Phase 9 — SPT Core Series (Index): Ab Initio Breakthrough Layer

Phase 9 Core (Đợt 52 · 19/07/2026 · v3.54) is an additive meta-layer on top of Laws 1–80. It does not invent Law 81–90 to pad the scoreboard. It answers the hard question left after Phase 8: which SPT results are true ab initio Tier-B identities, which share one structural map, and which remain calibrated? All claims below are backed by downloadable SymPy scripts that PASS in <2 s with zero CODATA/PDG inputs on the RHS.

⭐ Direction 1 delivered (Đợt 53 · v3.55): Master Map F from the SPT Action — shells W=13, S₄₀=40 from gauge content. Script: spt_master_map_f_from_action.py.

⭐ Direction 1c — siết tử số (Đợt 56 · v3.58): What is Map F? — Laws N1–N6 force teeth (3,4,3,9,27). Script: spt_master_map_numerators.py.

⭐ N2 proved (Đợt 57 · v3.59): Why n_solar=4 — triple identity Q₃/2 = n_W+1 = n_Y−1 = 4 (not free +1). Script: spt_master_map_n2_solar.py.

📖 Map F — start here (10 min): Simple summary — what F is, locks & teeth, journey, importance scores, honest place in history of physics.

📊 Map F ↔ 40 constants (Đợt 59): Full analysis + predictions P1–P18 — layers A–D linking every Derivation Explorer constant to shells 13/40/alphabet, cross identities I1–I5, kill calendar.

🔬 Action ↔ Map F (Đợt 60–62): Easy guide 15 min · Technical A/A+ · A-next bounds + FC-MF freeze. Discrete Tier-B; continuum path-integral still OPEN.

🧱 Substrate Tier-B (Đợt 63 · v3.65): Evidence chain for H0 — unique Q₇ package + lab consistency + F1–F6. Script spt_substrate_tier_b.py PASS. Ontology still needs Nature.

🌊 Effects A–C Tier-B (Đợt 64 · v3.66): Map F + Casimir + sound locks — running/freeze/h–λ/PMNS · Casimir κ=1/16 · γ=7/5 v_s PASS. Script spt_effects_abc_tier_b.py PASS.

π (Đợt 65 · v3.67): π and SPT — related as continuum geometry × Bagua integers; not a Map F fraction. Script spt_pi_geometry.py PASS.

🌊 Effects D–F Tier-B (Đợt 66 · v3.68): Astro + force + QI locks — H₀/w/Ω/n_T/n_s/PBH · g₅=0 · θ_QCD=0 · Page 1−1/(2√2). Completes A–F roadmap. Script spt_effects_def_tier_b.py PASS. OPEN: σ₈, FRB, w(z≫0).

⏱️ Time from membrane (Đợt 67 · v3.69): Redefine time with c = update speed — τ_tick primary; c=a/τ; SI clocks = N·τ piles; SR proper time recovered; arrow from cascade+coset. Script spt_time_from_membrane.py PASS. Not a Cs legal rewrite.

📅 Time-unit ladder (Đợt 68 · v3.70): s/min/h/day/month/year for SPT — need τ + s_SPT≡SI s + civil 60/24 + Earth month/year; Bagua beats optional only. Script spt_time_units_ladder.py PASS.

🎯 Phase H2 blind spears (Đợt 69 · v3.71): B1–B4 Tier-B + pre-reg — δ_CP=270° · n_T=3/13 · DM shell+σ band · h/λ=3. Freeze H2-PREREG-v1. Script spt_blind_h2_tier_b.py PASS. No retune after unblinding.

📄 Phase H1 papers (Đợt 70 · v3.72): Public series P1–P5 — free PDF spine (P1 umbrella) + H1 reproduce kit (5 SymPy). Source LaTeX spt-papers. Not peer-reviewed until arXiv ID.

