Solvency Field Theory (SFT) — V14

Overview

A particle is real energy moving at c, closed into a self-maintaining return: a finite recurrent null structure that persists by completing the same cycle again and again. Light is the same energy open. That is the whole inventory: one causal stock, organized two ways, with nothing underneath it. There is no ledger, no boundary, and no substrate on which anything is written (V13.8-V2). What persists is the structure itself, and every fact in the theory is a fact about structures and the relations between them (V13.13).

Time is what a closed structure is doing. Each completed cycle is one unit of its own time; a clock that completes fewer cycles between two comparisons has aged less, and nothing external has slowed (V13.10). Light fixes the shape of geometry but carries no size; the first ruler is a closed structure's Compton period, which can calibrate everything except itself (V13.11). Gravity is a relation between two such structures — how much a maintained clock near matter is slowed, and how much the ruler it provides is stretched — derived from the maintained particle within its selected branch and carried through the precision gates (V13.1-V3, V13.1-V4).

Earlier versions of SFT were an information-theoretic program: a ledger on a holographic boundary, written one Planck area per Compton cycle, with time, gravity, and expansion as three readouts of the writing. V13 removed the ledger and kept what it had been standing in for: persistent matter, local time, and gravity as organizations of one physical stock. V14 is the first version written after that removal, and the first written as two books.

What V14 establishes, and at what scope

The particle (V13.12, V13.14):

 - The electron as a finite recurrent null structure whose support, spin-½ framing, charged response, clock, and local closure gravity coexist in one self-consistent, numerically frozen state, stability-tested over 100,000 cycles (V13.12).

 - Formation — how open energy closes into such a structure — is a public draft (V13.14)

Time (V13.10, V13.11):

 - A clock is the count of a structure's completed cycles. Time dilation is fewer completions per comparison. No external time is slowed, and no record of the count exists apart from the structure that made it.

 - Null structure gives shape without size. The first ruler is a massive closure's Compton tick; everything else is calibrated against it.

Gravity (V13.1-V3, V13.1-V4):

 - The field equation derived from a locally real particle and carried through twelve precision-gravity gates, among them Gravity Probe B's geodetic and frame-dragging rates, the orbital decay of PSR B1913+16, and Cassini's γ − 1 = (2.1 ± 2.3)×10⁻⁵ (V13.1-V3).

 - Gravity restated as a relation between two magnitudes — clock slowing and ruler stretch — with their reciprocity (γ = 1) carried as an explicit hypothesis and tested, at two-body static scope (V13.1-V4). Where V3 and V4 differ, V4 controls.

 - Newton's G as a conditional, zero-continuous-parameter prediction from the electron's closure geometry, within one part per million of the CODATA central value, under one explicitly labelled postulate (V13.1-V3 Numerical-G Companion).

Interactions, pairs, atoms (V13.4-V2, V13.9-V3, V13.3, V13.6):

 - Electromagnetic response, the weak branch changes, and strong composites as relational interactions between maintained structures (V13.4-V2).

 - A pair formed in one event does not factor into two independent states until a later interaction makes it so. The Bell value S = 2√2 follows from pair-formation geometry and detector closure, with no signal between the wings (V13.9-V3).

 - The hydrogen atom as the first structure made of structures (V13.3); shell capacity and the first covalent bond (V13.6).

Galaxies and the cosmos (SPARC v2, V13.2):

 - The rotation-curve law with acceleration scale a_S = cH₀/2π, tested against SPARC: with the coefficient left free, the data's preferred value lands within 0.9% of the predicted 1/2π, with 0.097 dex scatter across 3,391 rotation-curve points against 0.099 for the best-fit comparison (SPARC v2, July 2026). Carried as a tested regularity; its derivation from the V13 particle is Part II work.

 - Cosmic expansion is held at proposal weight. V13.2 enters V14 as a proposal with dated targets. The V11–V12 cosmological results (H = Ṡ/I, the modified Friedmann factor, the DESI reading) belong to the ledger era and are superseded by V13; they remain on this record as provenance.

