# SFT Master Chain — Lagrangian → All Observables

## Complete Traceability Map

Every certified result traces back to the single 6-term Lagrangian
through the unique physical hedgehog branch. This document maps
every Lean file to its role in the derivation chain.

**Total**: 75 Lean files, 795+ theorems, 83 certified observables, zero sorry.

---

## The Lagrangian Terms

```
Term 1: (f²/4) Tr(D_μ U D^μ U⁻¹)           — σ-model kinetic
Term 2: (1/(32 e_Sk²)) Tr([L_μ, L_ν]²)      — Skyrme stabilizer
Term 3: L_WZW                                 — Wess–Zumino–Witten topological
Term 4: -(m²/4) Tr(U + U† - 2)               — Pion mass / chiral breaking
Term 5: -(g/Λ²) J_B^μ j_μ^φ                  — Baryon-scalar coupling
Term 6: +(ξ/(f² e_Sk²)) J_B^μ J_{B,μ}        — Sextic stabilizer
        +(η/2) g_skin^{μν} J_B^μ J_B^ν        — η metric-skin coupling
```

---

## Layer 0: Foundation

| File | Role | Depends On |
|------|------|------------|
| `Core/Params.lean` | Locked physical parameters (ρ_skin, AB_skin, f, e_Sk, η, ...) | Lagrangian |
| `Core/HedgehogBasic.lean` | F_phys(r) = π·exp(-\|r\|), B=1, uniqueness | Core/Params |

## Layer 1: Hedgehog ODE & Physical Branch

| File | Role | Derives From |
|------|------|-------------|
| `ODE/Defs.lean` | Core ODE definitions, denominator D>0, topological charge B=1 | Terms 1+2+6 |
| `ODE/HedgehogODE.lean` | ODE coefficients a(ρ,F), solution structure, coeff_a > 0 | Terms 1+2+6 |
| `ODE/NumericalFramework.lean` | Trapezoidal quadrature, error bounds, I_η computation | ODE/Defs |
| `ODE/ConleyIndex.lean` | Isolating blocks, Conley index S⁰ → unique orbit | ODE/HedgehogODE |
| `ODE/TopologicalDegree.lean` | Leray-Schauder degree = 1, homotopy λ₆: 0→1 | ODE/HedgehogODE |
| `ODE/PhysicalBranch.lean` | Physical branch existence + uniqueness + isolation | ConleyIndex + TopologicalDegree |
| `ODE/DeltaDerivation.lean` | δ self-consistency, WZW overlap Γ = -1 | ODE/Defs + NumericalFramework |

## Layer 2: Parameter Derivations

| File | Role | Derives From |
|------|------|-------------|
| `ODE/ParameterDerivations.lean` | N=11 unique, e_Sk, ξ, f, ζ, η, 1/α_GUT, all 72 params | Layer 1 |
| `ODE/CKM_PMNS.lean` | CKM matrix, PMNS parameters, unitarity | ParameterDerivations |
| `ODE/GravityCoarseGraining.lean` | G_eff, Λ_cc from etebuda density | ParameterDerivations |
| `ODE/NoFreeParameters.lean` | **Strong form**: all 72 parameters uniquely fixed | All of Layer 1+2 |

## Layer 3: Electroweak & Gauge Sector

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/AnomalyCancellation/Embedding.lean` | SU(11) adjoint dim=120, SM embedding | Term 3, N=11 |
| `Mechanisms/AnomalyCancellation/ZeroModes.lean` | N_gen = 3 from index theorem | Embedding |
| `Mechanisms/AnomalyCancellation/AnomalyCoefficients.lean` | 4 anomalies vanish | ZeroModes + Embedding |
| `Mechanisms/ElectroweakMasses/RadialHiggsProfile.lean` | Higgs = breathing mode | Term 1, Layer 1 |
| `Mechanisms/ElectroweakMasses/EWGaugeKKReduction.lean` | g₂, g' from KK reduction | RadialHiggsProfile |
| `Mechanisms/ElectroweakMasses/OverlapIntegrals.lean` | κ_W, κ_Z overlap computations | RadialHiggsProfile |
| `Mechanisms/ElectroweakMasses/MassesAndRho.lean` | m_W, m_Z, ρ=1 | EWGaugeKKReduction |

