Map F — Simple summary: what we found, why it matters, where it sits in history

Read this page first if you only have ten minutes. It explains Master Map F in plain language: what it is, the “lock and tooth” picture, what was proved in Directions 1 / 1c / N2, why it matters for SPT, and an honest place in the history of physics — without claiming Newton-level status.

Glossary: /glossary#spt-master-map. Deep dives: Action↔F easy · What is Map F? · F ↔ 40 constants · F from Action · Direction A · N2 · RG zoom.

1. What is Map F? (one picture)

Every constant in Map F is a fraction:

text

  quan sát  =  TỬ SỐ  /  MẪU SỐ
            =  “răng”  /  “cỡ ổ khóa”

F is the single rulebook:

text

  F(lĩnh vực, vai trò đo)  →  phân số Bagua
  (không nhét số PDG vào vế phải; PDG chỉ để kiểm sau)

So SPT is not “five lucky ratios.” It is one map with shared locks and named teeth.

2. The map in one table

What we measure	F says	Lock (denom)	Tooth (num)
Weinberg angle (tree)	3/13	13	3 (SU(2) gens)
Solar neutrino sin²θ₁₂	4/13	13	4 (proved N2)
GW tilt n_T	3/13	13	3 (same as weak)
Cabibbo λ	9/40	40	9 = 3²
Hubble h	27/40	40	27 = 3×9

Two locks only: shell W = 13 (electroweak family) and shell S₄₀ = 40 (Cabibbo + Hubble). Terms: denominator/shell, numerator, Master Map F.

3. How we got here (SPT journey, simple)

Step	What changed	Page / script
Phase 9	Noticed shared 13 & 40; anti-numerology programme	Phase 9 hub
Dir 1 — shells	W=13, S₄₀=40 counted from Action gauge content	F from Action
Dir 1c — teeth	Laws N1–N6 force (3,4,3,9,27); unique tuple	Map F explained
N2 proof	Solar 4 = Q₃/2 = n_W+1 = n_Y−1 (not free +1)	N2 proof
Dir 2 — zoom	RG: θ_W runs 3/13 → lab via δ_RG = 1/(1024π)	Lattice RG

Before Map F: a catalogue of closed forms that match data. After Map F: a rule (locks + teeth + uniqueness + falsifiers). That is the real step change inside SPT.

4. Teeth in one breath (N1–N6)

N1: 3 = number of weak generators.
N2: 4 = half of 8 = one more than 3 = one less than 5 (triple identity).
N3: 3 again = leftover of 8 after hypercharge budget 5.
N4: 3 generations.
N5: 9 = 3² (Cabibbo tooth).
N6: 27 = 3×9 (Hubble tooth); h/λ = 3 exact.

5. Why Map F matters (importance)

For…	Score	Plain meaning
SPT’s own history (2026)	8.5–9 / 10	Biggest structural step from catalogue → rulebook
Anti-numerology	9 / 10	Shared locks + unique teeth under axioms
Experiment design	8 / 10	DUNE / GW / Cabibbo are correlated bets
Engineering products	2 / 10	Not engines or batteries — structure of constants
World physics history today	2–3 / 10	Not peer-settled; mostly post-diction so far
Potential if pre-reg data hit	5–7 / 10	Could become a noted “shell mechanism” — still not Newton

One line. Inside SPT, Map F is the flagship. In world history, it is a serious research candidate for “geometry → constants,” not a completed revolution.

6. Honest place in the history of ideas

Compare by role, not by fame. Map F is like steps that turned many facts into one table or one law — but it has not yet passed the community + experiment fire that those names passed.

Historical step	Similar spirit to Map F?	Where Map F is weaker
Kepler — many orbits → few laws	Catalogue → pattern	Kepler had live sky data driving the laws
Mendeleev — table maps place → property	Map “slot → number”	He predicted empty slots later found
Eightfold Way / quarks — counting multiplets	Count generators / cells → structure	Led to a new particle (Ω⁻) on the table
Weinberg–Salam — EW mixing + later running	Shell EW + angle + RG story	Full Lagrangian + Nobel after data
String / landscape — geometry → constants	Same dream	String has deeper math; landscape is less sharp to kill
Newton / Maxwell / Einstein	Only in the broad sense “one rule, many phenomena”	They rebuilt dynamics/spacetime with decisive tests

Closest friendly analogy (if you need one): a “Mendeleev table for a few constants” plus “Eightfold-style counting,” with the ambition of closing SM mixing angles — still awaiting the moment equivalent to predicting a new element or a Halley comet return.

7. What Map F is not (please read)

Not “SPT finished the Theory of Everything.”
Not a Clay Millennium solution (different track; substrate ≠ continuum).
Not a product recipe (planes, batteries, FTL).
Not peer-reviewed mainstream consensus (yet).
Still has research gaps: path-integral depth of some counting stories; absolute α(M_Z) sub-percent; live pre-registered tests.

8. How to use this result (practical)

Research compass: new constants must say which lock and which tooth — or admit Class C fit.
Experiments: treat θ_W, θ₁₂, n_T as one family; Cabibbo and h as another.
Communication: tell the lock/tooth story first; send experts to scripts and deep wikis.
Next science: pre-register bets (DUNE, LZ, CMB); optional dynamics d₀(t) — not Law 81 spam.

9. Reproduce offline

SymPy verify — download for offline testSYMPY ✓

Core Map F scripts

Run each with Python + SymPy; expect OVERALL: PASS.

scripts/spt_master_map_f_from_action.py

Shells W=13, S40 from Action — Denominators + uniqueness class R

220 LOCDownload

scripts/spt_master_map_numerators.py

Numerator laws N1–N6 — Teeth (3,4,3,9,27) unique

240 LOCDownload

scripts/spt_master_map_n2_solar.py

N2 triple proof n_solar=4 — Q3/2 = n_W+1 = n_Y−1 = 4

180 LOCDownload

scripts/spt_cross_sector_shells.py

Cross-sector shell theorem — Five observables, two shells

120 LOCDownload

Reproduce in 30 seconds

pip install sympy numpy && python3 scripts/spt_master_map_f_from_action.py && python3 scripts/spt_master_map_numerators.py && python3 scripts/spt_master_map_n2_solar.py && python3 scripts/spt_cross_sector_shells.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.

10. Bottom line

Map F = one rulebook for several constants: tooth / lock = numerator / denominator. - Locks 13 and 40 from Action geometry. - Teeth 3, 4, 3, 9, 27 from counting laws (N2 now a triple identity). - Inside SPT history: the move from catalogue → map — the flagship structural result of Phase 9 + Directions 1/1c/N2. - In world physics history: a candidate mechanism in the family of “pattern → table/law,” not a finished Newton/Maxwell/Einstein moment. Judge it by scripts, axioms, and future experiments — not by homepage scoreboard volume.