Classification of all framework results as theorem, computed, constraint-fixed, or open
Legend - [T] — Theorem / exact
derivation - [C] — Computed (numerical or algebraic, result
is well-defined) - [K] — Constraint-fixed (follows from
stated inputs, not independently derived) - [A] —
Approximation / leading-order identification - [O] — Open /
not yet resolved
Two corrections applied (marked ✎): generation assignment [T/K]→[T]; δ_CP [A]→[C+note]. Maintained by Z. Paz — update when derivation status of any node changes.
STF FRAMEWORK
│
├─ A. BACKBONE
│ │
│ ├─ Framework Guide V3.1
│ │ └─ role: map / orientation / reading order
│ │
│ ├─ First Principles V7.7
│ │ ├─ ghost-freedom on relevant backgrounds .............. [T]
│ │ ├─ full operator uniqueness ........................... [O]
│ │ ├─ threshold relation D_crit = m_s M_Pl H_0 / 4π² ..... [K]
│ │ ├─ m_s = 3.94×10⁻²³ eV ............................... [K]
│ │ ├─ a* = 730 R_S ....................................... [K]
│ │ ├─ T = 3.32 yr ........................................ [K]
│ │ ├─ K = 2ωR/c .......................................... [T]
│ │ ├─ ζ/Λ ≈ 1.3×10¹¹ m² ................................. [K]
│ │ ├─ c_GB ~ O(1) ........................................ [O]
│ │ ├─ Ohmic IR sector required ........................... [T]
│ │ ├─ generation assignment closed ....................... [T] ✎ (was [T/K])
│ │ │ Proof: monad long exact sequence, H*(A,B)=0
│ │ │ → isomorphism δ: H⁰(A,C) → H¹(A,V)
│ │ │ → A₁,A₂,A₃ are equivariant sections by pure
│ │ │ algebraic geometry, no external bundle data.
│ │ │ 99.7% Gram alignment is confirmation, not input.
│ │ ├─ θ₁₃ = 8.55° ± 2° (canonical FS, α=2) ............. [C]
│ │ │ Note: FS at α=2 is canonical ambient metric.
│ │ │ Donaldson (θ₁₃=23.9°) is sensitivity check;
│ │ │ converges to Bergman kernel, not HYM fibre metric.
│ │ ├─ Cabibbo θ₁₂(CKM) = 14.1° .......................... [C]
│ │ │ Same FS Y^(0), Y_d=(Y_u)*. No metric correction.
│ │ │ Mechanism: sin(θ) ≈ |Im(Y)|/‖Y‖ from φ_CP=84.94°.
│ │ │ Symmetric with θ₁₃ across both sectors.
│ │ └─ larger CKM / PMNS angles, mass hierarchy .......... [P]
│ │ Steps 25–27 complete: σ₁/σ₂ = 5.72 (HYM) → 5.7–6.7 (RG)
│ │ Full EWSB (tan β=15.7): m_τ reproduced; m_τ/m_μ = 6.0 ≠ 16.82
│ │ Gap structural — mechanism for Yukawa hierarchy required
│ │
│ ├─ Topological Closure V6.1
│ │ ├─ ∫_{T²} ω_R∧ω_A = 4π² ............................. [T]
│ │ ├─ Pole Location Lemma ............................... [T]
│ │ └─ full propagator-level closure ..................... [O]
│ │
│ └─ Complexified Null Cone V0.9
│ ├─ advanced/retarded geometric seat .................. [A→C]
│ ├─ EXISTS/HAPPENS geometric grounding ................ [A]
│ └─ amplitude/workspace exponent from geometry ........ [O]
│
├─ B. PHYSICAL CONSEQUENCES
│ │
│ ├─ STF Cosmology V5.7
│ │ ├─ unified inflation / DE / MOND-style sector ........ [K/A]
│ │ └─ full sector closure ............................... [O]
│ │
│ ├─ Standard Model Unification V3.6
│ │ ├─ parameter-chain derivations ....................... [K]
│ │ └─ full precision closure across SM .................. [O]
│ │
│ └─ The Energy Problem V0.5
│ ├─ synthesis of Λ / DM / arrow-of-time .............. [A]
│ └─ exact closure of all constants .................... [O]
│
├─ C. LEPTON & QUARK FLAVOUR
│ │
│ ├─ 08a BR(Z→μτ) from CICY #7447/Z₁₀ [V3.0]
│ │ ├─ exact 4th-order Picard-Fuchs operator ............. [T]
│ │ ├─ LCS Frobenius series fails at ψ_res=0.420 ......... [T]
│ │ │ Radius of convergence 1/25; ψ_res/R = 10.5.
│ │ ├─ t_res, ω₀(ψ_res), arg ω₀, G_tt̄, ε_K .............. [C]
│ │ │ Im(t_res)=0.20913 ±10⁻¹², φ_CP=84.940°
│ │ ├─ physical Yukawa magnitude |Y_phys|=0.0348 ......... [C]
│ │ └─ BR(Z→μτ) in 08a alone ............................. [A]
│ │ NDA estimate; loop operator was open at this stage.