## Layer 4: Higgs & Yukawa Couplings

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/HiggsCouplings/Defs.lean` | SFTParams, OnUniqueBranch | Core/Params |
| `Mechanisms/HiggsCouplings/RadialProfile.lean` | Higgs radial profile, m_H² > 0 | Defs |
| `Mechanisms/HiggsCouplings/GaugeCouplings.lean` | \|κ_W - 1\| < 0.01 | Defs |
| `Mechanisms/HiggsCouplings/YukawaCouplings.lean` | \|κ_f - 1\| < 0.05 | Defs |
| `Mechanisms/HiggsCouplings/Master.lean` | All 5 couplings certified SM-like | Gauge + Yukawa |
| `Mechanisms/HiggsCouplings/Summary.lean` | Module summary | Master |

## Layer 5: QED & Photon Sector

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/PhotonPairProduction/PhotonProfile.lean` | Photon normalization | Layer 2 params |
| `Mechanisms/PhotonPairProduction/FermionZeroMode.lean` | Fermion zero-mode profile | PhotonProfile |
| `Mechanisms/PhotonPairProduction/OverlapIntegral.lean` | \|O_γee - 1\| < 0.05 | PhotonProfile + FermionZeroMode |
| `Mechanisms/PhotonPairProduction/EffectiveVertex.lean` | σ_SFT ≈ σ_QED | All PhotonPair files |

## Layer 6: Gravity

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/PostNewtonian/Defs.lean` | PPN parameters, G_eff | Term 6b, Layer 2 |
| `Mechanisms/PostNewtonian/Theorems.lean` | γ=1, β=1 (1PN) | PostNewtonian/Defs |
| `Mechanisms/PostNewtonianHigher/Defs.lean` | 2PN metric | Term 6b |
| `Mechanisms/PostNewtonianHigher/Theorems.lean` | 2PN certification | PostNewtonianHigher/Defs |

## Layer 7: Flavor Physics & Rare Decays

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/Anomalies/BToKNuNu.lean` | B⁺→K⁺νν̄ | Terms 3+5, Layer 2 |
| `Mechanisms/Anomalies/BMesonRGRunning.lean` | b→sμ⁺μ⁻ negligible | Terms 3+5 |
| `Mechanisms/Anomalies/EpsilonPrime.lean` | ε'/ε from WZW phase | Term 3 |
| `Mechanisms/Anomalies/NeutronEDM.lean` | d_n below bound | Terms 3+5 |
| `Mechanisms/Anomalies/RDstar.lean` | R(D*) tension < 0.3σ | Terms 3+5, WZW phase |

## Layer 8: Nuclear Physics

| File | Role | Derives From |
|------|------|-------------|
| `Mechanisms/Nuclear/Defs.lean` | Nuclear parameters, Bethe-Weizsäcker coefficients | Terms 1+2, multi-soliton |
| `Mechanisms/Nuclear/BindingEnergy.lean` | Binding energy, magic numbers | Nuclear/Defs |
| `Mechanisms/Nuclear/PeriodicTable.lean` | Electron shells, noble gases, Madelung rule | Nuclear/Defs + Core/Params |
| `Mechanisms/Nuclear/FissionFusion.lean` | Fission threshold, fusion energetics | Nuclear/Defs |
| `Mechanisms/Nuclear/Master.lean` | Nuclear physics master theorem | All Nuclear files |
| `Mechanisms/Nuclear/SuperheavyDefs.lean` | Superheavy element predictions (Z>118) | Terms 1+2, multi-soliton |
| `Mechanisms/Nuclear/SuperheavyTheorems.lean` | Island of stability, decay chains | SuperheavyDefs |

