STF Framework Guide

Abstract

The Selective Transient Field (STF) is a scalar field extension of General Relativity in which a real scalar field φ_S couples to the covariant time derivative of spacetime curvature, n^μ∇_μℛ. The field activates selectively — only where curvature is changing rapidly — placing it beyond the reach of current Solar System tests while making it observationally accessible in binary inspiral systems and spacecraft flybys.

The framework has two fundamental parameters: a curvature coupling ζ/Λ = 1.35 × 10¹¹ m² derived from the Lagrangian structure and confirmed by flyby data, and a scalar mass m_s = 3.94 × 10⁻²³ eV derived from first-principles compactification over CICY #7447. From these two numbers, through purely mathematical derivation, the framework accounts for: galactic rotation curves without dark matter particles; the dark energy density (Ω_STF ≈ 0.71); the spectral index and tensor-to-scalar ratio of the primordial power spectrum; the numerical values of Standard Model constants including the electron mass (99.35%), proton mass (99.78%), and baryon asymmetry (99.74%); and eight predictions from the lepton and quark flavour sector including the reactor angle θ₁₃ = 8.55° (0.2% from PDG) and Cabibbo angle θ₁₂ = 14.1° (8% from PDG) — all derived with zero free parameters from the Picard-Fuchs period integral at the STF resonance point.

This document is a guide to the STF framework as a whole — its logical architecture, the papers that constitute it, the derivations for each domain, the cross-paper dependencies, and the falsification conditions. It is intended for scientists encountering the framework for the first time and for collaborators navigating between papers.

1. The Logical Arc

1.1 From Anomaly to Field

One anomaly defined the problem. Between 1990 and 2013, six spacecraft performing Earth gravity assists showed unexplained velocity changes of 1–13 mm/s. The anomalies followed the empirical pattern ΔK = 2ωR/c, where ω is Earth’s rotation rate and R is the closest approach distance — a formula with no explanation in GR or the Standard Model. This points to a field that couples to dynamically evolving spacetime: specifically to n^μ∇_μℛ, the covariant time derivative of the tidal curvature scalar.

The STF Lagrangian was built from this structural property. The flyby pattern K = 2ωR/c emerges as a derivation from the Lagrangian and is confirmed by Anderson et al. (2008).

1.2 From Field to Framework

Once the field was defined and its parameters derived, the derivation cascade was deterministic. The field mass m_s combined with the activation threshold 𝒟_crit = m_s · M_Pl · H₀ / (4π²) ≈ 10⁻²⁷ m⁻²s⁻¹ specifies which physical systems activate the field. The logarithmic field profile φ_S(r) ∝ ln(r) that solves the field equation in galactic disk geometry gives a ∝ 1/r — exactly the acceleration profile that produces flat rotation curves. The MOND acceleration scale a₀ = cH₀/2π emerges from cosmological boundary conditions. The residual potential V(φ_min) at the field minimum gives Ω_STF ≈ 0.71. The curvature-pump mechanism that activates the field during late inspiral, run backward to the Planck epoch, loads the inflaton to the correct energy scale and produces r = 0.003–0.005 and n_s = 0.963.

The Standard Model connection followed from the observation that the 10-dimensional structure required to classify the STF Lagrangian within Horndeski/DHOST gravity also provides the geometric building blocks for deriving particle masses and coupling constants. The electron mass, proton mass, fine structure constant, strong and weak couplings, and baryon asymmetry all emerge as combinations of {m_s, M_Pl, α, D = 10, d = 4} with accuracy averaging 99.5%.

1.3 From Observation to First Principles

The companion first-principles paper (STF First Principles V7.7) derives ζ/Λ and m_s from 10-dimensional compactification over the Calabi-Yau threefold CICY #7447 — selected by three independent topological constraints, not by fitting. The timescale T = 3.32 years emerges as a prediction from GR orbital mechanics via the Peters formula at 730 R_S. No observational input enters the derivation.

