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 · 246 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.
♪ audio▸ video
Essays and commentary · 8 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
Six working habits that multiply what one person can do with AI, the case study of how Evidence Press runs on them, and a way to measure the gain.
What could each release be used for in practice? See Applications, a plain-English note per release.
4 November 2026
On a huge clique with a private leaf on every vertex and one extra path of length L, an adversary nudging transition probabilities can be tolerated up to a fixed ε ≈ 0.293 before cover time doubles, but only ε ≈ 0.628/L before hitting time doubles, refuting Zuckerman's conjecture that the two tolerances always agree up to a constant.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
For any graph, the fraction of k-vertex sets that contain an edge forms a log-concave sequence in k, even with vertex weights, proving Xie and Xu's Conjecture 4.1; witnesses of size three already break it.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
4 November 2026
In location models with light-tailed errors, a hypothesis is calibrated at every threshold at a parameter exactly when that parameter is not strictly inside its essential convex hull, and a finite test warns of high confidence in a false hypothesis.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
A Gaussian kernel space is invariant under an Ornstein–Uhlenbeck process exactly when AP + PAᵀ ⪯ 4BBᵀ, twice the range of the earlier sufficient condition, and among Gaussian or fixed-noise transitions only affine maps can preserve it at all.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
Geodesic sliced Wasserstein distance on hyperbolic space is exactly a weak-convergence metric on the compact closed Klein ball: it has an exact diameter, barely sees depth far from the centre, gives squared distance π·α between boundary points at angle α in two dimensions, and can be estimated at optimal rates with no assumptions on the data.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
A three-unit example, observable and controllable, makes the isolated Kalman filter's reported variances grow at least like (5/4)(9/5)^k while the ordinary Kalman filter stays at or below 3/4, refuting its authors' conjecture that the reported covariance always settles to a unique steady state.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
A 2025 conjecture bounded the product of the k-th Laplacian eigenvalue of a graph and of its complement by n(n−k); a 14-vertex graph built from the Fano plane gives 115.85 > 112, and the true largest product is found to leading order, with a sudden drop at the middle rank.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
For the complex weight (1 − t²)ᵅ e^(ixt) on [−1, 1], every even-size Hankel determinant is strictly positive for every α > −1 and every real frequency x, so the even-degree orthogonal polynomials behind complex Gaussian quadrature always exist; odd sizes vanish infinitely often.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
Two complementary measurements on a qutrit can score at most 8/3 (out of a trivial 4) when telling two orthogonal states apart, proved by an exact certificate with every best case identified; and for a qubit paired with a system of dimension n ≥ 4, every choice of complementary measurements is fooled by some unentangled state (previously known only from n = 164).
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
The reciprocal of the Mittag–Leffler function E is completely monotone for every 0 < β ≤ α when 1 < α < 2, and, for α near 2, exactly for 0 < β ≤ b(α) with b(2) = 3, so the conjectured band α − 1 ≤ β ≤ α is too narrow on both sides.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
Rotation helps every observable exactly when friction is at least √2 — and what happens below it: for kinetic Langevin samplers of a Gaussian target, a target-preserving rotation never increases the long-run variance of any square-integrable position average if and only if the friction is at least √2.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
A waiting time of m slow exponential stages and one fast stage of random speed has Pólya frequency order exactly m+1, never more, and m+1 is also its largest matrix-lift dimension; this proves the parameter region of Sra's q-Gindikin Conjecture 6.1.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
4 November 2026
The published worst-case guarantees for a throughput-matched static price with a capacity cap are exact for every number of servers, with an explicit worst congestion load and an exact revenue-congestion curve.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
Guo (2026) already gives the curvature tensor Q/16 and the first sphere and circle bias for diffusion operators; this candidate proves the rigorous inverse-metric theorem: on a closed curved surface with straight-line cost the Sinkhorn metric converges to the Wasserstein metric, reads short at small ε by (ε/4) times a bending term, and a cheap positive correction removes the error.
availability and archiving · internal replay · 5 dimensions not assessed
4 November 2026
Identical Kuramoto oscillators scattered at random on a flat torus of any dimension have stable twisted equilibria near every integer winding up to a growing limit, proving the Cirelli–Groisman–Huang–Vivas conjecture for every kernel in their class with |z|K(z) bounded.
