# Syncre Form Theory (SFT)

# Solar–Lunar Local Time & Convergence Pack

This bundle formalizes the idea:

- At any fixed global instant, the globe contains **every local time-of-day at once** (a positional phase field over longitude).
- The **solar local-time phase** and **lunar local-time phase** can be written as circle-valued observables.
- Their **difference is a global lunar-cycle phase** (independent of longitude).
- Daily + annual + lunar modulations naturally live on a **torus flow**; “convergence” is expressed as **convergence of time-averages / distributions** (unique ergodicity in the idealized model), plus a clean **stroboscopic map** sampled once per solar day.

## Files

- `SolarLunar_LocalTime_Convergence.md`  
  Main write-up (definitions, lemmas, convergence statements), including a new section on **Syncre at massive scale** (global phase field, slicing, and Earth as a pullback).

- `SolarLunar_LocalTime_Convergence.tex`  
  LaTeX version of the same write-up.

- `example_simulation.py`  
  Numerical demo: checks identities and illustrates equidistribution of the lunar phase under daily sampling in the idealized mean-motion model.

## Quick start (simulation)

```bash
python example_simulation.py
```

The script prints identity checks and writes images to `outputs/`.

- `Syncre_ProofProgram.md`  
  Proof-program framing: Syncre frames, witness theorems, and universe-scale witness constructions.