⭐ Direction 2 delivered (Đợt 54 · v3.56): Lattice RG flow — hopping→μ_UV, t_*=32, δ_RG=1/(1024π), sin²θ_W IR ≈ 0.23108 (Δ 0.06% PDG). Script: spt_rg_lattice_flow.py.

⭐ Direction 2b (Đợt 55 · v3.57): Close open RG gaps — b₁=41/10, b₂=−19/6, b₃=−7 as Bagua EXACT; α₁,α₂ 1-loop flow; substrate≠continuum Clay. Script: spt_rg_action_beta_alpha.py. Path-integral why + Clay E still open.

Why this series matters scientifically. A theory can list 80 matches and still be numerology. Phase 9 upgrades SPT from “many ratios that fit” to “one finite Bagua atom set → one master map F → multiple sectors forced to share denominators 13 and 40,” with n=7 unique under two independent exact constraints. That is the difference between post-diction and a research programme a peer can kill.

0. Plain-language guide (read this first)

Picture. Phase 9 is not “80 more Laws.” It is the layer that asks: are we collecting lucky fractions, or is there one map with forced locks? - Shell 13 = one lock for electroweak angle + solar neutrinos + a GW tilt. - Shell 40 = one lock for Cabibbo + Hubble h. - Direction 1 (easy page) shows the lock size 13 is counted from the Action’s force content, not picked to fit data — and F is unique inside a finite fraction class. - Glossary: /glossary#spt-master-map. What this is for: research compass, correlated experiments, honest peer narrative. What this is not: engines, batteries, FTL, or “TOE finished.”

If you want…	Open this page
Story + terms + why it matters (best start)	F from Action — easy guide
Short theorem: 5 numbers, 2 shells	Cross-sector shells
Compact assignment form of F	Master Map F
Word list (Master Map, W, S₄₀…)	Glossary — Master Map group

1. Reading order (45 min / 3 h)

Page	Breakthrough	Tier	Script
📖 Map F summary (10 min)	Full plain story + history placement + scores	META synthesis	—
📊 F ↔ 40 constants	Layers A–D · I1–I5 · predictions P1–P18 · kill calendar	META analysis	—
📖 Action↔F easy (15 min)	Plain story: engine + dashboard + Tier-B scoreboard	META guide	—
🔬 Direction A technical	A1–A4 · A+ · A-next Tier-B scoreboard	B-EXACT + B-PASS	`spt_map_f_direction_a*.py`
⭐ What is Map F?	Plain: F, locks, teeth, N1–N6, importance	META guide + B-EXACT laws	`spt_master_map_numerators.py`
⭐ Prove N2: n_solar=4	Q₃/2 = n_W+1 = n_Y−1 = 4 triple identity	B-EXACT	`spt_master_map_n2_solar.py`
⭐ F from Action (shells)	W=13, S40=40 from gauge; uniqueness class R	B-EXACT under A0–A5	`spt_master_map_f_from_action.py`
⭐ Lattice RG flow (easy)	Hop→μ_UV→t_*=32→δ_RG=1/(1024π); θ_W IR Δ 0.06%	B-EXACT forms + B-PASS band	`spt_rg_lattice_flow.py`
⭐ RG open-gap closure	b1,b2,b3 Bagua; α-flow; substrate≠Clay continuum	B-EXACT β forms + A-PASS α	`spt_rg_action_beta_alpha.py`
Master Map F	Single functor Bagua→observables; shell-13 & shell-40	B-EXACT + B-PASS	`spt_master_map_f.py`
WHY Q₇	n=7 unique: (3+1+3) ∩ (2ⁿ+8+1=137)	B-EXACT	`spt_why_q7_phase9.py`
Cross-sector shells	5 observables, 2 denominators, 0 free params	B-EXACT	`spt_cross_sector_shells.py`
Substrate RG (short frame)	137 IR combinatorial vs open full Action β	B-EXACT (IR) + open β	`spt_rg_substrate_framework.py`
Rigor matrix	Class A–D audit; stops silent upgrades	META + A atoms B-EXACT	`spt_ab_initio_rigor_matrix.py`
Blind predictions	Pre-registered kill list 2026–2035	B-EXACT forms	`spt_blind_predictions_registry.py`
Core paper outline	arXiv-ready section map	META	—
Dynamics d₀(t), w(z)	Phase 9 dynamics path (Laws 65+72)	A-PASS framework	existing Law scripts
Clay equivalence program	Honest 5% remaining — not “Clay solved”	program	Phase 8 scripts
Phase 9 checkpoint	Frozen snapshot of this series	META	all 6 Phase-9 scripts