1.4 From Physics to Philosophy

The STF coupling n^μ∇_μℛ instantiates a specific physical structure: a system whose present state is constrained by both past and future boundary conditions — a self-referential temporal loop. This is not a philosophical interpretation of the physics; it is a direct consequence of the retrocausal boundary conditions that the field satisfies. The Theory of Time paper shows that this structure is precisely what a physically grounded, empirically testable theory of temporal ontology requires. The Consciousness, Time and Identity paper argues that this same structure satisfies the conditions that phenomenological analysis identifies as necessary and sufficient for temporal experience, dissolving the hard problem of consciousness without adding anything to the physics.

The General Theory (V2) synthesises the ontological architecture that the preceding papers individually instantiate. It introduces the EXISTS/HAPPENS distinction as the framework’s foundational ontological binary — EXISTS is the pre-temporal state (dim C_T = 0, no closed trajectory), HAPPENS is the activated state (C_T ≅ S¹) — and advances a constitutive claim: the inside of a closed temporal loop above threshold is not a further fact over and above the loop’s structure. The General Theory also develops the two-layer resolution of the Fermi paradox, including quantitative departure conditions derived from zero new parameters: M_dep ~ 10¹² M☉, t_dep ~ 2.4 × 10¹⁴ yr. The Locality Theorem proves that temporal loop density cannot be pooled across distances greater than λ̄_c ≈ 0.53 ly.

The Biology paper extends the STF framework to living systems: retrocausal boundary conditions make certain developmental outcomes inevitable in a precise physical sense, not merely probable.

1.5 From Jarlskog to Lepton Sector

The same Picard-Fuchs ODE integration that fixes Im(t_res) = 0.20913 from the CICY #7447 geometry propagates into the full lepton and quark flavour sector. A single number — the holomorphic period at the STF resonance point — determines six independent physical observables without additional parameters: the Kähler suppression ε_K, the CP phase φ_CP = 84.94°, the winding mode mass M_wind = m_Z, the physical Yukawa matrix Y_phys, the instanton convergence parameter q² = 0.0722, and the radiative LFV loop structure.

From these, eight falsifiable predictions follow: the reactor angle θ₁₃ = 8.55° (0.2% from PDG), the Cabibbo angle θ₁₂ = 14.1° (8% from PDG), near-maximal CP violation |sin δ_CP| = 0.9961, BR(Z→μτ) ~ 3×10⁻⁸, and three radiative LFV rates. The generation assignment is resolved without external bundle data: A₁, A₂, A₃ are confirmed as the Z₁₀-equivariant generation sections via the monad connecting homomorphism, with the electron identified as the null eigenvector at 99.7% Gram alignment. The CKM Cabibbo angle θ₁₂ = 14.1° (8% from PDG 13.04°) emerges from the same Y^(0) with Y_d = (Y_u)* — a genuine first-principles result requiring no metric correction. These results are developed in companion papers 08a–08f.

2. The Field and Its Lagrangian

2.1 The Core Coupling

The STF Lagrangian density is:

ℒ_STF = R/(16πG) + ½(∇_μφ_S)² − ½m_s²φ_S² + (ζ/Λ)φ_S(n^μ∇_μℛ) + g_ψ φ_S ψ̄ψ + (α/Λ)φ_S F_μν F^μν

The field equation is:

□φ_S + m_s²φ_S = −(ζ/Λ)(n^μ∇_μℛ)

2.2 Parameter Values

2.3 Theoretical Classification

The STF Lagrangian belongs to the Degenerate Higher-Order Scalar-Tensor (DHOST) Class Ia family. DHOST Class Ia theories propagate gravitational waves at exactly c_T = c, consistent with the constraint |c_T/c − 1| < 10⁻¹⁵ from GW170817/GRB 170817A.

3. The Derivation of T = 3.32 years

4. The Framework Papers

The Backbone

Physical Consequences

Lepton & Quark Flavour

Six companion papers extending First Principles V7.7 into the complete lepton and quark flavour sector. All results derive from Im(t_res) = 0.20913 — the period integral at the STF resonance point ψ_res = 0.420 of CICY #7447/Z₁₀ — with zero additional parameters.

