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Supreme Polarity Theory

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Chapter

Science

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Getting Started

Physics

Mathematical Evidence

Mathematical Evidence — OverviewThe One SPT Action — Foundation, Audit, Refined FormBagua Cascade — The Underlying Data StructureDANode in Q_7 — rigorous Tier-B-EXACT lattice theoremsAb-initio Derivations — 6 Roadmap Steps + 4 Toy Toggles TestedComputational Accuracy — SPT vs String, LQG, MOND, SM+GRSPT Honest Status — What's Derived, What's Calibrated, What's Missing2026 SymPy Breakthrough — d₀ = √7/4 algebraic exact, d_s(Q₇) PASSΩ_b PASS path — why CLOSE, what it would take to flip, and how to verify with SymPyZero-parameter authenticity — what "no CODATA, no PDG, no α_em" really means in SPTSpeed of light from the SPT membrane — c as emergent rate, SymPy-verified to all ordersCross-relation 5.1 — c → Light: c IS the membrane flip rateCross-relation 5.2 — c → Electricity: c² = 1/(ε₀μ₀) and α_em from Bagua geometryCross-relation 5.3 — c → Matter: cascade slope d₀ = √7/4 from same membrane spacingCross-relation 5.4 — c → Forces: gravity, EM, strong, weak from one membraneTier 1 + Tier 2 verification status — May 2026 PARTIAL closuresDiscovered principles — SPT axioms verified by SymPy (10 May 2026 v3 synthesis)Cross-correlation test — c and d₀ from the SAME membrane spacing (PASS)Yin-Yang Z₂ symmetry — the SPT discrete invariance behind θ_QCD ≡ 0 and m_ν1 ≡ 0Yin-Yang Node internal geometry — pole separation r_yy = √(7/8)·ℓ_Planck and 7 dynamical processesSPT Laws — formal synthesis vs. modern physics (10/05/2026 v3.6 · 34 Laws)Open physics problems vs SPT status (comprehensive · 10/05/2026 v3.5)Law 25 — Three SM generations from Bagua mod-6 (Đợt 3 · 10/05/2026 v3.4)Law 26 — Normal neutrino mass hierarchy from yin-yang Z₂ + cascade (Đợt 3 · 10/05/2026 v3.4)Law 27 — Top mass m_t = v/√2 from cascade entry depth (Đợt 3 · 10/05/2026 v3.4)Law 28 — Higgs mass m_H = v · √(33/128) from Bagua shell (Tier-B EXACT · 10/05/2026 v3.5)Law 29 — Cosmological Λ from m_ν cascade re-anchor (Tier-B EXACT · 10/05/2026 v3.5)Law 30 — Dark matter = yin-dominated Bagua nodes, Ω_DM = 34/128 (Tier-B EXACT · 10/05/2026 v3.5)Law 31 — V(φ) upgrade META (chiral/color/EW phase bias · 10/05/2026 v3.6)Law 32 — Baryogenesis η_B from δ_chiral phase bias (Tier-A · 10/05/2026 v3.6)Law 33 — α_s(M_Z) + Λ_QCD from δ_color SU(3) Casimir (Tier-A · 10/05/2026 v3.6)Law 34 — Muon g−2 + Hubble tension via phase evolution (Tier-A · 10/05/2026 v3.6)SPT Framework Checkpoint — Đợt 50 (12/05/2026 v3.52, Phase 8 SUBSTANTIAL COMPLETION)Clay Yang–Mills via SPT: Substrate-Cutoff Partial Framework (NOT a Clay Solution)Law 20 — Noether's theorem from membrane Action (Đợt 2 · 10/05/2026 v3.3)Law 21 — Heisenberg uncertainty Δx · Δp ≥ ℏ/2 (Đợt 2 · 10/05/2026 v3.3)Law 22 — Wigner classification of particles (Đợt 2 · 10/05/2026 v3.3)Law 23 — Goldstone's theorem from broken U(1) (Đợt 2 · 10/05/2026 v3.3)Law 24 — B + L conservation from yao parity (Đợt 2 · 10/05/2026 v3.3)Law 34 — Muon g−2 anomaly Δa_μ from δ_EW phase bias (Tier-A · 10/05/2026 v3.6)Law 35 — Hubble tension H_0(z) via phase evolution (Tier-A · 10/05/2026 v3.6)Law 80 — Phase 8 SUBSTANTIAL COMPLETION Synthesis META (Đợt 50 · 12/05/2026 v3.52) [META]Law 79 — Section C Gravity: Master Constraint Inner Product (Đợt 49 · 12/05/2026 v3.51) [Section C gravity closure]Law 78 — Phase 8d UNCONDITIONAL: Mass Gap m_gap = Λ_QCD·√(6π) (Đợt 48 · 12/05/2026 v3.50) [Phase 8d unconditional]Law 77 — Phase 8c-rest: OS-1 SO(4) Emergence (Đợt 47 · 12/05/2026 v3.49) [Phase 8c-rest CLOSES Conjecture 2]Law 76 — Phase 8+ Section C: Physical Inner Product on DA Gauge Sector (Đợt 46 · 12/05/2026 v3.48) [Phase 8+ Section C step]Law 75 — Phase 8d: Mass Gap RG-Flow CONDITIONAL (Đợt 45 · 12/05/2026 v3.47) [Phase 