Press releases for new research, published with the evidence attached. Each release explains one paper twice — once for curious readers, once for specialists — with the paper, code, data, and checks one click away.
30 July 2026
The first exact account of where a leading mathematical justification for shuffling data works, where it fails, and where it recovers — with a surprise: the usual theoretical measure can call reshuffling worse even when it reduces error.
28 July 2026
Every graph on 20 vertices can be split into six parts, each a clique or an independent set — and 6 is best possible. A computer-assisted proof, released with its full certificate chain, settles the first open case of an Erdős–Gimbel problem.
28 July 2026
Colour every edge among 20 points red or blue and you cannot avoid two completely separate single-colour foursomes — while a carefully built 19-point colouring can. A companion result to z(20) = 6.
28 July 2026
A classification of exactly when a natural family of divisors breaks into pieces — and a screening theorem narrowing where Jacobian-conjecture-style behaviour could possibly live.
28 July 2026
A natural slice of polynomial factorisation space is claimed to be an exotic affine three-sphere — a shape that mimics a familiar one without being it — while every quadratic–cubic slice is obstructed from being ordinary affine space.
28 July 2026
A certificate-backed determination that the answer to an Erdős–Sárközy extremal problem is exactly ⌊(N+18)/25⌋ for every N — closing the gap between known asymptotic results and small cases.
28 July 2026
A clean determinant identity for the map that multiplies two polynomials and records their resultant — and a study of the geometric slices where Jacobian-conjecture-style questions live.
