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 map · 57 releases · source-driven
Trace declared methods, broad clusters, evidence-backed lineages, parent dependencies and internal citations. Every connection exposes its basis and inference limit.
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.
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Essays and commentary · 1 article
Long-form arguments, syntheses and research notes, with sources, scope and corrections made explicit. Articles are not certificate-backed research releases.
Practice programme · 8 August 2026
Bounded, downloadable workflows for using AI agents, each with separate assurance and work-evidence status. Human and company impact is not yet measured.
6 September 2026
An exact five-vertex example shows that omitting one predetermined update can leave a ferromagnetic three-colour Potts model closer to equilibrium at a fixed horizon.
availability and archiving · internal replay · 5 dimensions not assessed
6 September 2026
An explicit eight-state distribution cannot be approximated arbitrarily well by a classical binary model with four visible and three hidden units.
availability and archiving · internal replay · 5 dimensions not assessed
5 September 2026
A constructive proof candidate shows that non-backtracking Jordan blocks can grow linearly with graph order, even under one fixed maximum-degree bound.
availability and archiving · internal replay · 5 dimensions not assessed
5 September 2026
A computer-assisted proof candidate gives the exact worst-case error of two Bernoulli products on three bits, attained only by the two uniform parity distributions.
availability and archiving · internal replay · 5 dimensions not assessed
5 September 2026
A written proof candidate gives the exact exponents preserving real roots for every positive-coefficient quartic, with a sharp threshold and an exclusive equality case.
availability and archiving · internal replay · 5 dimensions not assessed
4 September 2026
For every fixed finite d at least two in characteristic zero, a two-color Toeplitz family gives a morphism of finite-degree-presented FI_d-modules with no kernel inside that subcategory.
availability and archiving · internal replay · 5 dimensions not assessed
4 September 2026
Coordinate Schubert surface unions are Cohen–Macaulay exactly for connected active graphs, but deform to integral surfaces exactly for complete multipartite graphs.
availability and archiving · internal replay · 5 dimensions not assessed
3 September 2026
Checked SAT certificates establish that 27 is the minimum inside [1,37]; the unrestricted sparse value and the AIM asymptotic questions remain open.
availability and archiving · internal replay · 5 dimensions not assessed
1 September 2026
Exact positive-coefficient Bezout certificates prove real negative roots and strict arbitrary-deletion interlacing for Fisk's 3x3 Toeplitz-minor transform through five positive alphabet entries; the all-degree and zero-boundary problems remain open.
availability and archiving · internal replay · 5 dimensions not assessed
1 September 2026
Exact certificates narrow a degree-five repeated-factor boundary of full HC4—the all-degree Hessian Conjecture in four variables—without proving secant closure, full HC4 or JC2.
availability and archiving · internal replay · 5 dimensions not assessed
1 September 2026
A fixed free normal cover is argued to give infinitely many all-Fuchsian critical exponents approaching one from below, with an explicit linear pinching rate and a carefully limited relation to AIM Problem 4.3.
availability and archiving · internal replay · 5 dimensions not assessed
31 August 2026
A factor-3 rhombus condition is proposed as a degree-independent ternary stability criterion, while three higher-dimensional readings meet explicit obstructions and the normalized cases in four through six variables remain open.
availability and archiving · internal replay · 5 dimensions not assessed
31 August 2026
A characteristic-free sub-FI-algebra has affine Noetherian components at every finite width but a strict infinite chain of FI-ideals across widths.
availability and archiving · internal replay · 5 dimensions not assessed
31 August 2026
For every m>=2, an explicit linearly growing free-by-cyclic group has first Betti number m+2, exactly 2m+2 BNS components, and at least m+1 component orbits under its outer automorphism group.
availability and archiving · internal replay · 5 dimensions not assessed
30 August 2026
A non-graded four-element rooted tree has infinite-order birational and piecewise-linear rowmotion, and exhaustive exact replay proves that no smaller finite poset can do so.
availability and archiving · internal replay · 5 dimensions not assessed
30 August 2026
A directed four-point closure space sends a nonzero integral relative one-cycle to zero, disproving interior-cover excision for normalized (J+, boxdot)-cubical homology.
