Optimize homology certificate generation - #1
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Prove the simplicial chain condition at the coefficient level in a new `Boundary/ChainCondition.lean`: - `eraseIdx_eraseIdx_of_le`/`_of_lt`: list-level simplicial face identity (the `List.eraseIdx` analogue of `SimplicialObject.δ_comp_δ`). - `boundaryCoeff_eraseIdx` / `boundaryCoeff_eq_zero_iff`: characterize the incidence coefficient on faces and non-faces (needs `Nodup`). - `boundaryCoeff_eq_sum`: express `boundaryCoeff` as an explicit sum over deletion indices, exposing the inner index. - `boundary_sq_coeff`: the headline — the alternating sum over deletion indices of the iterated boundary coefficient into a fixed target vanishes, proved by a sign-reversing involution on index pairs (`Finset.sum_involution`). This is the basis-independent combinatorial core of ∂∘∂ = 0; bridging it to `boundaryMatrix` (via canonicalBasisRaw completeness) is still TODO. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
- Remove the sparse `(row,col,val)` matrix encoding (`lookupSparseMatrix`, `sparseRowsToMatrix`) from `SageDecode.lean` and the corresponding `decodeSerializableSparseEntriesExpr`/`mkSparseEntryExpr`/ `sparseEntriesToMatrixExpr` pipeline in `SNF/Tactic.lean`; the tactic now builds all SNF witness matrices through the dense `rowsToMatrix` path (U,U⁻¹ at m×m, D at m×n, V,V⁻¹ at n×n). - Prove the U·U⁻¹ = 1 and V·V⁻¹ = 1 obligations via a reflected Bool computation (`MatrixReflect.mulIsOneB` + `rowsToMatrix_mul_eq_one`) instead of `native_decide` on Mathlib matrix multiplication. - Drop the deferred `Later/` SNF bridge/quotient experiments. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
lucyhorowitz
marked this pull request as ready for review
June 1, 2026 14:15
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update certificate proof generation to be efficient for once