# Syncre Form Theory: 10-Pass Universality Argument Refinement

## Goal

Perfect the “universality of mechanism” argument so it is:

- precisely scoped (no overclaiming)
- theorem-driven (not catalog-driven)
- robust (supports perturbations and embedded witnesses)
- readable (clear tiers: global vs embedded, full torus vs coupled subtorus)
- consistent with SFT core principles (RFP/PIP → Syncre spine)

## Pass map

| Pass | Goal | Deliverables | Acceptance gates |
|---|---|---|---|
| Univ Pass 1 | Scope discipline and universality thesis | `universality/UNIV_PASS_1_SCOPE.md` | Defines “universality of mechanism” vs “universality of coverage”; introduces global vs embedded witnesses; updates paper skeleton universality claims |
| Univ Pass 2 | Meta-witness theorem (S¹-action) | `universality/UNIV_PASS_2_META_WITNESS_S1.md` | One theorem subsumes rotating/orbit/wave witnesses using equivariant action; includes proof and hypotheses check-list |
| Univ Pass 3 | Embedded witness formalism and taxonomy | `universality/UNIV_PASS_3_EMBEDDED.md` | Defines embedded Syncre witness as first-class; connects to loop-degree/holonomy; obstruction taxonomy updated |
| Univ Pass 4 | Robustness layer for universality | `universality/UNIV_PASS_4_ROBUSTNESS.md` | States perturbation model and shows witness persistence; includes “witness stability certificate” fields |
| Univ Pass 5 | Coupled universality (multi-cycle) | `universality/UNIV_PASS_5_COUPLED_UNIVERSALITY.md` | Defines universality target as coupled Haar on CST; meta-theorem for SOL-style couplings |
| Univ Pass 6 | Dynamics universality (transport) | `universality/UNIV_PASS_6_DYNAMICS_UNIVERSALITY.md` | Shows which dynamic classes preserve witnesses and which do not; clear boundary statements |
| Univ Pass 7 | Mixing universality (diffusion/noise) | `universality/UNIV_PASS_7_MIXING_UNIVERSALITY.md` | States when convergence to Haar is universal under a noise model; ties to stability signatures |
| Univ Pass 8 | Physical interpretability notes | `universality/UNIV_PASS_8_PHYSICS_NOTES.md` | Carefully translates theorem hypotheses to physical conditions without handwaving |
| Univ Pass 9 | Referee-hard tightening | `universality/UNIV_PASS_9_REFEREE_CHECKLIST.md` | A checklist mapping every claim to a theorem/assumption; lists nonclaims explicitly |
| Univ Pass 10 | Final universality section for paper | `universality/UNIV_PASS_10_PAPER_SECTION.md` | Copy-ready universality section; consistent terminology; ready to paste into paper draft |

## Status

- Completed: Univ Pass 1, Univ Pass 2, Univ Pass 3, Univ Pass 4
- Next: integrate `UNIV_PASS_10_PAPER_SECTION.md` into the main paper draft