availability and archiving · internal replay · 5 dimensions not assessed
30 August 2026
A five-vertex graph gives the smallest exact decrease-then-increase in negative adjacency square energy, refuting universal prescribed-order peak-unimodality while leaving favourable-order existence open.
availability and archiving · internal replay · 5 dimensions not assessed
30 August 2026
A side-two pure trilinear tensor refutes one literal, unnormalised analytic-rank tensorization comparator, while the powered-identity diagonal ratio remains exactly (k/n)^m.
availability and archiving · internal replay · 5 dimensions not assessed
29 August 2026
A four-state monotone reversible heat-bath chain is furthest apart at two incomparable states—not its minimum and maximum—at every positive time.
availability and archiving · internal replay · 5 dimensions not assessed
29 August 2026
An eight-point subset of Z/21Z refutes the strict one-third AIM question, while a three-layer family obstructs every fixed threshold below 2/5 in odd cyclic groups.
availability and archiving · internal replay · 5 dimensions not assessed
28 August 2026
Two all-amplitude family classifications and a general ordinary coefficient-Bautin bound turn inverse support into explicit modules, attainable ranks and a finite d−1 cutoff.
availability and archiving · internal replay · 5 dimensions not assessed
28 August 2026
Exact polar-fibre and Hermite reductions, four rejected proof architectures, and a four-gate executable handoff sharpen an open all-index transversality problem.
availability and archiving · internal replay · 5 dimensions not assessed
25 August 2026
A complementary-minor duality compresses a growing Polydegree obstruction to a fixed-width flag, while repaired quartic and p-adic certificates expose the remaining uniform radical-membership target.
availability and archiving · internal replay · 5 dimensions not assessed
24 August 2026
Exact arithmetic and symbolic checks, a standalone conductor-adjoint theorem candidate, and source-conditional Hodge and deformation calculations extend a claimed—but unverified—complex structure on S6.
availability and archiving · internal replay · 5 dimensions not assessed
24 August 2026
An explicit connected cubic graph has minimum maximal matching number 15 but independent domination number 16, lowering the candidate counterexample-order upper bound from 50 to 48.
availability and archiving · internal replay · 5 dimensions not assessed
23 August 2026
An exact residue branch, 14,985 outward-rounded finite certificates and a uniform Fourier envelope yield the e=4 Polydegree containment for every degree d at least 2.
availability and archiving · internal replay · 4 dimensions not assessed
22 August 2026
A producer-side candidate exact oracle gives a rational three-item max-frequency relaxation-gap lower bound of 1.1487291464748206... and a verifier-checked route to instance-specific logistics stress tests.
availability and archiving · internal replay · 5 dimensions not assessed
21 August 2026
A reconstructed tree can fit many speciation-and-extinction histories. Under a fixed-stem model, this candidate turns that ambiguity into rigorous finite-sample decisions—showing which conclusions survive every compatible history and when plug-in estimates or finite CRABS clouds are too confident.
availability and archiving · internal replay · 5 dimensions not assessed
20 August 2026
A combined unrefereed candidate extends the all-degree fixed-seed atlas to every polynomial amplitude, specified zero-cycles, all endpoint moments for q(P)≤3, and an exact Laurent local-channel criterion.
availability and archiving · internal replay · 4 dimensions not assessed
14 August 2026
An exact counterdirection blocks a printed joint-concavity step in Liu's arXiv v1, while independent three-atom reductions, endpoint control and bounded certificates survive; no new Frankl bound is proved.
availability and archiving · internal replay · 5 dimensions not assessed
14 August 2026
Exact same-prime special-fibre certificates prove Furter's R(3,n) for every 1 <= n <= 299, while a fixed-prime zero-band theorem and an executable challenge isolate what remains open.
availability and archiving · internal replay · 5 dimensions not assessed
13 August 2026
A summary can be correct yet still omit information needed for a decision; an aggregation licence tests what that summary may safely determine.