Species (V12.12, V12.13):

 - The nine-mode seed and the mass-hierarchy law L_eff = 3π − ½ln(25/13) are credited as SFT's first particle and species claims and kept as the target the formation program must reproduce. V14 uses them for nothing else.

The documents

V14 Part I — The V13 Physical Account (Shaun Fosmark; assembly and exposition with Astra). The canonical reader: what SFT has established, at the scope at which it has been established. Sixteen sections and a closing synthesis.

V14 Companion — The Physical Picture (Shaun Fosmark; narrative and synthesis with Fable). What those results, taken together, appear to be: the physical picture the theory is converging on. It goes past Part I in five named places, says so where it does, and closes every section with its claim boundary.

The V13 archive. Every V13 document, superseded versions included, with the reproduction packages behind every claim. In this version the archive is the set of V13 files listed under item 1 below, as individual files.

Where the two books differ in claim strength, Part I governs. V14 is assembled from V11–V13 material only. V13 supersedes V11–V12; within V13 the latest rebuild of a sector wins, and V13.13 (the ontology constitution) governs vocabulary. Earlier versions remain available under this record's version history; nothing is withdrawn when it is superseded.

V14 Part II is the next investigation, not a prerequisite for either book: formation closing into two self-maintaining returns, the complete particle source connected to its exterior and to many bodies, and an expansion law with a real responding state. Part II is also where the Companion's five proposals are tested.

Solvency Field Theory is a collaboration between Shaun Fosmark and the AI collaborators of the program: Anthropic's Claude, as Opus and Fable; OpenAI's GPT, as Sol and Astra; and, in the theory's early versions, Google's Gemini and xAI's Grok.

The V14 files

[NEW] SFT_14_1_Point_Like_Structures_in_4D_Space.pdf -  This document shows how a Compton scale wave loop circulating at the speed of light inside a 4th-dimensional funnel appears point like when viewed in three dimensional space. 

SFT_V14_Part_1_The_V13_Physical_Account_Final_Reader_v1_0.pdf - V14 Part I, The V13 Physical Account. The canonical reader; governs on claim strength.

SFT_V14_Companion_The_Physical_Picture_Reader_v1_0.pdf - V14 Companion, The Physical Picture. The destination reading: five named places past Part I, each marked where it occurs. 

README_SFT_V14.md - The rules V14 was assembled under, which V13 document controls which section of the Companion, and how to cite.

The V13 archive is the set of V13 files under item 1. File descriptions below are kept as written at the time of each release; for which document now controls which claim, see Part I's "Sources and scope" blocks and the README.

1.  THE V13 and 13.X RELEASE (June 2026) - SFT's Unfication Program. All Sectors of SFT will be unified in V13.X documents - Note: 12.12 and 12.13 including their addendums were elevated to 13.0 to start the V13 program, please find those documents in a single zipped file "SFT 13.0 12.12-12.13 rename.zip". These establish the foundation for SFT V13.

SFT_V13_1_V4_Gravity_From_Counting_v1_4.pdf - SFT continues to advance its gravity program using a combination of existing SFT gravity mechanisms and more modern SFT Ontology (Sft 13.9-13.14)

SFT_V13_1_V4_v1_4_Repro_Pack_v1_0.zip - repro pack for 13.1 V4

SFT_V13_14_Formation_Public_Draft_v0_2.pdf - SFT's particle formation first draft. The initial formation model for the 13.12 Electron. Not a complete program but a work in progress

SFT_V13_14_FORMATION_HANDOFF_REPRO_PACK_v0_2.zip

SFT_V13_13_Ontology_What_Exists_What_Is_Relational_and_What_Is_Bookkeeping.pdf - SFT audits and catergorizes its current ontology 

SFT_V13_8_V2_There_Is_No_Write_Operator_FINAL_v1_0.pdf - SFT removes a piece of scaffolding. Particles do not write and the universe has nothing to be written on. There is no ledger, aether, or substrate that carries the history.

