## Claim Scope
- Canonical-lane claim: inside the `manifold_constrained` lane, if the theorem chain in this repository holds and the guard certificate passes, the repository-level closure claim is satisfied.
- Standard target claim: carried by the in-repo bridge theorems tying the lane to the target statement.
## Theorem Dependency Chain
1. `EG1`: coercive response and active control floor.
2. `EG2`: capture and admissible continuation.
3. `EG3`: compactness and no-collapse spacing.
4. `EG4`: rigidity and transfer.
5. Identification bridge: strict coherence on the determining class.
6. Scalar closure: `BC_G1, BC_G2, BC_G3, BC_G4, BC_G5, BC_G6, BC_GM` all `PASS`.
Primary files:
- `paper/BAUM_CONNES_CONJECTURE_PREPRINT.md`
- `notes/EG1_public.md`
- `notes/EG2_public.md`
- `notes/EG3_public.md`
- `notes/EG4_public.md`
- `notes/IDENTIFICATION_BRIDGE.md`
## Closure Gates
| Gate | Constant | Description |
|------|----------|-------------|
| `BC_G1` | `kappa_analytic` | projected analytic assembly response has a strict positive floor |
| BC_G2 | sigma_equivariant | equivariant defect stays above capture floor across admissible operator losses |
| BC_G3 | kappa_compact | normalized near-failure families are precompact and equivariant windows do not collapse |
| BC_G4 | rho_rigidity | bad nonisomorphic Baum-Connes countermodels are excluded |
| BC_G5 | assembly_transfer | rigid limit transfers to the analytic assembly endpoint class |
| BC_G6 | eps_coh | strict coherence / identification closure |
| BC_GM | derived | final strict margin |
## Falsification Conditions
- `repro/certificate_runtime.json` has any non-`PASS` gate.
- `lane.active_lane != "manifold_constrained"`.
- `all_pass != true`.
- Any manifest hash mismatch under `repro/repro_manifest.json`.
- A verified counterexample to any EG theorem statement used in the paper.