availability and archiving · internal replay · 4 dimensions not assessed
4 November 2026
With a real, mirror-symmetric probe such as a Gaussian beam, finite cyclic ptychography can only confuse an object with its twin, a conjugate pair on two opposite pixels in the object or its Fourier transform, and one extra coherent intensity measurement tells every twin pair apart.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
A proof of the Luner–Grimmer conjecture: when two convex sets share a ball, the slowest possible run of alternating projections is exactly a thin two-half-plane wedge, in every dimension, with exact extensions to unequal balls and residuals.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
A 14-alternative counterexample shows that the best Bradley–Terry paired-comparison design can use a set of pairs with a chordless four-cycle and irrational weights, disproving a 2025 conjecture; the paper also proves which structure does survive.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
Hold fixed the rate at which each cultural trait is passed on and change only how bundled learning is: expected trait counts do not change, but every count becomes more variable (convex order), so shortfalls and total loss grow more likely; at the source simulations’ setting, copying 93% of traits per encounter leaves a third of the whole-repertoire variance.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
Snyder and Hakim's conjecture that canonical coordinates are the best basis for ensemble covariance localisation fails when error is measured in physical variables, at every ensemble size for a single observation, but holds at leading order when error is measured relative to the forecast uncertainty; in their own test case symmetric whitening removes about half the canonical basis's excess error.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
For every matrix size n and number of matrices m, the exact least constant for which the DDVV commutator inequality has a quadratic sum-of-squares proof: the true constant 1 only when n or m is 2, 9/8 for 3 × 3 real symmetric matrices, approaching but never reaching 3; for Hermitian matrices the true constant (4/3, or 1 for two matrices) only when n = 2, m = 2, or m = 3 with n ≤ 7, up to 4 in general.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
3 November 2026
In the fixed-parameter diffusion model with a free, shared nondecision-time distribution, response times determine the split between deciding and everything else exactly when the response-time distributions for the different responses are not all identical; the common unbiased design with opposite, equally strong stimuli never does.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
Mix two noisy copies of a near-Gaussian symmetric signal: the entropy of the blend is guaranteed concave in the mixing weight exactly when the noise variance exceeds three quarters of the signal variance (signal fraction below 4/7, signal-to-noise ratio 4/3); whether 4/7 itself qualifies is open.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
3 November 2026
For a weighted sum of independent exponential or gamma waiting times with its variance fixed, the weights that make the q-th moment smallest climb a staircase (one weight up to q = 5.32, then two, three, … equal weights), proving the Brazitikos–Pandis conjecture for every real q; the largest moment is found too, and for three or more variables the best weights jump.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
A conjectured bound on how strongly a driven Markov ring can oscillate holds for all rates exactly when the ring has three or an even number of states, and fails for every odd ring with five or more states, at every driving strength.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
Every value the matrix geometric mean can approach near a singular pair is described by one rank condition, and the same mechanism gives bounded positive definite GLT sequences with identical symbols whose geometric means have symbol 4/5 instead of 1 on half the interval, refuting a published theorem; the formula is safe exactly when the symbols share no zero region or never overlap.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
With three or more categories the two-category impossibility for simultaneous group homophily disappears; an exact test and a closed-form ceiling with a named binding budget say what is possible, and a school example shows the same 4,600 groups passing for 10/10 classrooms but 0/5 school years.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
3 November 2026
If the source distribution satisfies one Poincaré inequality and the cost's source gradients lie in balls of radius L, every full Sinkhorn iteration shrinks the entropic dual gap by at least the factor C_P L²/(C_P L² + λ²), from the first step and for any target, so about (C_P L²/λ²) log(1/ε) iterations suffice; explicit one-dimensional examples show that the exponent 2 cannot be lowered in general.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
For every count of independent yes/no events with unequal chances, no outcome or event is more likely than under the Poisson law with the same mean by more than the factor mean ÷ variance, proving the 2020 Dümbgen–Wellner conjecture; the factor is not sharp for large means.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
3 November 2026
The worst-case entropy loss of reverse erasure depends only on the rarest symbol, which settles a complete-bipartite conjecture.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
For a population spread over patches with fixed migration, making periodic environmental change faster can never raise the long-run growth rate exactly when migration satisfies detailed balance; any circulating migration admits a weak environment where an intermediate speed is best, and for reversible migration random switching strictly lowers growth, proving a 2025 conjecture.
