Core 2.5 source/statement review
This is an additional source-and-proof inspection in the same assistant session, not an independent external referee or separate proof kernel.
| Source clause | Actual formal route | Boundary retained |
|---|---|---|
| Real vector space and convex cone | ConvexCone ℝ V, actual cone membership |
No ambient dimension or closedness added |
| Strict positivity of mass | StrictMass and mass_zero_iff |
Not mere nonnegativity |
| Finite complete maps | Fintype I, Complete |
No countably infinite sums |
| Nonnegative weights and total one | weight_nonneg, sum_weights_one |
Input has mass one |
| Positive normalized components | PositiveIndex, normalized_isState |
No inverse-zero normalized state |
| Zero weights vanish | weight_zero_iff |
Requires actual cone preservation |
| Exact mixture reconstruction | mixture_reconstruction |
Every omitted term is proved zero |
| Standard-cone idempotents | Coordinate.classification_iff |
Coordinate cone and idempotence explicit |
| Disjoint coordinate selection | source_core25_coordinate |
Derived, not assumed |
| Coordinate dependence of signs | Transport, real shear example |
Cone and mass change together |
The source propositions and proof text remain byte-identical. The formalization has separate endpoints for the two source sectors. The raw API checks their joint coverage. The theorem map also includes covariance as supporting material, not an additional source-result count. The empty-coordinate example and empty-index normalization impossibility prevent accidental strengthening by positivity of cardinality. No claim of full-book formalization follows from this one admission.