Solvency Field Theory (SFT): The V13 Framework

Overview

A particle is real energy moving at c, either open as light or closed into a self-maintaining orbit as mass, leaving permanent settlement history as it writes. Gravity is what that settlement looks like from the outside. Expansion is what the growing ledger looks like from the inside. Time is what the ticking looks like from within.

Solvency Field Theory (SFT) is a locally real foundation for particles, gravity, and cosmology. It derives the particle spectrum, the fermion mass hierarchy, the gravitational coupling, and the cosmological expansion rate from one postulate: energy at c writes irreversible settlement history on a holographic boundary, and no write can be undone.

The framework requires no dark matter, no dark energy, no new particles, no extra dimensions, and no free parameters for mode selection or mass hierarchy. It rests on four established axioms — Landauer's principle, Connes-Rovelli thermal time, the holographic bound, and geometric expansion as maintenance cost — unified through the Compton Maintenance Postulate: everything in the universe moves at c, and maintained particles tick at their Compton frequency, one write per cycle, one Planck area per write.

Core Results

Particle program (V13.0):

 - Locally real particle definition: A particle is real energy at c, closed into a self-maintaining orbit at radius r_spin = ℏ/(2mc), with 4π spinor closure and 2π frame/gauge completion per Compton period. Photons are the open branch of the same energy — no internal clock, no closure, no mass.

 - Closure-fit identity: The photon wavelength at a particle's rest energy exactly equals the fermion's full 4π spinor closure path: λ_γ(E = mc²) = 4π r_spin. Formation is wavelength-to-closure matching.

 - Nine stable modes from binary no-overwrite and 3+1 slot capacity, with primitive anchors {1, 1/2, 1/3} generating the full seed {1/2, 2/3, 3/4, 1, 5/4, 4/3, 3/2, 5/3, 2}.

 - Conditional mass hierarchy law: M_i = G_i × exp(L_eff × u_i) with L_eff = 3π − ½ln(25/13), derived from self-gravitational compounding with a 3:2 amplitude-channel tax (three spatial support coordinates versus two phase closure completions). Hits the base dynamic range D = 17,877 to 0.032% with zero free parameters.

 - Conditional top-sector closure: Under the minimal terminal completion theorem, the full hierarchy span is D × 6π ≈ 337,000, within 0.63% of the observed top/electron mass ratio. The 6π is 4π spinor curvature crossing plus 2π frame holonomy — the same numbers that enter L_eff additively enter the top-sector bridge multiplicatively.

Gravity program (V13.1):

 - Gravity as accumulated particle maintenance: Each particle's Compton tick simultaneously advances proper time (creating time) and adds operation density (creating gravity). Stellar gravity is the continuum limit of trillions of particles maintaining themselves.

 - Compactness equation: C_A(E, r) = A_write E/(ℏcr), where compactness equals boundary write-area coverage times source phase accumulated over one light-crossing radius. One equation from photons to black holes, with no G.

 - Newton's G reframed: G = A_write c³/ℏ, where A_write is the primitive boundary settlement-area quantum. G is not a fundamental coupling constant — it is the macroscopic SI expression of boundary write area. The dimensionless coupling γ = 8π² = 4π × 2π is derived from universal spatial solid angle times temporal phase completion.

 - Black holes from maximum compactness: Setting C_A = 1 and solving for r recovers the Schwarzschild radius in three lines. The event horizon is the surface where settlement is saturated. Adding one particle expands the horizon by exactly the amount required to maintain maximum compactness.

Cosmological program (V11–V12):

 - Master equation: H = Ṡ/I — the expansion rate equals the total write rate divided by the total information, derived as a thermodynamic identity from the four axioms.

 - Modified Friedmann equation: H² = 2Gρ/(3π), differing from the standard result by the factor 2/(3π) from correct boundary counting. No dark energy required.

 - DESI DR2 match: The dark energy equation of state is natively generated as a forced structural transition at pipeline-level reconstruction agreement.

 - SPARC galaxies: The derived acceleration scale a_SFT = cH₀/(2π) = 1.04 × 10⁻¹⁰ m/s², confirmed against 175 SPARC galaxies. The morphology-dependent interpolating function uses κ = 3/4 derived from the same no-overwrite constraint that selects the nine particle modes.

 - Covariant action: Five-term covariant Lagrangian with exact Schwarzschild exterior recovery and modified TOV interior.

The one-sentence version

One kind of stuff (energy at c), one rule (no overwrite), one consequence at three scales: time at the particle scale, gravity at the regional scale, expansion at the cosmic scale.

1.  THE V13 and 13.X RELEASE (June 2026) - SFT's Unfication Program. All Sectors of SFT will be unified in V13.X documents

[NEW] SFT_13_7_Master_Action_II.pdf - SFT's updated master Lagrangian derived from SFT's locally real particle program

[NEW] SFT_13_7_Master_Action_II_Derivation.zip - Scripts, results, and derivation papers for 13.7

[NEW] SFT_SPARC_v2_arXiv.pdf - Updated SPARC rotation prediction that beats the best fit model.