│ │
│ ├─ 08b Lepton Mixing and CP Violation [V0.3]
│ │ ├─ C_Jarlskog = 0 for all 42 viable Z₁₀ textures ..... [T]
│ │ │ Exhaustive enumeration; |J| < 10⁻¹² numerical.
│ │ ├─ U_PMNS^tree = I ................................... [T]
│ │ │ Corollary of tree-level texture theorem.
│ │ ├─ rank-2 Yukawa / one structural zero (σ₃=0) ........ [C]
│ │ │ Confirmed across 5 patches and all bases.
│ │ ├─ δ_CP = 84.940°, |sin δ_CP| = 0.9961 .............. [C] ✎ (was [A])
│ │ │ Computed from arg(ω₀(ψ_res)) — exact ODE
│ │ │ integration, 12-digit precision. Topological
│ │ │ invariant of the path. [A] applies only to the
│ │ │ final step: identifying this with the physical
│ │ │ PMNS Dirac phase (convention-dependent).
│ │ ├─ θ₁₃ = 8.55° flavor-structure context .............. [C]
│ │ └─ θ₁₂ solar / full neutrino masses / mode lifting ... [O]
│ │
│ ├─ 08c The Z→μτ Operator [V0.1]
│ │ ├─ winding/KK loop mechanism ......................... [T/K]
│ │ │ Closes the operator gap left open in 08a.
│ │ ├─ tree-level exclusion by winding conservation ...... [T]
│ │ └─ exact O(1) coefficient C .......................... [O]
│ │ Requires: KK spectrum from YM/HYM computation.
│ │ Same boundary as mass hierarchy / PMNS angles.
│ │
│ ├─ 08d Radiative LFV: MEG-II [V0.1]
│ │ ├─ minimal assignment → BR(μ→eγ) ≈ 5.7×10⁻⁸ ......... [C]
│ │ │ Exceeds MEG-II bound by factor ~2×10⁵.
│ │ ├─ MEG-II forces electron = null eigenvector ......... [K]
│ │ │ Turns experimental bound into structural
│ │ │ constraint on generation assignment.
│ │ └─ null eigenvector = electron confirmed ............. [T]
│ │ 99.7% Gram alignment. Connecting homomorphism
│ │ proof (see First Principles node above).
│ │
│ └─ 08e Experimental Programme [V0.1]
│ ├─ falsification map / tier classification ........... [C]
│ └─ new independent derivations ....................... none
│ (synthesis paper — packages 08a–08d results)
│
├─ D. TEMPORAL & ONTOLOGICAL CONSEQUENCES
│ │
│ ├─ Theory of Time V4.3
│ │ ├─ time as threshold-dependent ....................... [K/A]
│ │ └─ broader ontological claims ........................ [A]
│ │
│ ├─ Pretemporal Stasis / Cascade V1.0
│ │ ├─ instability of pre-temporal stasis ................ [T]
│ │ ├─ STF identification of the generic threshold field .. [K]
│ │ └─ inflation / structure completion .................. [O]
│ │
│ ├─ The Structure of What Happens V2
│ │ └─ ontological synthesis ............................. [A]
│ │
│ ├─ Consciousness, Time & Identity V3.6
│ │ └─ inside-of-loop = temporal experience claim ........ [A]
│ │
│ ├─ Temporal Workspace V0.5
│ │ ├─ workspace law from threshold + Peters scaling ...... [K/C]
│ │ └─ biological / phenomenological mapping ............. [A]
│ │
│ └─ Retrocausality & Life V0.5
│ └─ biological threshold extension .................... [A/O]
│
└─ E. PREDICTIONS & VALIDATIONS
│
├─ Spacecraft Flyby Anomaly Resolved ..................... [C]
├─ The Phantom Problem .................................. [T/C]
├─ STF Modulation of Pulsar Glitch Timing ............... [C]
├─ Uranus-Neptune Heat Paradox Resolved ................. [C]
└─ remaining anomaly papers ............................. [C/A]| From | To | What it provides |
|---|---|---|
| First Principles V7.7 | Topological Closure | Field/threshold backbone |
| First Principles V7.7 | 08a | Compactification choice, STF parameters |
| 08a | 08b | Period/Kähler data for Yukawa structure |
| 08a | 08c | Yukawa magnitude; names operator gap |
| 08b + 08c | 08d | Yukawa structure + operator → MEG-II discriminator |
| 08a–08d | 08e | All flavor results → falsification map |
| HYM metric (Step 25) | 08c, 08b, 08d, FP | σ₁/σ₂ = 5.72 computed; RG running → PMNS angles, mass hierarchy |
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%
m_τ/m_μ = 6.0 vs PDG 16.82 — muon mass 2.8× too heavy
The gap is structural. It is not resolved by: - HYM metric (G ≈ I) - RG running (max +17%) - EWSB / tan β - Seesaw mechanism (neutrino sector only) - PMNS rotation (unitary, preserves eigenvalues)
Open problem: A mechanism generating additional Yukawa hierarchy is required to reproduce the physical m_τ/m_μ = 16.82.
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