## Layer 9: Quantum (Fermion Sector)

| File | Role | Derives From |
|------|------|-------------|
| `Quantum/FermionMasses.lean` | Mass hierarchy from localization | Term 5, γ_i |
| `Quantum/NeutrinoMasses.lean` | See-saw from hedgehog boundary | Terms 3+5 |
| `Quantum/QuantumClosure.lean` | Muon g-2, quark masses, CKM | All quantum |
| `Quantum/RareFlavorEDM.lean` | Rare flavor + EDM bounds | Terms 3+5 |
| `Quantum/RareDecays.lean` | Universal (1+δ)² enhancement | Term 5 |
| `Quantum/RunningConstants.lean` | RG running | Layer 2 |
| `Quantum/ElectroweakClosure.lean` | EW sector closure, S/T/U | Layers 3+4 |
| `Quantum/LambdaQCD.lean` | Λ_QCD prediction | Layer 2 |
| `Quantum/ProtonRadius.lean` | Proton charge radius | Layer 1 profile |
| `Quantum/Quantum_AtomicParityViolation.lean` | Cesium APV, Q_W | sin²θ_W, Layer 2 |

## Layer 10: Cosmology

| File | Role | Derives From |
|------|------|-------------|
| `Cosmology/Parameters.lean` | Cosmological parameters | Layer 2 |
| `Cosmology/Friedmann.lean` | Modified Friedmann equation | Term 6b |
| `Cosmology/CouplingPersistence.lean` | Decoupling transition | Friedmann |
| `Cosmology/Primordial.lean` | Primordial power spectrum | Term 1, Parameters |
| `Cosmology/PowerSpectrum.lean` | Matter power spectrum | Parameters |
| `Cosmology/BAO.lean` | BAO sound horizon | Friedmann + CouplingPersistence |
| `Cosmology/RippleSchrodinger.lean` | Ripple propagation | Core/Params |
| `Cosmology/HubbleTension.lean` | H₀ tension resolution | Term 6b |
| `Cosmology/CMBDefs.lean` | CMB observable definitions | — |
| `Cosmology/CMBTheorems.lean` | CMB predictions | CMBDefs |
| `Cosmology/CMBHigherOrder.lean` | Higher-order CMB effects | — |

## Layer 11: Spectral (Riemann Zeta Connection)

| File | Role | Derives From |
|------|------|-------------|
| `Spectral/Spectrum.lean` | Spectral operator eigenvalues, Casimir C₂(k) | SU(11), ODE α_RH |
| `Spectral/FirstPrinciples.lean` | Complete first-principles eigenvalue equation | Spectrum |
| `Spectral/PrimeCorrection.lean` | Prime oscillatory correction S(t) | Spectrum |
| `Spectral/SelbergTrace.lean` | Selberg trace = Z-function identity | SU(11) root data |
| `Spectral/RecurrenceDiverges.lean` | k(n) → ∞ (monotone recurrence) | — |

## Layer 12: Master Files

| File | Role | Derives From |
|------|------|-------------|
| `MasterIndex.lean` | Re-exports all 72 module files | All layers |
| `PaperDerivations.lean` | 22 derivation sections for master paper | MasterIndex |
| `SFT_FinalPrecisionSweep.lean` | Precision sweep: all observables with bounds | Mathlib |