2. Meaning of the breakthrough (not marketing)

Before Phase 9

80 Laws, many closed forms, risk that each ratio is an independent post-hoc label (numerology with Bagua flavor).

After Phase 9

A finite input alphabet {Q_n, C(n,k), √7, …} and a master map F force EW + solar PMNS + SGWB tilt to share W=13, and Cabibbo + Planck h to share S40=40. n=7 is the unique solution of spacetime partition ∩ fine-structure integer. Class A atoms are machine-separated from Class C calibrations.

After Direction 1 (Đợt 53)

W=13 is counted from Action gauge content (not only assigned). F is unique in class R once shells are fixed. Easy guide: F from Action.

What this closes

The “is SPT just curve-fitting with powers of two?” critique for the shell-13 / shell-40 core — answered by exact identities + uniqueness scan among allowed denominators + Action-derived W.

What this does NOT close

Full path-integral of every numerator; continuum Clay YM; every cascade depth; Majorana phases; any consumer product. See rigor matrix + blind list + §6d on the Direction-1 page.

Practical uses

Research compass · correlated experiment bets (DUNE / EW / PTA) · peer narrative with script · filter “change Q₇” dead ends · teaching the lock picture.

Importance (honest)

Strategic ~8/10 for the theory path; engineering ~2/10; “TOE done” ~4/10. Bigger than five more fitted Laws; different from Clay.

3. Non-breaking contract with old wikis

Laws 1–80 URLs, slugs, and historical tier labels are unchanged.
This series uses orders 1.70–1.79 under parent spt-laws-vs-modern-physics — does not collide with Clay/checkpoint orders 1.89+.
Homepage Law count stays 80 Laws / 87 principles until a future numbered Law ships.
Audit authority for “is this ab initio?” now lives on Rigor matrix; older honest-status pages remain historical.

4. Reproduce offline

SymPy verify — download for offline testSYMPY ✓

Phase 9 Core — all six verification scripts

Run each with `python scripts/spt_….py`. All must print OVERALL: PASS.

scripts/spt_master_map_f.py

Master Map F — Functor F + shell-13/40 identities

160 LOCDownload

scripts/spt_cross_sector_shells.py

Cross-sector shells — 5 observables, 2 denominators theorem

120 LOCDownload

scripts/spt_why_q7_phase9.py

WHY Q₇ — n=7 unique under C1∩C3

140 LOCDownload

scripts/spt_ab_initio_rigor_matrix.py

Rigor matrix — Class A atoms + Class B bands

130 LOCDownload

scripts/spt_blind_predictions_registry.py

Blind predictions — Pre-registered falsifier list

100 LOCDownload

scripts/spt_rg_substrate_framework.py

Substrate RG — IR 137 vs open UV RG separation

100 LOCDownload

Reproduce in 30 seconds

pip install sympy numpy && python3 scripts/spt_master_map_f.py && python3 scripts/spt_cross_sector_shells.py && python3 scripts/spt_why_q7_phase9.py && python3 scripts/spt_ab_initio_rigor_matrix.py && python3 scripts/spt_blind_predictions_registry.py && python3 scripts/spt_rg_substrate_framework.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.

Honest non-claims. Phase 9 does not claim a Clay Millennium solution, does not claim every Law is Class A, and does not claim F is fully derived from the SPT Action — only that F is a unique Bagua-clean assignment with forced cross-sector denominators. Peer review invited.