availability and archiving · internal replay · 5 dimensions not assessed
3 November 2026
Two points maximise one ratio of negative-exponent Riesz capacities on every compact metric space, the regular simplex maximises the reverse ratio in Euclidean space when the smaller exponent is at least 2, and that threshold is exact: below 2, splitting one simplex vertex wins.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
As fractional Brownian motion becomes very rough (Hurst parameter H → 0), √H times its expected maximum on [0, 1] tends to √2, settling a 2022 conjecture; a uniform grid of n points sees half of that maximum once H log n reaches ½.
availability and archiving · internal replay · 4 dimensions not assessed
3 November 2026
For edges of a complete bipartite graph labelled by vectors (for example k colours), some perfect matching lands within 17k of any fractional target in any k-dimensional norm, improving the previous O(k²); order k is necessary for arbitrary targets, and the key step cuts all leftover fractional paths at once.
availability and archiving · internal replay · 5 dimensions not assessed
1 November 2026
Matching a standard Gaussian plane to a standard Gaussian line, the closed-form Gaussian Gromov–Wasserstein answer is 12, but a curved rearrangement that keeps the line exactly Gaussian provably scores below 76/7 ≈ 10.86; the paper shows the Gaussian shortcut is exact if and only if the two spectra are proportional, and is never off by more than a factor of two.
availability and archiving · internal replay · 4 dimensions not assessed
1 November 2026
At or below the tipping point R0 = 1, the average infection level in the standard network SIS model never fades more slowly than 1/(1+t), whatever the network — proving two 2024 conjectures — but exactly at the tipping point network shape matters: the same epidemic takes about 920 recovery times to fall below 0.1% on a small-world network and about 40 on a spatial one.
availability and archiving · internal replay · 5 dimensions not assessed
1 November 2026
A statistics method that is valid if you look once silently fails if you keep checking it as data arrive: recomputed after every new observation, the universal-inference split likelihood-ratio interval has long-run guarantee zero, not 1 − ε, although at 95% the error first exceeds nominal only after about 10⁴ times the first look.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
In the standard circular model of injection-driven slow slip, the slip rate at the injection point decides when the whole fault first stops sliding forward: under stated conditions the centre stops first, almost any abrupt cut ends full sliding, and for a point source no linear taper can halve the rate.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
For m copies of a pure single-mode Gaussian state, no Gaussian measurement beats combining the copies into one bright output and measuring every output by homodyne detection; the exact optimum is a one-angle formula.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
Answering Anderson's 2026 question: when molecules are made in random bursts, only geometric burst sizes stop feedback from making every species quieter than baseline; any other burst law lets a two-species loop do it, by about one part in a million.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
Two simple chemistries that are safe on their own explode once dividing compartments keep the substrate together and export the inhibitor, with no inflow reactions or fusion; the exact thresholds are d + λE[log Q] < b and bλ(1 − EQ) > dc.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
Answering Bosman et al.'s 2022 question: rounding each client's clock events, not its period, to whole days gives delivery calendars that never miss a deadline and cost at most 1/ln 2 ≈ 1.44 times the optimum on trees, improving the factor two; constant-gap calendars can reach only about 1.60.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
Answering a 2022 question: in the logistic patch model, three patches allow exactly five switches between migration helping and harming total biomass, not three; n patches allow between n + 2 and 2ⁿ − 3. The effects are a few parts per million.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
Under the regularity conditions of Xie, Zhu and Shishkin (2025), no range of small sample sizes guarantees that one pooled empirical price beats segmented empirical pricing, for any number of markets.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
31 October 2026
In Tullock contests with convex costs, players who repeatedly move part of the way towards their best reply reach the unique equilibrium even when expensive players drop out, answering the zero-floor question left open by Elkind, Ghosh and Goldberg (2024).