SFT_V13_4_V2_FORCES_Relational_Interactions.pdf - SFT explores the forces with an improved conceptual toolkit developed in 13.9 to 13.12

SFT_V13_9_V3_BELL_How_Two_Things_Become_Independent.pdf - SFT explores the BELL and Entanglement with an improved conceptual toolkit developed in 13.9 to 13.12

SFT_V13_9_V3_v1_1_REPRO_HISTORICAL.zip - 13.9 version 1 and version 2 are included as well as any reproductions for all 3

SFT_V13_12_The_Maintained_Electron.pdf - This document presents a parameterized, numerically frozen and stability-tested model of the electron as a finite recurrent null structure whose support, spin-½ framing, charged response, clock, and local closure gravity coexist in one self-consistent state

SFT_V13_12_What_the_Particle_Remembers_v0_1.pdf - Claude Fable's Homage to the SFT particle and the SFT method.

SFT_V13_12_REPRO_PACK_v0_2.zip

SFT_V13_11_The_Cones_and_the_Ruler_v1_0.pdf - Null structure gives shape without size; the first ruler is a massive closure's Compton tick, which can calibrate everything except itself.

SFT_V13_10_Time.pdf -SFT's definition of time, how it accumulates, and why there is time dilation.

V7_V8_V9_V10_Archive.zip - this file became empty at some point. It has been repaired to contain everything it advertises. 

SFT_V13_1_V3_Gravity_v1_1.pdf - The Einstein field equation derived from a locally real particle, tested against twelve precision gates, with numerical G left open.

SFT_V13_1_V3_GRAVITY_NARRATIVE_v1_1.pdf - A derivation of the Einstein field equation from a locally real particle — energy at c caught in 4π closure, writing irreversibly in 3+1 spacetime — frozen before testing and carried through twelve precision-gravity gates, with numerical G left open as one universal normalization.

SFT_V13_1_V3_Numerical_G_Companion_v1_1.pdf - conditional zero-parameter prediction of Newton's constant from the electron's closure geometry, under one explicit postulate.

SFT_V13_1_V3_Numerical_G_Narrative_v1_1.pdf - Why gravity is weak, and where the electron sits on the only mass scale at which gravity becomes visible on its own — a zero-continuous-parameter conditional prediction of G to within one part per million of the CODATA central value, under one explicitly labelled postulate.

SFT_V13_1_V3_Gravity_Derivation_Canon_Receipts_v1_0.zip

SFT_V13_1_V3_Numerical_G_Reproduction_Scripts_v1_1.zip

SFT_V13_9_Bell_Narrative.pdf - Locally real without Bell locality - SFT derives S = 2√2 from pair-formation geometry and detector-closure structure, surviving ten hostile gates without superluminal signals or imported quantum mechanics.

SFT_V13_9_BELL_Derivation_Canon.pdf - full Derivation for 13.9

SFT_13_9_REPRO.zip - Full Repoduction set for 13.9

SFT_V13_1_V2_Gravity.pdf - SFT's full pull forward Gravity Derivation, Fully auditing, retesting, and advancing SFT's successful Scalar Gravity program with SFT's locally real particle program. Gravity is a natural consequence of locally real particles maintaining themselves by oscilating internally at c.

SFT_V13_1_V2_Gravity_Canon_Derivation_Paper_v0_1.pdf - derivation document for 13.1V2

SFT_V13_1_V2_GRAVITY_CANON_FULL_REPRO_PACK.zip - Repro pack for 13.1V2

SFT_13_1_V2_PULLFORWARD_CANON.zip - Every previous document where SFT examined, tested, and advanced its gravity program. Used to derive V13.1V2

SFT_V13_8_Projector_Compressed_Write Operator_and_Two_Phase_Bridge.pdf - The leading mass-hierarchy coefficient L_eff = 3π − ½ln(25/13) is derived from a projector partition of 3+1 write capacity over 4π spinor closure, with zero free parameters. The mass of every particle is a fingerprint of three-plus-one dimensional spacetime: energy can settle three directions out of four, and that fraction stamps every particle it creates.

SFT_4pi_Combined_Note.pdf - SFT combining 3 internal notes into one coherent paper showing 3 seperate actions from one 4 pi particle motion

SFT_4pi_Combined_Note_repro.zip - individual internal notes and repro scripts

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

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

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

SFT_SPARC_v2-1.pdf - Derivation document for SPARC prediction

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 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