# Syncre Form Theory: 10-Pass Workflow

## Scope

This workflow advances from an Earth-scale Syncre witness to a universe-scale witness program, then to nonlinear phase-time deformation, diagnostics, and dynamics.

## Pass map

| Pass | Goal | Primary deliverables | Acceptance gates |
|---|---|---|---|
| Pass A | Foundations: objects, axioms, first theorems | `passes/pass_A/PASS_A_DELIVERABLE.md` | Syncre frame and coverage are defined; coverage templates are proved; Earth-longitude is a corollary; degree/winding is defined and used correctly |
| Pass B | Robustness: stability and quantitative coverage notions | `passes/pass_B/ROBUSTNESS_LEMMAS.md` | Loop-degree witness implies coverage; degree stability lemmas are proved; at least one quantitative diagnostic is defined with clear meaning |
| Pass C | Frame conditions, new invariants, obstructions, canonical nonlinear class | `passes/pass_C/PASS_C_DELIVERABLE.md` | Admissible slicing and frame equivalence are defined; SCM/SUD/SDF are defined; obstruction taxonomy is precise; a canonical nonlinear class is fixed and at least one quantitative theorem is proved |
| Pass D | Lift calculus on general \(\Sigma\): atlas, cocycle, connection, holonomy; nonlinear-time constraints | `passes/pass_D/LIFT_CALCULUS.md` | Local lift atlas and obstruction class are defined; connection/holonomy is formalized and gauge invariant; admissible future direction and bounded-rate conditions are defined; normal form is stated and justified |
| Pass E | Universe witness catalog: fully formalized flagship models | `passes/pass_E/WITNESS_CATALOG.md` | At least four witness classes are presented with explicit \((M,\{\Sigma_s\},\Phi)\); each verification cites a proven template (phase-coordinate, circle action, or loop-degree witness) |
| Pass F | Multi-cycle torus upgrade and coupling laws | `passes/pass_F/TORUS_COUPLING.md` | Vector-valued Syncre fields to a torus are defined; solar–lunar coupling is stated as a global constraint; at least one structural lemma about torus coverage or coupling invariants is proved |
| Pass G | Diagnostics and convergence program | `passes/pass_G/DIAGNOSTICS_AND_CONVERGENCE.md` | Pushforward measures are formalized; SCM/SUD/SDF are connected to convergence claims; a stroboscopic map model is stated; at least one convergence theorem is stated with clear assumptions |
| Pass H | Syncre dynamics (fluid form) and preservation results | `passes/pass_H/FIELD_DYNAMICS.md` | A minimal dynamics law on lifts is proposed; at least one preservation lemma (degree/holonomy/coverage modulus) is proved under explicit conditions |
| Pass I | Unification and sharpening | `passes/pass_I/UNIFIED_THEOREM_CHAIN.md` | A single coherent theorem chain is assembled; redundancy removed; canonical equation and symbol are referenced; Earth plus at least two universe witnesses appear as corollaries |
| Pass J | Paper skeleton and submission-ready draft plan | `passes/pass_J/PAPER_SKELETON.md` | Claims are scoped and defensible; theorem statements are stable; witness catalog is integrated; appendix plan is clear |

## Status

- Completed: Pass A, Pass B, Pass C, Pass D, Pass E, Pass F, Pass G, Pass H, Pass I, Pass J
- Next: Complete breakthrough targets BP-1 to BP-3

## Canonical references

- `SYNCRE_CANONICAL_EQUATION.md` — SCL (coverage law) and SLL (lift law)
- `SYNCRE_SYMBOL_DEFINITION.md` — \(\mathscr{S}_{\!\mathrm{r}}\) and \(\mathscr{S}^{\uparrow}_{\!\mathrm{r}}\)


## Breakthrough passes

- Breakthrough Pass 1 completed: `breakthrough/BREAKTHROUGH_PASS_1.md`
- Next: strengthen BP-1 (weaker hypotheses, sharper metrics) and BP-2 (coupled-subtorus convergence bounds)

- Breakthrough Pass 2 completed: `breakthrough/BREAKTHROUGH_PASS_2.md`
- Breakthrough Pass 3 completed: `breakthrough/BREAKTHROUGH_PASS_3.md`
- Breakthrough Pass 4 completed: `breakthrough/BREAKTHROUGH_PASS_4.md`
- Breakthrough Pass 5 completed: `breakthrough/BREAKTHROUGH_PASS_5.md`
- Breakthrough Pass 6 completed: `breakthrough/BREAKTHROUGH_PASS_6.md`

- Breakthrough Pass 7 completed: `breakthrough/BREAKTHROUGH_PASS_7.md`