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
31 October 2026
Five orders, two bins: plans (1,2,2) and (2,2,1) both take three trips, but a picker who reoptimises as orders arrive and always takes the remainder first is overwhelmed at about 76% of capacity, while filling the cart first is stable to full capacity; the paper also proves the Lorenz–Otto–Gendreau low-rate conjecture.
availability and archiving · internal replay · 4 dimensions not assessed
31 October 2026
For wide binary stars seen at a random moment from a random direction, the angle between separation and motion has a closed-form likelihood; its distribution determines the population's eccentricity distribution exactly, and simple averages of the angle estimate eccentricity summaries directly.
availability and archiving · internal replay · 4 dimensions not assessed
28 October 2026
One fixed time-asymmetric covariance is shared by Markov models with every positive entropy-production rate, so its Gaussian value, 1/3, is not the lower bound on dissipation that Seara, Machta and Murrell (2021) stated for nonlinear systems.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
28 October 2026
The smallest hidden Markov model that reproduces an exactly known two-level signal can overstate its least possible dissipation: a four-state mechanism produces exactly the same signal as every three-state one yet dissipates strictly less, and a sharp floor holds for any hidden size.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
28 October 2026
A simple cone test rules out Mpemba-type crossings at every time; for bosonic baths with common coupling it holds exactly when the emission weight is concave, so Ohmic and Drude–Lorentz baths pass and super-Ohmic baths can produce a certified crossing.
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
The rescaled eigenvalues of Markov rate matrices do not always fill the affinity-squashed Karpelevich region conjectured by Xu, Kolchinsky, Delvenne and Ito (2025): an integer four-state network escapes it, three states cannot, and on fully connected networks every size from four up fails; the single-cycle case remains open.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
27 October 2026
Answering an open question of Sinha et al. (2025): PnP-ISTA and PnP-ADMM with row-normalised Gaussian kernel denoisers are always stable in dimensions one to three but can diverge from dimension four, by at most about 1.7×10⁻⁵ per iteration; safe steps scale with the mixing gap, and symmetrised denoisers are stable.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
27 October 2026
Storing a random geometric graph with n vertices takes d(1 − μ(Uᵣ)) n log₂ n bits up to O(n), where Uᵣ is the set of positions joined to everyone; this refutes the exact cube coefficient conjectured by Vippathalla, Coon and Badiu for d ≥ 2 and √d/2 < r < √d, and proves their torus conjecture at every radius.
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
In the noisy weighted voter model, a freshly initialised swarm reaches the better decision strictly more often than Conjecture 2 of Ganesh, Hauert and Valla predicts, so the conjecture fails as stated; under the equilibrium start the source simulated, it is exact for a constant favourable rate and is replaced by a mean-quality formula otherwise.
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
Answering Bai and Li's open question: under uniform global dispersal, total population can have any number of peaks as the dispersal rate varies — the peaks are real but tiny, so the result is qualitative.
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
Every ±1 signed Kuramoto network sits exactly inside a network with only positive couplings, with equilibria and stability preserved; this yields a 324-oscillator attractive network whose stable equilibria form a cone over a torus, refuting the closed-manifold and immersed readings of Sclosa's Conjecture 1.3, while its literal arXiv v1 reading is true.
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
For a stationary spectrally negative Lévy process with Poisson resetting, a high maximum in a fixed window leaves the endpoint either just below the peak (no reset yet) or at an ordinary level (reset since), with explicit odds, an explicit total-variation error and the constant left open in Remark 3 of Dębicki, Hashorva and Michna (2026).
availability and archiving · internal replay · 4 dimensions not assessed
27 October 2026
Two conjectured sign rules for heat-current fluctuations in classical thermal networks are false: three states with a rarely visited trap make the third and fourth cumulant ratios arbitrarily negative at fixed thermodynamic data, while variance-based bounds remain intact.
availability and archiving · internal replay · 4 dimensions not assessed
23 October 2026
An exact, closed-form solution of the two-server fluid dispatching problem of Xie, Hyytiä and Righter: small jobs go to the shorter queue, the size cutoff rises as the queues drift apart, and their conjecture that the relative imbalance always grows is proved; seeded simulations of the random system are numerical evidence only.
availability and archiving · internal replay · 4 dimensions not assessed
23 October 2026
As a PageRank walker's weight for stepping straight back is turned up, a vertex score can fall and then rise again, so two cheap scores cannot tell which side the expensive non-backtracking score lies on; a five-vertex house graph refutes Conjectures 3.1 and 3.2 of Glover, Jones, Kempton and Oveson (2026).
availability and archiving · internal replay · 4 dimensions not assessed
23 October 2026
A quantum system reset at independent random times settles, for every gate and reset state, exactly when resets surely recur and are not locked to a lattice, even if the mean time between resets is infinite; imperfect resets reduce to complete ones under a checkable condition, and at the critical power-law hazard settling can take more than a billion steps.
