Claim ledger
Status uses evidence categories, not estimated probabilities of success.
| ID | Claim | Evidence | Boundary |
|---|---|---|---|
| C1 | Complete row-orthogonal positive rank-one interface classification, d>=2 | Full proof, exact examples, symbolic identity | Prescribed common tangent hyperplane; coframe rows convention |
| C2 | Three-or-more-active-components locking and affine propagation | Corollary of C1 | Field-dependent generic-face subgraph; not every mesh/field |
| C3 | Quantitative shear/jump inequality and necessary shear lower bound | Full proof, 120 rational cases | Reference side exactly orthogonal; positive orientation; stated normal margin |
| C4 | Positive scale kernel from local traces and balanced gains | Full proof, graph compiler, 100 rational planted cases | Fixed coframe directions and matchings |
| C5 | Complete component mobility and nearest diagonal-weight scales with bounds | Full proof | Tangential scale subsystem; period/boundary constraints can couple components |
| C6 | PL coordinate reconstruction | Full proof, actual-gradient checks | H^1=0 for the existence implication; code verifies a supplied vector directly |
| C7 | Primitive real-origin gauge criterion | Full proof, Smith identities, exact counterexample to false torsion | Real origins; integer gauge would be a different problem |
| C8 | Residual dimension dbeta-d+f <= dbeta | Full proof, 40 rational graph cases | Specified connected chart graph only |
| C9 | Coupled bounded integer projection with attained global optimum | Full proof, exhaustive exact reference optimizer | Rational compact finite model; no scalable solver claim |
| C10 | Homogeneous rational quantization by common scaling | Full proof | No fixed nonhomogeneous size constraints or resolution cap |
| C11 | Supplied-boundary global inversion endpoint | Cited established theorem and corollary | Boundary homeomorphism is an independent input hypothesis |
Historical novelty of C1–C3 and the full synthesis remains unverified. C4, C7, and the optimization identities are explicitly connected to classical mathematics. The project does not claim to have solved 11 pre-existing open problems.
Completion accounting
The version-1.0.0 artifact scope (manuscript, proof statements, reference routines, tests, audit, examples, metadata) is complete. The executed named test pass rate is 100% = 43/43. This is not a percentage of mathematical certainty. Independent reviews completed: 0. General meshing benchmarks completed: 0. No overall percentage is assigned to the unrestricted open research problem.