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.
Research programme · 2 August 2026
A standing agent-native research programme that determines what policy evidence supports, what it does not support, and which decisions remain defensible under uncertainty.
♪ audio▸ video
Observatory essay · 4 August 2026
Why checking AI-generated evidence, not producing it, binds government use of AI agents — four quantitative bounds, the research avenues that would relax the constraint, and sixteen ranked projects. Includes a plain-English companion essay.
♪ audio▸ video
2 August 2026
In an exact quadratic model of learning, some fair choices inside ordinary data shuffling admit a same-baseline value certificate; popular ordering proxies can fail without bound, while global threshold ordering is NP-complete when the stable step is instance-encoded and approaches 2.
availability and archiving · internal replay · 6 dimensions not assessed
1 August 2026
England's tenure shift is real; the aggregate housing data do not reveal how much, if any, was caused by rising resources at the top.
availability and archiving · internal replay · 6 dimensions not assessed
1 August 2026
A stalled attack yields two standalone tools: one turns irreducibility into geometric separation, and the other detects exact rank collapse in a quartic transition; Furter's R(3) remains open.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
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.
availability and archiving · internal replay · 6 dimensions not assessed