availability and archiving · internal replay · 4 dimensions not assessed
23 October 2026
Standard Padé approximants to a Stieltjes series keep every pole on the branch cut, but Weniger's delta transformation does not: for every Stieltjes measure its denominator is real-rooted at orders one and two, at order three exactly when n + β ≤ (√33 − 5)/2, and from order four never, refuting Borghi's 2026 conjecture.
availability and archiving · internal replay · 4 dimensions not assessed
22 October 2026
Refutes Zuckerman's Conjecture 1.16 (ITCS 2026): explicit cubic and diameter-three graph families on which relative transition errors of size ε with ε·diameter → 0 still slow random-walk hitting times by unbounded factors, because the short routes are rarely used; with a proved resistance bound of 684 on the cubic family and a two-sided robustness bracket on the diameter-three family.
availability and archiving · internal replay · 4 dimensions not assessed
22 October 2026
Integration matrices built on Gaussian nodes for the weight xᵅ[log(1/x)]ᵐ are stable at every size exactly when α ≤ 1 when integrating forward; integrating backward fails for m > 1, and an exact certificate at α = −9/10, m = 1, n = 13 disproves the reverse clause of a 2019 Gautschi–Hairer conjecture as worded.
availability and archiving · internal replay · 4 dimensions not assessed
22 October 2026
A proof of van der Kamp's conjecture that Lotka–Volterra systems built on different trees are never the same equation in disguise: for generic parameters, and with genericity needed on one side only. The proof rests on an exact list of a tree system's invariant planes, which also yields every coordinate system in which the equation keeps its form, closed counts for paths and caterpillars, and a test for recognising a tree system.
availability and archiving · internal replay · 5 dimensions not assessed
22 October 2026
Answers the open question of Balazi, Allaire, Jolivet and Omnes: no fifteen quintics complete a fourth-order moment-based Stokes element on tetrahedra, because the 50 moments satisfy a hidden relation on all quintics; one sextic repairs it, and for every order degree n+2 misses exactly (n−1)(n−2)/2 directions while degree n+3 always works.
availability and archiving · internal replay · 4 dimensions not assessed
22 October 2026
Answers to two open questions of Cominetti, Dose and Scarsini on selfish traffic routing: equilibrium link flows stay smooth while the set of cheapest routes is fixed, even for standard BPR costs, but a new route can switch on with no visible kink in total travel time or the price of anarchy; five links are the minimum for this with a common BPR exponent, and such hidden switches are exceptional.
availability and archiving · internal replay · 5 dimensions not assessed
21 October 2026
A successor to an earlier Evidence Press refutation of the Chan–Crommelin–Mandjes exponential-extinction conjecture: a four-compartment spreading model with both graphs acyclic fades like t^(-3/2) with an exact solution, nothing slower is possible with four compartments, and such slow tails need finely tuned starts and can be ruled out by checkable conditions.
availability and archiving · internal replay · 5 dimensions not assessed
21 October 2026
A conjecture of Garcia, Bermolen, Jonckheere and Shneer on restart-based rare-event simulation holds up to a constant, but the constant is not one (0.850 in their own example), and idealised quasi-stationary restart saturates at budgets of order exp(ηL), far below the range stated in their restart theorem.
availability and archiving · internal replay · 4 dimensions not assessed
21 October 2026
In Gavish and Katriel's model of seasonal control, raising the yearly effort budget never makes it optimal to do less at any time of year; the paper proves this and shows exactly where it stops holding.
availability and archiving · internal replay · 4 dimensions not assessed
21 October 2026
For windowed sinc reconstruction with the sinh and Kaiser–Bessel windows, the error decays fastest exactly when the shape parameter grows like dm, as Kircheis, Potts and Tasche conjectured; over-tuning costs far more than under-tuning, a gap in the general error estimate is corrected, and the published explicit bounds survive.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
21 October 2026
Fixed-size network SIS models admit linear continuation, growing networks do not admit one dimension-free linear factor, and an explicit Hölder bound restores uniform control.
availability and archiving · internal replay · 4 dimensions not assessed
21 October 2026
A forward-only waiting-time statistic conjectured to be a lower bound on the entropy production of periodically driven systems can report dissipation where there is none, and can overstate it by more than 31 per cent (certified) in the very model class where the conjecture was tested.
availability and archiving · internal replay · 4 dimensions not assessed
20 October 2026
A minimal four-state counterexample separates finite total activity from exponential extinction, then identifies the missing trajectory-level spectral condition.