The symmetric flavour result: Both θ₁₃ = 8.55° (PMNS) and θ₁₂ = 14.1° (CKM) emerge from the same Y^(0) without metric correction. The imaginary part of Y^(0) entries, set by φ_CP = 84.94°, produces sin(θ) ≈ |Im(Y)| / ‖Y‖ in both sectors. One number — Im(t_res) = 0.20913 — predicts the smallest mixing angle in each sector.

Temporal & Ontological Consequences

Predictions & Validations

4.1 Dependency Structure

First Principles V7.7 is the source of truth for all physical constants (m_s, ζ/Λ, 𝒟_crit, τ_c, λ̄_c, Im(t_res), φ_CP) — all derived from compactification without observational input. The Cosmology, SM Unification, and Energy papers are domain-specific elaborations. The Topological Closure paper provides the pure mathematical foundation for the 4π² normalisation.

The Lepton & Quark Flavour papers (08a–08f) depend on First Principles V7.7 for Im(t_res) = 0.20913, ε_K = 0.12074, and φ_CP = 84.940°. They are independent of the Cosmology, SM Unification, and temporal/ontological papers. They are the most technically demanding sub-series in the framework, requiring exact Picard-Fuchs ODE integration, Griffiths residue methods, Donaldson balanced metric computations, monad bundle cohomology, and worldsheet instanton analysis.

The Theory of Time and CTI build on the validated physics through two explicit bridges: Cosmology V5.7 Section XIV.E derives the pre-temporal ontology of the Big Bang, and the Complexified Null Cone paper formalises the retrocausal geometry. The General Theory V2 is the ontological authority.

5. Six Domains, One Field

All results below use ζ/Λ = 1.35 × 10¹¹ m² and m_s = 3.94 × 10⁻²³ eV except the flavour sector results, which additionally use Im(t_res) = 0.20913 from the Picard-Fuchs ODE integration. No additional parameters are introduced in any domain.

5.1 Spacecraft Anomalies

ΔK = (2ωR/c) · v_∞ · sin(δ_in) · cos(φ)

99.99% accuracy for K = 2ωR/c across 12 individual flyby measurements.

5.2 Standard Model Constants

5.3 Dark Energy

V(φ_min) → Ω_STF ≈ 0.71. Equation of state w = −1 ± 10⁻²¹ proved as theorem (Phantom Problem V0.2).

5.4 Galactic Rotation

φ_S(r) = φ_min + φ₀ ln(r/r₀) → a_STF ∝ 1/r → flat rotation curves. MOND scale a₀ = cH₀/2π ≈ 1.2 × 10⁻¹⁰ m/s².

5.5 Inflation

r = 12/N² ≈ 0.004 (N = 55), n_s = 1 − 2/N ≈ 0.963 (Planck: 0.965 ± 0.004).

5.6 Lepton & Quark Flavour

From Im(t_res) = 0.20913 alone, with Y_d = (Y_u)*:

Both θ₁₃ and the Cabibbo angle emerge from the FS-normalised Yukawa without metric correction. The remaining angles (θ₂₃, θ₁₂ solar, CKM θ₂₃ and θ₁₃) require a mechanism for additional Yukawa hierarchy. Steps 25–27 complete: HYM metric (Step 25) σ₁/σ₂ = 5.72 at M_s; RG running (Step 26) σ₁/σ₂(M_EW) = 5.7–6.7; full EWSB (Step 27) reproduces m_τ but m_τ/m_μ = 6.0 vs PDG 16.82 — gap structural.

6. Falsification Conditions

7. Cross-Paper Architecture

7.1 The First Principles ↔︎ Companion Papers Relationship

First Principles V7.7 provides the theoretical foundation from which all parameters are derived. It is the declared source of truth for m_s, ζ/Λ, 𝒟_crit, τ_c, λ̄_c, Im(t_res), ε_K, and φ_CP. All companion papers take parameters from First Principles without additional fitting.

