Every genuine first-row minor · arbitrary alternating sums · T13 partial · Constructive arithmetic

Complete signed cofactor families and alternating Laplace folds

∀M,q. ∃ family. ∀j<S(q). family[j]=SignedMinor(M,0,j)

Twenty-nine independently checked constructive theorems simultaneously encode every genuine signed first-row cofactor minor, prove exact parity-adjusted finite Laplace folds and establish uniqueness in every unrestricted finite dimension.

Open the definition-aware map Read the final theorem See campaign milestone T13

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact certificate

Fully expanded arithmetic

Inspect all 1370 native tactic lines and 51 actual proof prerequisites with every definition fully expanded.

Open the exact edition →

Focused route

Final dependency cone

Start at theorem CE001D and follow only the lemmas and conservative definitions supporting signed_matrix_cofactor_family_and_fold_exists.

Trace prerequisites →
Zoom between mathematical scales: complete research atlas → research domain → proof family → T13 milestone → theorem and definition dependencies.
Major independently established statements: CE0003 matrix_minor_four_code_components_injective · CE0009 signed_cofactor_minor_family_exists · CE000B signed_cofactor_minor_family_entry_projects_minor · CE0015 signed_alternating_product_prefix_exact_term · CE0017 signed_alternating_cofactor_fold_exists · CE0018 signed_alternating_cofactor_fold_functional · CE0019 signed_alternating_cofactor_fold_exists_unique · CE001C signed_first_row_cofactor_fold_exists · CE001D signed_matrix_cofactor_family_and_fold_exists.
Independently verified Alpha v34 checked-use theorem family: 29 dependency-curried kernel-checked theorem bodies · 51 proof prerequisites · 19 linked definitions · 26 definition-dependency arrows · 1370 exact tactic lines · first admitted v25 · not Stable. The unchanged intuitionistic kernel and separately compiled Lean verifier independently accept all 302 bundle nodes; SHA-256 d4532076049be869e4e397d0fcee81b668bd3fd5c7d9173028bb1bdb80b9793a.
Exact mathematical boundary: Historical partial components only: this chapter proves genuine signed first-row minors and unique alternating folds, with supplied cofactor values. T13 is now closed in the separate Alpha-v27 integer-linear-algebra branch with actual arbitrary determinant data, rank, and integer column spans; lattice index and normal forms are not claimed.

Separate complete second-wave branches: Full T13 proof · Alpha v27.