availability and archiving · internal replay · 5 dimensions not assessed
20 October 2026
A complete phase diagram identifies when a finite-catalyst compartment population is conservative and when infinitely many events occur in finite time.
availability and archiving · internal replay · 5 dimensions not assessed
20 October 2026
An exact decomposition gives the sharp averaged comparison-gap coefficient across the full unrelaxed step range and explains why the worst case is usually approached but not attained.
availability and archiving · internal replay · 5 dimensions not assessed
20 October 2026
A positivity-preserving MPRK22 scheme with only positive coefficients can lock into a two-cycle instead of reaching the correct steady state, refuting the natural reading of a 2024 global-stability conjecture.
availability and archiving · internal replay · 4 dimensions not assessed
20 October 2026
Capping the swaps in pass-and-swap queues can trap the system in arrangements the product-form theory excludes: a 2024 conjecture fails for every cap of two or more, exactly on rings of 2kw+1 jobs and beyond, but holds for bipartite swapping graphs with odd caps.
availability and archiving · internal replay · data and environment reproducibility · 4 dimensions not assessed
20 October 2026
In a stationary processor-sharing queue, the lower end of the service distribution determines the heavy-traffic age scale, even when queue populations look identical.
availability and archiving · internal replay · 4 dimensions not assessed
20 October 2026
A division-free tensor identity transfers classical order through six; three explicit extra tests give a conditional criterion at order seven.
availability and archiving · internal replay · 4 dimensions not assessed
19 October 2026
An exact rational certificate proves the sharp order-five rank-three permanent inequality, classifies equality, and yields the sharp two-matrix form.
availability and archiving · internal replay · 5 dimensions not assessed
19 October 2026
Exact certificates exclude two complete graded compression families and a uniform Hessian family, while leaving the global five-dimensional problem open.
availability and archiving · internal replay · 4 dimensions not assessed
18 October 2026
A neuron can rank its assigned meaning well while its thresholded label loses information needed for decisions and edits.
availability and archiving · internal replay · 6 dimensions not assessed
18 October 2026
Equally spaced planar directions are strict local minima for Gaussian minimum moments, even against rank-increasing perturbations, for every n ≥ 3 and p > 1.
availability and archiving · internal replay · 6 dimensions not assessed
18 October 2026
An exact edge-energy criterion separates finite from divergent stationary variance rates, with functional limits and a joint-count covariance extension.
availability and archiving · internal replay · 6 dimensions not assessed
18 October 2026
An explicit three-species mass-action network gains an attracting periodic orbit when one reverse reaction is restored, while the deleted network converges globally.
availability and archiving · internal replay · 5 dimensions not assessed
18 October 2026
Sign-adapted localisation controls continuous-time entropy decay and mixing under strong disorder, without an upper bound on finite field strengths.
availability and archiving · internal replay · 6 dimensions not assessed
18 October 2026
A spectral linear estimator attains asymptotically optimal normalized robust risk with a uniform additive guarantee, and anisotropic jitter can implement it at population level.
availability and archiving · internal replay · 5 dimensions not assessed
18 October 2026
An exact parameter family overturns a proposed coexistence-convergence claim, and a certified local Hopf bifurcation creates attracting cycles.
availability and archiving · internal replay · 6 dimensions not assessed
18 October 2026
An existence classification leaves two all-order boundary counts, certifies them through 51 vertices, and controls explicit probability intervals at every order.
availability and archiving · internal replay · 6 dimensions not assessed
17 October 2026
An unrefereed candidate proves a limiting guarantee for i.i.d. prophet inequalities over time, with certified bounds below the inverse golden ratio.
availability and archiving · internal replay · 5 dimensions not assessed
15 October 2026
A finite convex criterion decides a specified diminishing-returns property for two finite signals and a scalar quadratic prediction target, including impossible signal combinations.
availability and archiving · 5 dimensions not assessed
15 October 2026
An unrefereed mathematical candidate characterises the long-horizon worst-case ratio for every fixed selection budget and certifies a narrow interval near 83.7% for two choices.
availability and archiving · internal replay · 5 dimensions not assessed
15 October 2026
A computer-assisted mathematical candidate proves the predicted switch between Laplace and centred-exponential extremisers, with equality cases and qualitative stability.