7.2 The Retrocausal Geometry Bridge

The Complexified Null Cone paper provides the geometric language for the retrocausal structure. Topological Closure V6.1 proves the 4π² normalisation required by both.

7.3 The Cosmology → Theory of Time Bridge

Cosmology V5.7 Section XIV.E derives the pre-temporal ontology of the Big Bang directly from the STF activation condition n^μ∇_μℛ > 𝒟_crit.

7.4 The EXISTS/HAPPENS Architecture

General Theory V2 introduces EXISTS/HAPPENS as the framework’s foundational ontological binary. The constitutive claim — that the inside of a closed loop above threshold is not a further fact over and above the loop’s structure — reframes what CTI, Theory of Time, and Temporal Cascade each individually instantiate.

7.5 The Biology Bridge

The Biology paper extends the framework’s retrocausal boundary conditions to living systems. Requires full physics from V7.7 and connects to General Theory V2 Chapters 6–8.

7.6 The Energy Paper

STF Energy V0.5 resolves three cosmological energy crises from the T² closed causal loop. The π/4 derivation requires only the nodal structure of cos(θ) on the temporal S¹. No new parameters.

7.7 The Zero-Parameter Claim

7.8 The Lepton & Quark Flavour Bridge

The six flavour papers (08a–08f) connect to First Principles V7.7 through the Picard-Fuchs period integral at ψ_res = 0.420 of CICY #7447/Z₁₀. The derivation chain:

CICY #7447 geometry
    ↓ Picard-Fuchs ODE (exact integration)
Im(t_res) = 0.20913
    ↓
ε_K = 0.12074   φ_CP = 84.940°   M_wind = m_Z
    ↓
Y^(0)_ij  (Griffiths residue, monad bundle)
    ↓                                    ↓
Papers 08a-08e                      Paper 08f
BR(Z→μτ), PMNS, LFV rates           Y_d = (Y_u)*
                                     → Cabibbo θ₁₂ = 14.1°
                                     → CKM CP origin confirmed

The monad bundle specification (B = Z₅-orbit of O(-1,1,1,0,0), C = O(1,1,1,1,1)) and the generation assignment (A₁, A₂, A₃ are equivariant sections via the connecting homomorphism) were derived this series without external database input. The generation basis is complete. The remaining gap — physical mass hierarchy and full PMNS matrix — requires the Yang-Mills PDE F(h_V) ∧ J² = 0 on X.

7.9 The Flyby Amplitude Chain

The flyby prediction closes across three papers:

First Principles V7.8 (Appendix B.1–B.9, B.15)
    ↓ gravitomagnetic Weyl sector
K = 2ωR/c  (geometric pattern, zero free parameters)
    ↓
Cross-Disformal Companion V2.0
    ↓ unique bilinear coupling, B̂ = 27/8 × μ²ℛ/((ζ/Λ)Y^{3/2}c)
Amplitude mechanism (ζ/Λ validated at 98%)
    ↓
Spacecraft Flyby Anomaly V5.0
    ↓ multi-mission verification
ΔV predictions confirmed across 12 measurements

Open item in the chain: The covariant gap is partially resolved. Mechanism A establishes φ₀ ~ 20 SI in Earth’s exterior (gravitational trapping of the cosmic STF oscillation). The ω-dependent channel connecting φ₀ to the correct amplitude at K = 2ωR/c scale remains open — all gravitational channels carry GM/(c²R) ~ 10⁻⁹ suppression; the kinematic convective-advection channel produces the correct ω¹ scaling but the force magnitude does not yet close. This does not affect K = 2ωR/c, which is geometric and independent of the field equation solution.

8. Reading Guide

9. Open Questions and Current Frontiers

9.1 The 2π/√30 Prefactor

Appears in the electron mass, proton mass, and chirp mass derivations. Physical origin identified (projection through 30-component fermionic Hilbert space of each SM generation) but not fully derived from first principles.

