pattern on the SAME lock
n_T (GW tilt)   = 3 / 13   ← same lock again

If one of these three drifts alone while the others stay put, the whole lock fails. That is the scientific power of Map F.

Lock S₄₀ = 40 (Cabibbo + Hubble)

Cabibbo λ = 9 / 40
Hubble h  = 27 / 40
⇒ h / λ = 3 exactly (always, under F)

Flavor geometry (8) and the next cosmo ladder shell (32) add to 40 seats. Cabibbo and Hubble share that lock — they are not free to wander independently.

5. What “Tier-B PASS” means (no jargon trap)

6. Scoreboard of what passed (A → A-next)

7. Everyday analogy

The Action is the car’s engine and chassis. Map F is the dashboard: speed, fuel, temperature must show values that fit the same wiring. Direction A/A+/A-next checked the wiring diagram with math and showed the dashboard fractions are forced by that wiring — and wrote four red kill switches (FC-MF) that experiments can flip. We still have not rebuilt the engine from pure continuum quantum field theory (that OPEN box).

8. What this is useful for

• Explain SPT in one breath: one Action → shared locks 13 & 40 → correlated experiments.
• Design tests: watch θ₁₂, δ_CP, n_T, h/λ together — not one constant in isolation.
• Write papers honestly: claim Tier-B discrete bridge; leave continuum OPEN.
• Stop numerology drift: no new 5/13 “because it fits” without a counting law.

9. Run the proofs yourself

pip install sympy numpy && python3 scripts/spt_master_map_f_from_action.py && python3 scripts/spt_map_f_direction_a.py && python3 scripts/spt_map_f_direction_a_plus.py && python3 scripts/spt_map_f_direction_a_next.py

10. Bottom line