8d conditional]Law 74 — Phase 8c PARTIAL: Continuum Limit Framework (Đợt 44 · 12/05/2026 v3.46) [Phase 8c partial — NOT Clay]Law 73 — Phase 8b: Thermodynamic Limit V→∞ Existence (Đợt 43 · 12/05/2026 v3.45) [Phase 8b]Law 72 — Cosmological-Constant w(z) Evolution from d_0(t) (Đợt 42 · 12/05/2026 v3.44) [Phase 7+]Law 71 — Bounce Quantum Dynamics (Đợt 41 · 12/05/2026 v3.43) [Phase 7+]Law 70 — Page Curve from Virtual-DA Correlations (Đợt 40 · 12/05/2026 v3.42) [Phase 7+]Law 36 — sin²θ_W Weinberg angle from Bagua 3/13 + RG (Đợt 6 · 10/05/2026 v3.7)Law 69 — Quantum SPT Action with Dirac Constraints (Đợt 39 · 12/05/2026 v3.41) [Phase 7+]Law 37 — Cascade depths {d_i} as Hamming + Casimir algebraic identity (Đợt 6 · 10/05/2026 v3.7)Law 38 — Yang-Mills mass-gap from Q_3 → Q_6 hexagram closure (Đợt 6 · 10/05/2026 v3.7)Law 39 — V(φ) Phase-Bias Closure (Tier-B Upgrade · Đợt 7 · 10/05/2026 v3.8)Law 40 — Full Tier-B Closure of the last 7 Tier-A laws (Đợt 8 · 10/05/2026 v3.9)Law 68 — Phase 8a Rigorous Lattice Gauge Construction (Đợt 38 · 12/05/2026 v3.40) [Phase 8a]Law 41 — Virtual DANode (Node Âm-Dương ảo) Existence Proof (Đợt 11 · 10/05/2026 v3.12)Law 67 — Yang-Mills OS-Axiom Partial Framework on Q_7 (Đợt 37 · 11/05/2026 v3.39) [Phase 7+ partial]Law 42 — Unified Force Mechanism from DANode Rotation (Đợt 12 · 10/05/2026 v3.13)Law 66 — DM Cascade Depth from C(7,4) Coset (Đợt 36 · 11/05/2026 v3.38) [Phase 7]Law 43 — Sound Wave from Collective DANode Rotation (Đợt 13 · 10/05/2026 v3.14)Law 65 — Cascade Dynamics EOM for d_0(t) (Đợt 35 · 11/05/2026 v3.37) [Phase 7]Law 44 — Wave-Particle Duality from DANode Regimes (Đợt 14 · 10/05/2026 v3.16)SPT Framework Statistics Checkpoint — Đợt 34 (11/05/2026 v3.36, Phase 6 complete)Law 45 — Entropy + Arrow of Time from DA Coset Decoherence (Đợt 15 · 11/05/2026 v3.17)Law 64 — DM Direct-Detection σ_SI from Virtual-DA (Đợt 34 · 11/05/2026 v3.36)Law 46 — Quantum Entanglement (Bell-CHSH) from Q_7 × Q_7 (Đợt 16 · 11/05/2026 v3.18)Law 63 — Stochastic GW Background Spectrum from Bounce (Đợt 33 · 11/05/2026 v3.35)Law 47 — Spin-2 Graviton Polarization from Q_7 yao-pair (Đợt 17 · 11/05/2026 v3.19)Law 62 — 0νββ Half-Life from PMNS + Majorana (Đợt 32 · 11/05/2026 v3.34)Law 48 — PMNS Angles Closed-Form from Q_7 Coset Overlaps (Đợt 18 · 11/05/2026 v3.20)Law 61 — Hawking Radiation T_H from Virtual-DA Tunneling (Đợt 31 · 11/05/2026 v3.33)Law 49 — Cascade-Depth Tier-B Closure (d_baryo, d_strong, d_μ) (Đợt 19 · 11/05/2026 v3.21)Law 60 — Big Bang Bounce Quantitative Dynamics (Đợt 30 · 11/05/2026 v3.32)Law 50 — Cosmological Inflation Potential from V(φ) = -λcos(φ/φ_0) (Đợt 20 · 11/05/2026 v3.22)Law 59 — Spacetime 3+1+3 Rigorous Uniqueness Proof (Đợt 29 · 11/05/2026 v3.31)Law 51 — Yang-Mills Mass-Gap: Lattice Continuum Argument (Đợt 21 · 11/05/2026 v3.23)Law 58 — Spacetime 3+1 Dimensions Emerge from Q_7 (Đợt 28 · 11/05/2026 v3.30)Law 52 — Big Bang Singularity Resolution via DA-Density Bound (Đợt 22 · 11/05/2026 v3.24)Law 57 — Hubble Constant H_0 Exact Value from Q_n (Đợt 27 · 11/05/2026 v3.29)Law 53 — Anomalous Electron Magnetic Moment Δa_e (Đợt 23 · 11/05/2026 v3.25)Law 56 — Hadron Masses (Proton, Neutron, Pion) from Q_3→Q_6 Closure (Đợt 26 · 11/05/2026 v3.28)Law 54 — CKM Matrix Closed-Form from Bagua Q_n Ratios (Đợt 24 · 11/05/2026 v3.26)Law 55 — Electroweak VEV v + Boson Masses M_W, M_Z (Đợt 25 · 11/05/2026 v3.27)SPT Framework Statistics Checkpoint — Đợt 28 (11/05/2026 v3.30)DANode Master Toy — Full DerivationPhoton — Electron Toy: Full DerivationEntanglement Toy — Full DerivationBlack-Hole Phase-Reversal Toy — Full DerivationLarge-N Gravity Toy — Full DerivationSM Mass Spectrum — Full DerivationHiggs / Electroweak Symmetry Breaking — Full DerivationCMB Power Spectrum — Full DerivationNeutrino Oscillation — Full DerivationGravitational-Wave Inspiral — Full Derivation
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