---

## Mapping Diagram

```
                          ┌─────────────────────────┐
                          │       LAGRANGIAN         │
                          │     6-term ℒ_SFT         │
                          │ f, e_Sk, m, g, ξ, η     │
                          └───────────┬─────────────┘
                                      │
               ┌──────────────────────┼──────────────────────┐
               ▼                      ▼                      ▼
        ┌────────────┐         ┌────────────┐         ┌────────────┐
        │  Terms 1+2 │         │   Term 3   │         │  Terms 5+6 │
        │  σ-model + │         │    WZW     │         │  Baryon-   │
        │   Skyrme   │         │ topological│         │  scalar +  │
        └─────┬──────┘         └─────┬──────┘         │  η-metric  │
              │                      │                └─────┬──────┘
              └───────────┬──────────┘                      │
                          ▼                                 │
                 ┌─────────────────┐                        │
                 │  HEDGEHOG ODE   │◄───────────────────────┘
                 │  F(ρ): F(0)=π  │
                 │    F(∞)→0      │
                 └────────┬───────┘
                          │
              ┌───────────┼───────────┐
              ▼           ▼           ▼
       ┌────────────┐ ┌────────┐ ┌──────────┐
       │  PHYSICAL  │ │ TOPOL. │ │ CONLEY   │
       │   BRANCH   │ │ DEG=1  │ │ INDEX=S⁰ │
       │ ρ_skin=    │ │        │ │          │
       │  0.9209    │ │        │ │          │
       └─────┬──────┘ └────────┘ └──────────┘
             │
    ┌────────┼──────────┬──────────┬──────────┐
    ▼        ▼          ▼          ▼          ▼
┌────────┐┌────────┐┌────────┐┌────────┐┌────────┐
│72 PARAM││OVERLAP ││ CKM/   ││ G_eff  ││α_GUT = │
│APPENDIX││INTEG-  ││ PMNS   ││ Λ_cc   ││ 1/24.7 │
│   A    ││ RALS   ││        ││        ││        │
└───┬────┘└───┬────┘└───┬────┘└───┬────┘└───┬────┘
    │         │         │         │         │
    ▼         ▼         ▼         ▼         ▼
┌────────┐┌────────┐┌────────┐┌────────┐┌────────┐
│ GAUGE  ││ HIGGS  ││FERMION ││GRAVITY ││ COSMO- │
│RUNNING ││COUPLING││ MASSES ││PPN γ=1 ││ LOGICAL│
│α_s,θ_W ││κ_V,κ_f ││CKM,ν_m ││PPN β=1 ││CONSTANT│
└───┬────┘└───┬────┘└───┬────┘└───┬────┘└───┬────┘
    │         │         │         │         │
    ├─────────┼─────────┼─────────┤         │
    ▼         ▼         ▼         ▼         ▼
┌────────┐┌────────┐┌────────┐┌────────┐┌────────┐
│ANOMALY ││ PHOTON ││ RARE   ││ POST-  ││FRIEDMAN│
│CANCEL  ││ PAIR   ││DECAYS  ││NEWTON  ││ BAO    │
│N_gen=3 ││PRODUCT.││EDM,g-2 ││1PN+2PN ││ CMB    │
└────────┘└────────┘└────────┘└────────┘└────────┘
    │         │         │         │         │
    ├─────────┼─────────┼─────────┤         │
    ▼         ▼         ▼         ▼         ▼
┌────────┐┌────────┐┌────────┐┌────────┐┌────────┐
│NUCLEAR ││ EW     ││QUANTUM ││HUBBLE  ││SPECTRAL│
│BINDING ││CLOSURE ││CLOSURE ││TENSION ││RIEMANN │
│PERIODIC││S/T/U=0 ││MASTER  ││ΔH₀,σ₈ ││ ZEROS  │
│ TABLE  ││APV     ││        ││        ││SELBERG │
└────────┘└────────┘└────────┘└────────┘└────────┘
    │         │         │         │         │
    └─────────┴─────────┴─────────┴─────────┘
                          │
                 ┌────────▼────────┐
                 │  MASTER INDEX   │
                 │ 72 imports      │
                 │ 83 observables  │
                 │ 0 sorry         │
                 └─────────────────┘
```

---

## File Count by Category

| Category | Files | Key Observables |
|----------|-------|-----------------|
| Core | 2 | ρ_skin, AB_skin, F_phys |
| ODE | 11 | N=11, 72 params, CKM, PMNS, G_eff, Λ_cc |
| Mechanisms/PhotonPairProduction | 4 | σ(γ→e⁺e⁻) |
| Mechanisms/AnomalyCancellation | 3 | N_gen=3, anomaly=0 |
| Mechanisms/ElectroweakMasses | 4 | m_W, m_Z, ρ=1 |
| Mechanisms/HiggsCouplings | 6 | κ_W, κ_Z, κ_t, κ_b, κ_τ |
| Mechanisms/PostNewtonian | 4 | γ_PPN=1, β_PPN=1, 2PN |
| Mechanisms/Anomalies | 5 | B→Kνν, ε'/ε, nEDM, R(D*) |
| Mechanisms/Nuclear | 7 | Binding energy, magic numbers, periodic table, superheavy |
| Quantum | 10 | Masses, g-2, Λ_QCD, proton radius, APV |
| Cosmology | 11 | n_s, r, H₀, σ₈, BAO |
| Spectral | 5 | ζ zeros, Selberg trace, recurrence |
| Master/Sweep | 3 | Full re-export + precision sweep |
| **Total** | **75** | **83 observables** |

---

*One Lagrangian. One unique physical hedgehog branch. 75 files. Zero sorry. Complete.*