STF Framework — Derivation Strength Tree

Three-Zone Summary

Zone 1 — Hardest core [T] and strong [C]

• Ghost-freedom reduction
• 4π² topological theorem (Topological Closure)
• K = 2ωR/c from Lagrangian
• Picard-Fuchs operator / LCS failure theorem (08a)
• C_Jarlskog = 0 texture theorem (08b)
• Tree-level U_PMNS = I (08b)
• Generation assignment via connecting homomorphism
• δ_CP = 84.940° from ODE integration
• t_res, ω₀, ε_K (08a)

Zone 2 — Middle layer [K] and [C]

• Threshold outputs: m_s, a*, T = 3.32 yr, ζ/Λ
• σ₃ = 0 structural zero (all bases confirmed)
• θ₁₃ = 8.55° (canonical FS, α=2)
• Cabibbo θ₁₂(CKM) = 14.1°
• Winding/KK loop mechanism (08c)
• MEG-II generation constraint (08d)
• Flyby anomaly, pulsar timing (validations)

Zone 3 — Soft edge [A] and [P]

• Exact Z→μτ normalization (O(1) coefficient C)
• Full PMNS matrix (θ₁₂ solar, θ₂₃)
• Full CKM matrix (θ₂₃, θ₁₃)
• Physical lepton mass hierarchy (σ₁/σ₂ = 5.72 at string scale, Step 25)
• δ_CP phase identification convention
• Full propagator-level closure (Topological Closure)
• Consciousness / biology extrapolations
• HYM fibre metric: computed (Step 25) σ₁/σ₂ = 5.72 ± 0.01 (Donaldson T-operator + MCMC, converged)
• RG running: computed (Step 26) σ₁/σ₂(M_EW) = 5.7–6.7 (tan β = 2–50), max shift 17% Gap to 16.82 requires full EWSB + mass matrix derivation (subsequent work)

Key Dependency Edges

The Single Leverage Point (Updated — Steps 25–26)

The HYM fibre metric has been computed:

3×3 vector Donaldson T-operator with MCMC uniform sampling on X σ₁/σ₂ = 5.72 ± 0.01 at the string compactification scale (converged)

One-loop MSSM RG running has been performed:

RG running M_s → M_EW (Step 26) σ₁/σ₂(M_EW) = 5.7–6.7 (tan β = 2–50) — max shift 17%

The remaining gap to physical values requires:

Full EWSB + mass matrix derivation Higgs vevs, seesaw mechanism, PMNS rotation, threshold corrections

Resolves simultaneously: - σ₁/σ₂ gap to m_τ/m_μ = 16.82 (lepton mass hierarchy) - θ₂₃, θ₁₂ solar (full PMNS matrix) - CKM θ₂₃, θ₁₃ (full CKM matrix) - MEG-II BR(μ→eγ) quantitative compliance - Coefficient C for exact BR(Z→μτ) - Q_wind, N_modes for KK spectrum

Last updated: 24 March 2026 — Steps 1–24 of derivations archive ORCID: 0009-0003-1690-3669