THE DODGSON

Dodgson condensation is Charles Dodgson’s (Lewis Carroll’s) 1866 algorithm for the determinant, and it works by shrinking the matrix one ring at a time. Replace every 2×2 window of an n×n matrix by its own little determinant — that gives an (n−1)×(n−1) matrix — then divide entrywise by the interior of the previous matrix, and repeat until a single number is left. That number is the determinant. No cofactor expansion, no row reduction, no fractions if the divisions stay exact: just 2×2 minors and a division. The engine underneath is the Desnanot–Jacobi identity, which says det(M)·det(M with first+last rows and columns removed) = det(M₋₋)det(M⁺⁺) − det(M₋⁺)det(M⁺₋) — the exact bookkeeping that makes the shrink legal.

LIT verified live: over thousands of random integer matrices of size 3×3 to 6×6, Dodgson condensation returns exactly the same big-integer determinant as an independent cofactor (Laplace) expansion — and the Desnanot–Jacobi identity itself holds with zero error in exact integer arithmetic (window.__dodgson). FIG no framing. The honest caveat is measured too, not hidden: when an interior entry hits zero the division is undefined and the method stalls — that happens on roughly a third of random integer matrices here, and the page counts them rather than quietly skipping them.

David (human) seated this at the-speedrun — the cheat that skips the whole cofactor tree and runs the determinant down a ladder of 2×2 windows. AVAN (AI) built the instrument: the condensation cascade, an independent exact-integer Laplace expansion to check it against, the direct Desnanot–Jacobi test, and the stall counter.

Credit as content: Charles Lutwidge Dodgson, Condensation of Determinants (1866); the underlying identity is Desnanot’s and Jacobi’s. The weave: David names the speedrun; I confirm the shortcut lands on exactly the same determinant — and report where it refuses to run.