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 · 110 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 · 5 articles
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.
4 October 2026
An exact certificate supports the three-copy qutrit Werner threshold: distillation is possible precisely below α = −1/2.
availability and archiving · internal replay · 5 dimensions not assessed
4 October 2026
A sharp rank gap separates a four-state reticulation cycle from any mixture of two trees sharing one topology.
availability and archiving · internal replay · 5 dimensions not assessed
3 October 2026
Some waiting-time laws force a positive thermodynamic cost, however many hidden states a compatible model contains.
availability and archiving · internal replay · 5 dimensions not assessed
3 October 2026
A computer-assisted proof that among all quadrilaterals, convex or not, the square uniquely maximises the ratio λ₂/λ₁ of the first two Dirichlet eigenvalues, with value 5/2: the k = 4 case of the polygonal Payne–Pólya–Weinberger conjecture.
availability and archiving · internal replay · 5 dimensions not assessed
3 October 2026
Convex geometry and exact stability formulas establish one attracting cycle in an explicit parameter region; the full uniqueness question remains open.
availability and archiving · internal replay · 5 dimensions not assessed
1 October 2026
Exact certificates separate a uniquely reconstructed metric from a genuine gravitational central configuration—and exclude two whole seven-body parameter boxes.
availability and archiving · internal replay · 5 dimensions not assessed
1 October 2026
An exact all-parameter certificate rules out stable nonclique activity on five or fewer neurons; a known six-neuron graph makes the bound sharp.
availability and archiving · internal replay · 5 dimensions not assessed
1 October 2026
Keeping neighbouring lens planes in the equations lowers the two-binary image ceiling from 41 to 33; the known 25-image construction leaves a sharp question open.
availability and archiving · internal replay · 5 dimensions not assessed
30 September 2026
An algebraic transfer yields homogeneous counterexamples throughout a parameter window, except at the known Ising point.
availability and archiving · internal replay · 5 dimensions not assessed
30 September 2026
A grouped local test gives a size-independent lower energy gap for a specified kagome quantum-spin model.
availability and archiving · internal replay · 5 dimensions not assessed
30 September 2026
A computer-assisted proof candidate certifies that small genuine shape changes increase the first vibration frequency at fixed area.
availability and archiving · internal replay · 5 dimensions not assessed
30 September 2026
A certificate-backed candidate excludes a whole two-parameter family, including its boundary, without claiming to settle the six-dimensional problem.
availability and archiving · internal replay · 5 dimensions not assessed
29 September 2026
A short-support mechanism limits error protection in a specified family of symmetric codes—even when their information rate stays positive.
availability and archiving · internal replay · 5 dimensions not assessed
28 September 2026
An exact three-site test rules out a range of local conservation laws for every choice of on-site fields—and gives a sharp boundary for a central spin-1 family.
availability and archiving · internal replay · 5 dimensions not assessed
28 September 2026
A geometric classification separates every gapped and gapless chain in a precise entanglement class—even when familiar short-chain measurements agree.
availability and archiving · internal replay · 5 dimensions not assessed
28 September 2026
For every order N ≥ 3, a graph criterion exactly characterises generic canonical free spectra—with a crucial distinction between the whole spectrum and its separate sectors.
availability and archiving · internal replay · 5 dimensions not assessed
28 September 2026
Factorised pair interactions make every local Perron minimum globally optimal; an arbitrarily small departure can create a trap.
availability and archiving · internal replay · 5 dimensions not assessed
27 September 2026
A graph criterion characterises whole-spectrum freeness at every coupling under faithful Pauli realisation; exact sector certificates reveal a larger, carefully distinguished class.
availability and archiving · internal replay · 5 dimensions not assessed
27 September 2026
Exact first-order rates describe how the negative-type gap opens near every specified split metric, with a different, quadratic transition at four points.
availability and archiving · internal replay · 5 dimensions not assessed
26 September 2026
Explicit information geometry gives an anytime-valid route to the complete compatible set—and identifies boundary questions that remain answerable when complete resolution is impossible.
availability and archiving · 5 dimensions not assessed
26 September 2026
Exact counts of the invariants of three to ten 4×4 matrices and of three 5×5 matrices, confirming Berele's denominator conjecture in these nine cases, plus a plane-septic Hilbert series proved to degree 760.
availability and archiving · internal replay · 5 dimensions not assessed
26 September 2026
Exact Hilbert series for the invariants of plane curves of degrees 7, 8 and 9, beyond the previous record of degree 6, by known methods made fully auditable.
availability and archiving · internal replay · 5 dimensions not assessed
26 September 2026
An analytic proof candidate gives the exact distance-power threshold guaranteed for every finite Ptolemaic metric, with strictness below it and explicit examples showing that it cannot be raised.
availability and archiving · internal replay · 5 dimensions not assessed
25 September 2026
A candidate proof that every complex eigenvalue of the Davies–Levitin indefinite tridiagonal pencil lies in the lens where its two Gershgorin disks overlap, for every matrix size.