- `PASS_WORKFLOW.md`  
  Ten-pass workflow from Syncre foundations to universe-scale witnesses and nonlinear time.
- `passes/pass_A/PASS_A_DELIVERABLE.md`  
  Pass A deliverable: axioms, objects, invariants, and core coverage theorems.
- `passes/pass_B/ROBUSTNESS_LEMMAS.md`  
  Pass B deliverable: robustness and stability lemmas for coverage under perturbations.
- `passes/pass_C/PASS_C_DELIVERABLE.md`  
  Pass C deliverable: frame conditions, new invariants, obstruction taxonomy, canonical nonlinear class, and quantitative coverage.
- `SYNCRE_SYMBOL_DEFINITION.md`  
  Syncre symbol \(\mathscr{S}_{\!\mathrm{r}}\) and formal class definition.
- `passes/pass_D/LIFT_CALCULUS.md`  
  Pass D deliverable: lift atlas, cocycle obstruction, Syncre connection/holonomy, and nonlinear-time constraints.
- `SYNCRE_CANONICAL_EQUATION.md`  
  Canonical Syncre equation reference (SCL + SLL).
- `PASS_RESTRUCTURE_NOTES.md`  
  Notes on pass restructuring and dependency cleanup.
- `passes/pass_E/WITNESS_CATALOG.md`  
  Pass E deliverable: fully formalized universe-scale Syncre witnesses.
- `passes/pass_F/TORUS_COUPLING.md`  
  Pass F deliverable: multi-cycle torus upgrade and coupling laws (including synodic offset).
- `passes/pass_G/DIAGNOSTICS_AND_CONVERGENCE.md`  
  Pass G deliverable: diagnostics, pushforward measures, and convergence program with stroboscopic maps.
- `passes/pass_H/FIELD_DYNAMICS.md`  
  Pass H deliverable: Syncre transport dynamics and preservation theorems (degree/holonomy/coverage).
- `passes/pass_I/UNIFIED_THEOREM_CHAIN.md`  
  Pass I deliverable: unified theorem chain and sharpened positioning.
- `BREAKTHROUGH_PUSH.md`  
  Breakthrough-oriented targets: quantitative robustness, coupled diagnostics, and modulus preservation under dynamics.
- `passes/pass_J/PAPER_SKELETON.md`  
  Pass J deliverable: paper skeleton and submission-ready draft plan.
- `breakthrough/BREAKTHROUGH_PASS_1.md`  
  Breakthrough Pass 1: quantitative robustness and explicit degradation bounds under Syncre transport dynamics.
- `breakthrough/BREAKTHROUGH_PASS_2.md`  
  Breakthrough Pass 2: forcing-robust anti-collapse under dynamics and coupled-subtorus equidistribution under SOL.
- `breakthrough/BREAKTHROUGH_PASS_3.md`  
  Breakthrough Pass 3: bounded-distortion uniformity bounds and Fourier-mode diagnostics.
- `breakthrough/BREAKTHROUGH_PASS_4.md`  
  Breakthrough Pass 4: diffusive Syncre smoothing with exponential Fourier damping (true convergence to Haar).
- `breakthrough/BREAKTHROUGH_PASS_5.md`  
  Breakthrough Pass 5: unified advection–diffusion model and Syncre Stability Signature certificate.
- `breakthrough/BREAKTHROUGH_PASS_6.md`  
  Breakthrough Pass 6: coupled-cycle diffusion convergence on SOL coupled subtori + coupled stability signature.
- `FOUNDATIONS_RFP_PIP.md`  
  Foundations: RFP (Relational Form Principle) and Syncre as PIP (Principle-Identical Proxy), plus the method principle.
- `SFT_CORE_PRINCIPLES.md`  
  Stable core principles and notation for Syncre Form Theory.
- `breakthrough/BREAKTHROUGH_PASS_7.md`  
  Breakthrough Pass 7: rigorous anti-collapse certification via the Monotone Branch Condition (MBC).
- `UNIVERSALITY_WORKFLOW.md`  
  Ten-pass plan to perfect the universality-of-mechanism argument.
- `universality/UNIV_PASS_1_SCOPE.md`  
  Univ Pass 1: scope discipline, global vs embedded witnesses, and a copy-ready universality thesis.
- `universality/UNIV_PASS_2_META_WITNESS_S1.md`  
  Univ Pass 2: meta-witness theorem from an \(S^1\)-action (universality engine) + embedded-orbit variant.
- `universality/UNIV_PASS_3_EMBEDDED.md`  
  Univ Pass 3: embedded witness formalism (degree + holonomy) and witness-specific obstruction taxonomy.
- `universality/UNIV_PASS_4_ROBUSTNESS.md`  
  Univ Pass 4: robustness layer, perturbation models, and witness stability certificates (WSC).
- `universality/UNIV_PASS_5_COUPLED_UNIVERSALITY.md`  
  Univ Pass 5: coupled universality (CTP/CHT) + SOL coupled-coverage meta-theorem.
- `universality/UNIV_PASS_6_DYNAMICS_UNIVERSALITY.md`  
  Univ Pass 6: dynamics universality boundary (witness-preserving vs witness-breaking).
- `universality/UNIV_PASS_7_MIXING_UNIVERSALITY.md`  
  Univ Pass 7: mixing universality via diffusion/noise, with an explicit mixing certificate (MXC).
- `universality/UNIV_PASS_8_PHYSICS_NOTES.md`  
  Univ Pass 8: physics interpretability map (how to check hypotheses in real systems).
- `universality/UNIV_PASS_9_REFEREE_CHECKLIST.md`  
  Univ Pass 9: referee checklist mapping claims to theorems/hypotheses, plus explicit nonclaims.
- `universality/UNIV_PASS_10_PAPER_SECTION.md`  
  Univ Pass 10: copy-ready universality section for the paper.
- `engine/schemas/`  
  SFT engine schemas: WSC, WOB, and universality report contracts.
- `engine/contracts/engine_contract.md`  
  Engine contract: certificate-or-obstruction discipline for universality claims.
- `engine/audit/audit_wsc.py`  
  Audit script: validates WSC required fields and margin inequalities.
- `breakthrough/INTEGRATION_PASS_ENGINE.md`  
  Breakthrough integration pass: what was imported and why.
- `DIRECTIONAL_IMPROVEMENT_PASSES.md`  
  Next 10 directional improvement passes toward a referee-hard breakthrough package.
- `NAME_NOTE_ETYM.md`  
  Etymology note: how “Syncre” (συν-) and “Form” are used in Syncre Form Theory.
- `engine/artifacts/`  
  Example WSC/WOB JSON artifacts for the SFT engine discipline (DI Pass A).
- `engine/contracts/DI_PASS_A_NOTE.md`  
  DI Pass A note: shipped WSC/WOB artifacts and audit instructions.
- `engine/contracts/DI_PASS_B_ARENA_UNIVERSALITY.md`  
  DI Pass B: arena-level universality theorem + FEQ invariance.
- `engine/contracts/DI_PASS_C_ESW_LIBRARY.md`  
  DI Pass C: embedded witness library templates + certificate recipes.
- `engine/contracts/DI_PASS_D_COUPLED_ATLAS.md`  
  DI Pass D: coupled atlas beyond SOL (affine + integer-matrix couplings).
- `engine/contracts/DI_PASS_E_NDB_DERIVATION.md`  
  DI Pass E: scoped noise-to-diffusion derivation track.
- `engine/contracts/DI_PASS_F_RATES.md`  
  DI Pass F: quantitative rate ledger update (convergence bounds).
- `engine/contracts/DI_PASS_G_WOB_ENGINE.md`  
  DI Pass G: obstruction engine evidence checklists for every WOB code.
- `engine/contracts/DI_PASS_H_REFEREE_MAP.md`  
  DI Pass H: completed referee map with theorem/hypothesis/artifact pointers.
- `appendix/DI_PASS_I_WORKED_EXAMPLE.md`  
  DI Pass I: worked example pack (Earth + SOL coupling) with audit instructions.
- `engine/artifacts/UNIVERSALITY_REPORT_EXAMPLE.json`  
  Example universality report artifact (scoped claims + nonclaims + pointers).
- `engine/contracts/DI_PASS_J_SUBMISSION_POLISH.md`  
  DI Pass J: submission polish integration plan (universality + engine appendix).
- `score10/SCORE10_WORKFLOW.md`  
  Score-10 program: ten passes to push core scores to 10; Pass 01–03 completed in this ZIP.
- `score10/pass_01_paper_draft/sft_paper_draft.tex`  
  Pass 01: full LaTeX draft conversion with universality + engine appendices.
- `score10/pass_01_paper_draft/sft_bibliography.bib`  
  Bibliography for the LaTeX draft.
- `score10/pass_02_ndb_derivation/NDB_STRONG.md`  
  Pass 02: strengthened NDB derivation track (random increments ⇒ advection–diffusion).
- `score10/pass_03_contributions_novelty/CONTRIBUTIONS.md`  
  Pass 03: contributions and novelty section (standard vs new boundary).
- `score10/pass_03_contributions_novelty/contributions_table.tex`  
  LaTeX table summarizing standard vs SFT contributions.
- `score10/pass_04_flagship_theorem/FLAGSHIP_THEOREM.md`  
  Pass 04: flagship theorem chain (certificate ⇒ robust witness ⇒ quantitative diagnostic bound).
- `score10/pass_05_artifacts_appendix/ARTIFACTS_APPENDIX.tex`  
  Pass 05: paper-ready artifacts appendix fragment.
- `score10/pass_06_referee_map/REFEREE_MAP.tex`  
  Pass 06: paper-ready referee map table (claim→theorem→artifact).
- `score10/pass_07_coupled_atlas/COUPLED_ATLAS.md`  
  Pass 07: coupled atlas tightened (SOL + affine + matrix) with CST targets and baselines.
- `score10/pass_08_dynamics/DYNAMICS_BOUNDARY.md`  
  Pass 08: dynamics boundary sharpened and tied to certificate margins (DMG).
- `score10/pass_09_examples/EXAMPLES_APPENDIX.md`  
  Pass 09: three worked examples (global/embedded/coupled) with WSC/WOB pointers and audit commands.
- `score10/pass_10_polish/POLISH_CHECKLIST.md`  
  Pass 10: final polish checklist for score-10 consistency.
- `engine/artifacts/WSC-E-HW-0002.json`  
  Additional HW example WSC artifact.
- `engine/artifacts/WSC-C-AFFINE-0002.json`  
  Additional coupled affine example WSC artifact.
- `finish_ready/paper/sft_form_theory.tex`  
  Finish-ready self-contained LaTeX paper build (no external inputs).
- `finish_ready/scripts/compile_pdf.sh`  
  Compile script for the finish-ready LaTeX build.
- `finish_ready/scripts/validate_artifacts.sh`  
  Validation script for core WSC artifacts.
- `finish_ready/qa/ARTIFACT_VALIDATION_LOG.txt`  
  QA log: artifact validation output.
- `finish_ready/qa/COMPILE_ATTEMPT_LOG.txt`  
  QA log: LaTeX compile attempt output.
- `finish_ready/FINISH_READINESS_PASSES_1_3.md`  
  Notes: finish-readiness passes 1–3.
- `finish_ready/paper/EXAMPLES_APPENDIX.tex`  
  Finish-ready LaTeX appendix for worked examples.
- `finish_ready/HASH_MANIFEST.json`  
  SHA-256 manifest for all finish-ready files (SFT-0.1.0).
- `finish_ready/submission_bundle.zip`  
  Nested submission bundle zip of the finish-ready kit.
- `finish_ready/VERSION.txt`  
  Version tag for the finish-ready package.
- `finish_ready/FINISH_READINESS_PASSES_1_6.md`  
  Notes: finish-readiness passes 1–6.