[NEW] SFT_SPARC_v2-1.pdf - Derivation document for SPARC prediction

[NEW] SPARC V13 Scripts Results.zip

SFT_V13_6_Quantum_to_Chemistry_Full_Writeup.pdf - SFT bridges gap from quantum to chemistry gaining compatability with Current-write uncertainty, D_eff = c r_spin = hbar/(2m), Pauli exclusion kernel, Tunneling from evanescent settlement intensity, Electron shell capacity skeleton, Qualitative Aufbau settlement ordering, First H2 covalent bond kernel

SFT_V13_6_Narrative.pdf - narrative companion to 13.6

SFT_V13_6_REPRO_SCRIPTS_ONLY.zip

SFT_13_5_Entanglement.pdf - SFT shows pair production is the root of entanglement and particles advance the frame while maintaining correlation

SFT_V13_5_Entanglement_Narrative.pdf - the narrative companion to 13.5

SFT_13_5_REPRO_SCRIPTS_ONLY.zip

SFT_V13_4_Forces_Full_Derivation.pdf - SFT's Forces program showing SFT's particle program recovers the Forces from internal motion

SFT_V13_4_Forces_Narrative.pdf - The narrative companion to 13.5

SFT_V13_4_REPRO_SCRIPTS_ONLY.zip

SFT_V13_3_First_Locally_Real_Atom.pdf - SFT's particle program proves that the Atom is a natural consequence of a locally real particle universe 

SFT_V13_3_Locally_Real_Atom_Narrative.pdf - The Narrative version of 13.3 

SFT_V13_3_R251_R257_Results_and_Scripts_QuickPack-1.zip - Results and Repro scripts for 13.3

SFT_V13_2_Expansion_Time_production.pdf - SFT ties Time and Global expansion to locally real particles and one mechanism

SFT_V13_2_Expansion_Time_Narrative.pdf - SFT's time and expansion with narrative tieing time production and expansion to locally real particles 

SFT_Particle_Reality_Inventory.pdf - SFT inventories the standard models particles into persistent, unstable, and hypothetical mathmatical particles used to make the SM work. SFT does this for the purpose of advancing the locally real particle program in 12.12 and 12.13.

SFT 13.0 12.12-12.13 rename.zip - V12.12 and 12.13 are being elevated to V13.0 as they represent the particle program bedrock for V13. You can download them seperately or they have been bundled together in one zip with repros. The Zip includes:

 - SFT_V12_13_Trace_Variational_D_Scale_Conditional_Top_Sector_6pi_Closure.PDF - Furthers SFT's Locally real particle program and sets Hiearchy law  L_eff = 3π − ½ln(25/13)

 - SFT_V12_13_Narrative.PDF - Narrative version of 12.13 that provides a vivid picture

 - SFT_12_3_Repro_pack - Scripts and results

 - SFT_V12_12A_Photon_Closure_Fit_Addendum.pdf - addendum to 12.12 where the electron's full 4π spinor closure path length equals the Compton wavelength, is derived

 - SFT_V12_12_Particle.pdf - SFT's Particle definition  narrative

 - SFT_V12_12_Particle_Program_Main.pdf - SFT's particle program derivation

 - SFT 12.12_repro_pack.zip

SFT_V13_1_Gravity_Narrative_v2.pdf - Everything SFT has to say about Gravity unified and advanced on one document. SFT has a successful Scalar Gravity program that recovers:

 - Gravity as accumulated particle maintenance: Each particle's Compton tick simultaneously advances proper time (creating time) and adds operation density (creating gravity). Stellar gravity is the continuum limit of trillions of particles maintaining themselves.

 - Compactness equation: C_A(E, r) = A_write E/(ℏcr), where compactness equals boundary write-area coverage times source phase accumulated over one light-crossing radius. One equation from photons to black holes, with no G.

 - Newton's G reframed: G = A_write c³/ℏ, where A_write is the primitive boundary settlement-area quantum. G is not a fundamental coupling constant — it is the macroscopic SI expression of boundary write area. The dimensionless coupling γ = 8π² = 4π × 2π is derived from universal spatial solid angle times temporal phase completion.

 - Black holes from maximum compactness: Setting C_A = 1 and solving for r recovers the Schwarzschild radius in three lines. The event horizon is the surface where settlement is saturated. Adding one particle expands the horizon by exactly the amount required to maintain maximum compactness.

SFT_V13_1_Gravity_Unification.pdf - Derivation document for SFT V13.1

SFT 13.1 Gravity Repro pack.zip - Reproduction scripts unifying and elevating SFT's Scalar gravity program current

3. 📚 THE ORIGINAL SYNTHESIS DOCUMENTS

The philosophical and structural bedrock of the SFT paradigm.

Structural_Synthesis_of_Modern_Physics.pdf The foundational entry point. Synthesizes modern physics into an information-theoretic framework, laying the conceptual groundwork for geometric expansion as a thermodynamic maintenance cost.

Appendix_A_and_B.pdf

Supporting foundational theorems establishing the mechanical parameters of the SFT ledger.

4. 📂 HISTORICAL ARCHIVES & REPRODUCIBILITY (ZIP Bundles)

The relevant machine shop history. Bundled in ZIP archives for mathematical provenance, tracking the evolution from V7 to V9, and including all computational repro-packs.

SFT V10.zip | V9_Archive.zip | V8_Archive.zip | V7_Archive.zip

Contains the immediate evolutionary proofs including V10, the original constrained minisuperspace action, the V8.4 SPARC galactic rotation curve derivations, the observer-side local environment closures, and early arXiv preprints (V7.1 Compton Maintenance, V7.3 Quantum Phase Origin).

Historical_and_Standalone_with_Repros.zip

The complete computational repository. Includes the V10.1_reproduction Python scripts for the CLASS Boltzmann patch, the V8.4_Weak_Field_Repo for SPARC galaxy verification, and the V6_Companion_and_Verify_Bundle for early bimodal expansion results.

*** Note: The core SFT framework (V10) was officially published on World Quantum Day (April 14, 2026), honoring the exact $h$ linear phase cycle that drives the universe's geometric expansion. The V11 Master Architecture incorporates multi-AI collaborative methodology in its mathematical audits and structural synthesis. SFT is an evolving framework. For any questions or comments, please visit: https://x.com/Shaun_Fosmark