Classification of all framework results as theorem, computed, constraint-fixed, or open
Status note, 5 September 2026 — the scalar mass is an explicit, measurable input. Every calculation in this paper stands unchanged, evaluated at ms = 3.94 × 10⁻²³ eV. What has changed is that value’s standing. From the Theory Edition (First Principles V9.7.2) the framework carries ms as its one free scale: the theory states how each prediction depends on it, and specifies how it is to be measured — the knee at τc = ℏ/(msc²) in an activation-timing distribution, never a centroid (V9.7.2 §III.B). That is the same footing as the graviton mass in massive gravity or the coupling in scalar–tensor gravity — a scale the theory fixes the dependence on and hands to experiment. Study 21 established it by auditing every internal route for fixing the mass. Results below are accordingly conditional on the evaluation scale; where this paper calls the mass “derived”, read “evaluated at”, the figure being the historical association-implied value. Withdrawn is not deleted.
Version: 1.0
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 V3.4
│ │ └─ role: map / orientation / reading order
│ │
│ ├─ First Principles V7.9
│ │ ├─ 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 V6.3
│ │ ├─ ∫_{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 V4.0
│ │ └─ 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 V0.7
│ └─ biological threshold extension .................... [A/O]
│
└─ E. PREDICTIONS & VALIDATIONS
│
├─ Spacecraft Flyby Anomaly (mechanism WITHDRAWN 08/26;
│ survives as measurement theorem, not validation) ..... [O] ✎ (was [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 V7.9 | Topological Closure | Field/threshold backbone |
| First Principles V7.9 | 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