## Global universality theorem package

A unified, theorem-first completion of the global universality workflow is provided in:

- `global_universality/GLOBAL_SYNCRE_UNIVERSALITY_THEOREM.md`
- `global_universality/GLOBAL_SYNCRE_UNIVERSALITY_THEOREM.tex`

These files contain:

- necessary-and-sufficient coverage conditions under equivariant circle actions
- a finite obstruction classification theorem
- robustness forcing with quantitative bounds
- torus and coupled-target forcing
- ergodic, dynamics-preservation, and diffusion universality upgrades
- a sharp boundary theorem and the capstone global universality statement
- `engine/contracts/WOB_CODEBOOK.md`  
  Canonical WOB codebook (resolves collisions; includes legacy mappings).
- `finish_ready/paper/GLOBAL_SYNCRE_UNIVERSALITY_THEOREM.tex`  
  Global universality theorem integrated into finish-ready LaTeX build.
- `finish_ready/paper/FRONT_MATTER.tex`  
  Front-matter purpose paragraph making RFP→PIP→Syncre inevitable.
- `finish_ready/paper/DIAGNOSTICS_TABLE.tex`  
  Canonical diagnostics table + baseline selection rule.
- `finish_ready/paper/OBSTRUCTION_TABLE.tex`  
  Obstruction→WOB code→evidence pointer table.
- `finish_ready/paper/CONVERGENCE_CERTIFICATES.tex`  
  Engine-native convergence certificate statement (RNF and NDB+MXC).
- `engine/audit/compute_fill_wsc.py`  
  Helper: compute degree from phase samples and emit a WSC JSON template.
- `finish_ready/paper/ESSAY_INTRO.tex`  
  English essay introduction used at the start of the publication PDF.
- `PUBLICATION_CLEAN_EDITION.md`  
  Summary of publication readability edits (no meta language).
- `finish_ready/paper/PROVES_BLOCK.tex`  
  Short bullet block near the start stating exactly what the paper proves.