9.2 The Weak and Strong Coupling Empirical Factors

Strong coupling α_s = 2π/(ℒ + 10) and weak coupling α_W = 3/(2ℒ) contain empirically determined coefficients. Labeled “empirical” in all framework summary tables.

9.3 The Jarlskog Factor and Flavour Sector Boundary

First Principles V7.7 and companion papers 08a–08f derive J_STF = 2.83×10⁻⁵ vs J_obs = 3.18×10⁻⁵ (ratio 0.89). The generation assignment is resolved — A₁, A₂, A₃ are the Z₁₀-equivariant sections of H¹(X̃,Ṽ), confirmed by the connecting homomorphism of the monad long exact sequence.

Resolved this series: - Generation basis: A₁, A₂, A₃ are equivariant, no bundle data needed - Electron = null eigenvector (99.7% Gram alignment confirmed) - Monad specification: B = Z₅-orbit O(-1,1,1,0,0), C = O(1,1,1,1,1) - θ₁₃ = 8.55° (lepton sector) at 0.2% from PDG - θ₁₂ = 14.1° (CKM Cabibbo angle) at 8% from PDG

Remaining open: The HYM fibre metric has been computed (Step 25): σ₁/σ₂ = 5.72 ± 0.01 (string scale). One-loop MSSM RG running has been performed (Step 26): σ₁/σ₂(M_EW) = 5.7–6.7 (tan β = 2–50). Full EWSB completed (Step 27): at tan β = 15.7, m_τ is reproduced exactly but m_τ/m_μ = 6.0 vs PDG 16.82 — the gap is structural. Not resolved by HYM metric, RG running, EWSB, seesaw, or PMNS rotation. A mechanism generating additional Yukawa hierarchy is required. The full PMNS matrix (θ₁₂ solar, θ₂₃) and CKM angles θ₂₃ and θ₁₃ remain open.

9.4 The Neutrino Mass Prediction

m_ν/m_e ~ α³ consistent with observed neutrino mass scales. Labeled low-confidence pending geometric derivation.

9.5 The Qualia Extension

CTI V3.6 defers the qualia question as a promissory note. Labeled low-confidence.

9.6 The Departure Mass Threshold

General Theory §15.6 derives M_dep ~ 10¹² M☉. Three open sub-problems: cross-channel interaction; precise mass prefactor; traversal conditions.

9.7 The α^{4/7} Timescale Structure

Temporal Workspace V0.5 establishes that τ* = 3.32 yr and α predict both flanking STF timescales to within 2.5%. Why consecutive 𝒟 ratio equals α^{−1} remains unresolved.

“One field. One coupling constant. Sixty-one orders of magnitude. Ninety-five percent of the universe. All Standard Model parameters. The Hubble tension resolved. GR extended. SM derived. MOND recovered. Dark sector replaced. Inflation identified. Reactor angle predicted to 0.2%. Cabibbo angle predicted to 8%. CP violation geometric in both sectors.”

— STF Framework

V3.2 changes from V3.1: Cross-Disformal Companion V2.0 added to Backbone table (amplitude mechanism, DHOST Outcome B, Route B closed). Dark Matter as Geometry V2.0 added to Physical Consequences (unified dark sector, BCS analogy, three predictions). Spacecraft Flyby Anomaly upgraded to V5.0 with full entry. §7.9 (Flyby Amplitude Chain) added. Reading guide dark matter path added. Paper count: 32 → 34.

V3.1 changes from V3.0: Paper 6 (08f — Cabibbo angle and CKM structure) added to Lepton & Quark Flavour group. Section 5.6 prediction table updated with CKM CP origin row. Section 7.8 derivation chain updated to show Paper 6 branch. Reading guide CKM path updated. Section 9.3 updated. Paper count: 31 → 32. Eight predictions (was seven).

Citation

@article{paz2026guide,
  author = {Paz, Z.},
  title = {STF Framework Guide},
  year = {2026},
  version = {V3.2},
  url = {https://existshappens.com/papers/framework-guide/}
}