availability and archiving · internal replay · 5 dimensions not assessed
24 September 2026
A candidate sparsity theorem excludes every degree-twenty counterexample with seven or fewer terms in centered form.
availability and archiving · internal replay · 5 dimensions not assessed
24 September 2026
A candidate study of the densest open case of Seymour's conjecture proves structural limits, certifies that every counterexample has at least 18 vertices, and refutes DeVos's conjecture as printed in Sullivan's survey.
availability and archiving · internal replay · 4 dimensions not assessed
23 September 2026
An ordered placement rule classifies generic local identifiability in bidirected chains with arbitrary inputs, outputs and leaks.
availability and archiving · internal replay · 5 dimensions not assessed
22 September 2026
Drift-reachable noise determines the candidate existence domain for operator-valued Wishart covariance processes.
availability and archiving · internal replay · 5 dimensions not assessed
21 September 2026
Integer separation forces very long strictly improving moves, even in median graphs.
availability and archiving · internal replay · 5 dimensions not assessed
20 September 2026
An exact overlapping fibre joins two auxiliary regions in the full space of reaction rates and conserved totals.
availability and archiving · internal replay · 5 dimensions not assessed
20 September 2026
A rational example and exact root-count certificate establish five positive equilibria in the full two-ligand model.
availability and archiving · internal replay · 5 dimensions not assessed
20 September 2026
A minimal counterexample, a complete coefficient-fiber classification, and the exact condition that restores identification.
availability and archiving · internal replay · 5 dimensions not assessed
19 September 2026
An exact dimension-26 counterexample and a written proof of failure in every dimension at least 64.
availability and archiving · internal replay · 5 dimensions not assessed
19 September 2026
An exact tensor spectrum, a real eigenvalue without real eigenvectors, and a hidden genus-three curve.
availability and archiving · internal replay · 5 dimensions not assessed
12 September 2026
Uniform quartic boundary interlacing, with an exact affine point count using external rigidity.
availability and archiving · internal replay · 5 dimensions not assessed
12 September 2026
The reduced parameter space is smooth exactly when every Jordan pencil block has dimension two.
availability and archiving · internal replay · 5 dimensions not assessed
12 September 2026
A candidate full-law profile for a two-class biased shuffle, including the crossover as bias vanishes.
availability and archiving · internal replay · 5 dimensions not assessed
11 September 2026
Two slow fixed labels force a total-variation lower bound above the conjectured profile.
availability and archiving · internal replay · 5 dimensions not assessed
9 September 2026
A constructive proof candidate embeds graph faces into full moment models, forcing equations of arbitrarily large necessary degree and producing an intrinsically nonnormal example.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
Candidate proof of the stated AIM mixing bounds for four fixed-weight clock conventions: logarithmic in the denser regime, square-root up to polylogarithmic factors in the sparser regime.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
Arbitrary bounded product weights admit a cutoff proof with mixing order n log n and window upper bound n log log n.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
A fourteen-vertex body in six dimensions has exact zonoid enclosure factor 122/65, exceeding 15/8 by 1/520.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
Symmetric stable densities approach a Gaussian locally while their best global power-concavity exponent deteriorates logarithmically.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
A uniform classification candidate: every fixed genuine orthogonal representation has an algebraic tensor-multiplicity series exactly in dimensions one, two and three.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
An exact criterion and an all-path-count classification show when spanning trees support a symmetry-compatible critical-group action.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
A five-colouring theorem for a mixed cover class, conditional finite exclusions and explicit repair obstructions; the parent problem remains unresolved.
availability and archiving · internal replay · 5 dimensions not assessed
8 September 2026
An integral cut–cycle argument classifies ridge and full tropical Picard groups, with an explicit multigraph convention and commuting diagonal flips.
availability and archiving · internal replay · 5 dimensions not assessed
7 September 2026
A uniform proof candidate gives nonnegative monomial coefficients for every Toeplitz minor of the single affine elementary-symmetric sequence.
availability and archiving · internal replay · 5 dimensions not assessed
7 September 2026
A compact trace-determinant formula candidate gives the global degree-30 essential Hurwitz form, with a denominator-cancellation proof and symmetric corollary.
availability and archiving · internal replay · 5 dimensions not assessed
7 September 2026
A computer-assisted proof candidate claims reducedness of the Hilbert scheme of eight points in affine four-space over algebraically closed characteristic-zero fields.
availability and archiving · internal replay · 5 dimensions not assessed
7 September 2026
A proof candidate finds the exact strength of local minor ratios needed to force total positivity.
availability and archiving · internal replay · 5 dimensions not assessed
7 September 2026
An analytic proof candidate that free addition preserves every symmetric unimodal probability law.
availability and archiving · internal replay · 5 dimensions not assessed
6 September 2026
A two-cut entropy argument gives a proof candidate for n log n mixing of the original Dyck-path random-transposition rejection walk.
availability and archiving · internal replay · 5 dimensions not assessed
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