availability and archiving · internal replay · 5 dimensions not assessed
12 August 2026
A Jacobian smooth-point reduction, Fourier-limit persistence, an exact eventual envelope and 97,033 finite Arb certificates prove the e=3 containment for every degree d at least 2.
availability and archiving · internal replay · 5 dimensions not assessed
11 August 2026
A finite expected site-frequency spectrum observes only finitely many exponential projections; this corrected candidate proves why sharp calendar-window targets can remain unidentified and supplies an exact positive collision.
availability and archiving · internal replay · 5 dimensions not assessed
11 August 2026
Across APC models, epidemic observation processes, sign-restricted SVARs and aerosol–climate inference, a unique fitted answer can come from a selector rather than from the observations.
availability and archiving · internal replay · 5 dimensions not assessed
11 August 2026
The first-year casualty decline is descriptively reproducible, but the frozen aggregate evidence identifies neither the point value nor the sign of the policy effect on affected roads.
availability and archiving · internal replay · 5 dimensions not assessed
9 August 2026
A residual-SAT parameter exactly measures the independent-domination gap for regular graphs equipped with a dominating induced matching, yielding connected cubic-DIM families and a DIM-qualified minimum order of 50.
availability and archiving · internal replay · 4 dimensions not assessed
9 August 2026
A conditional theorem turns fixed-seed cyclic rank into a count of independent inverse-root functions, classifies every indecomposable rank-one to rank-three phase, and exposes block fusion as the remaining compositional obstruction.
availability and archiving · internal replay · 5 dimensions not assessed
9 August 2026
A candidate all-factor determinant-line theorem and exact Smith calculation replace the rank-one degree difference by a complete character-lattice invariant.
availability and archiving · internal replay · 5 dimensions not assessed
9 August 2026
A stabiliser--cycle chain has the full Hahn count spectrum, an exact binomially layered word spectrum, and a parameter-dependent sharp stationary-average chi-square transition on the N/log N scale.
availability and archiving · internal replay · 5 dimensions not assessed
9 August 2026
The Lewis-Perry-Straub auxiliary determinant is a Jacobian: an exact Euler syzygy turns its specialisation test into a smooth-point criterion and yields a smaller Hensel certificate, while the uniform e=3 affine theorem remains open.
availability and archiving · internal replay · 5 dimensions not assessed
8 August 2026
For a fixed pulled speciation signal and explicit model restrictions, an affine measure coordinate turns alternative birth-death histories into a tractable feasible set with sharp bounds, incompatibility certificates, and a precise account of why finite random searches can miss extremes.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
8 August 2026
A candidate integral identity expresses every bordered Jacobian of binary-form multiplication as one resultant times one pairing with the lost scaling direction.
availability and archiving · internal replay · 3 dimensions not assessed
8 August 2026
An exact-rational candidate separates an abstract forced-source path model from its classical lot-sizing interpretation, then certifies how far forecast demand may move before a protected setup prefix can cease to be compulsory among optimal plans.
availability and archiving · internal replay · 5 dimensions not assessed
8 August 2026
Two periodic item schedules can share a setup cost only when their order times align. This candidate proves finite exact certification under average-rate constraints and shows that the standard two-item cap relaxation can be optimistic by at most—and sometimes exactly—about 11.19 per cent.
availability and archiving · internal replay · 5 dimensions not assessed
8 August 2026
Exact Krylov determinants locate where a chosen exponential-period amplitude loses differential rank, with complete quartic strata and a finite exact odd-quintic certificate.
availability and archiving · internal replay · 5 dimensions not assessed
8 August 2026
A connected cubic graph on 50 vertices has minimum maximal matching number 15 but independent domination number 16, giving a bounded candidate counterexample to the stated regular-graph inequality.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
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
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
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
30 July 2026
An exact low-length matrix-inequality classification becomes a metric-aware theory of data ordering: mean iterates, quadratic risk, fresh reshuffling, single shuffle and replica averaging can rank the same sampler differently.
availability and archiving · internal replay · 5 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
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 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 divisor classification and a conditional screening theorem that isolates one affine-space slice inside a precisely defined positive two-factor binary-form architecture; it does not classify the later Gallagher or Gao counterexample families.
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
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