availability and archiving · internal replay · 6 dimensions not assessed
15 October 2026
A duration veto can reject a debt contract that pays less at every date; exact certificates expose the conflict and give sharp payment bounds under declared information.
availability and archiving · internal replay · data and environment reproducibility · 5 dimensions not assessed
14 October 2026
In synthetic financial networks, reports can identify a loss together while each gives no worst-case improvement: accounting constraints, the menu, the criterion and noise all matter.
availability and archiving · internal replay · 6 dimensions not assessed
14 October 2026
A candidate near-linear single-site mixing bound covers the full strict field range of a heterogeneous ferromagnetic class, with unrestricted degrees and arbitrary starts.
availability and archiving · internal replay · 5 dimensions not assessed
14 October 2026
An explicit six-generator pair has the same Betti poset over every field, but ideal Stanley projective dimensions three and two; six generators is minimal.
availability and archiving · internal replay · 5 dimensions not assessed
14 October 2026
A candidate entropy proof gives an O(n log n) mixing bound for the original global exchange chain in two strict, source-defined regimes.
availability and archiving · internal replay · 5 dimensions not assessed
14 October 2026
A uniform logarithmic sweep bound removes a minimum-interaction assumption for nonnegative RBMs; an elementary disjoint-edge example shows the order is necessary.
availability and archiving · internal replay · 5 dimensions not assessed
14 October 2026
A fixed smooth circle model has a unique free-energy minimizer, yet unrestricted particle and global nonlinear entropy-dissipation constants remain strictly separated.
availability and archiving · internal replay · 5 dimensions not assessed
13 October 2026
A mixed extra qubit exposes a failure in a proposed entanglement upper bound; exact examples and sharp repairs identify what the statistic can guarantee.
availability and archiving · internal replay · 5 dimensions not assessed
13 October 2026
Exact model bounds show what debt summaries determine—and which missing repayment and funding details prevent a fiscal interpretation.
availability and archiving · internal replay · 5 dimensions not assessed
13 October 2026
A sharp partition theorem, weighted certificates beyond every majority cut, and an exact test for adding a leaf.
availability and archiving · internal replay · 5 dimensions not assessed
13 October 2026
A retained-set construction turns inclusion-link covariance control into scalar concentration, with a proposed mean-sensitive bound for variable-size samples.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
A short symmetry argument proves a weighted fixed-point identity for every Cayley-word length, linking it to classical rank counts.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
Three linked papers certify overpartition congruences and explain infinite towers through exact modular-form structure.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
A ten-vertex obstruction corrects Sun’s circular shifted-product conjecture; an exact sieve and finite replay establish the candidate classification.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
An exact sieve and 53 explicit cycles close the finite remainder of the Sun–Hou ordering conjecture for every finite field with more than seven elements.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
A weighted regrouping proves the next infinite family of theta graphs is e-positive, with exact control of the cancellation boundary.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
Four finite certificates and a complete modulo-eight parameter criterion reveal structured divisibility in two-colour overpartitions.
availability and archiving · internal replay · 5 dimensions not assessed
12 October 2026
The paper behind the August 2026 Wales 20 mph audit: the 28% first-year fall reproduces as a description, but the published totals identify neither the size nor the sign of the policy's effect on the roads that changed.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
An exact computer-assisted candidate closes the dimension-six gap: three classical symbols with free shared randomness simulate every allowed input–output correlation.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
A written-proof candidate recovers a hidden dense set from infection times in a specified random-graph model, while its small pilot records twelve failures.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
For every fixed dimension at least two and noninteger transport power above one, sliced transport uniformly controls full transport on the whole critical moment ball, without a higher-moment or support assumption.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
A uniform written proof excludes two ways of separating an existing family of topological superconductors into simpler factors.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
In one-dimensional long-range percolation with a small tail exponent, the threshold sits above the branching prediction by a two-step return weight, up to a cubic error as the exponent tends to zero; the same criterion handles summable additions and mixtures of tail exponents.
availability and archiving · internal replay · 5 dimensions not assessed
11 October 2026
Heavy-tailed coefficients leave a smooth but genuinely random microscopic distribution of root radii, with contrasting limits as the tail index approaches zero and two.
availability and archiving · internal replay · 5 dimensions not assessed
10 October 2026
A positive weighted construction gives the exact Schur–Agler quotient for every stable symmetric multiaffine polynomial, in every finite dimension.
availability and archiving · internal replay · 5 dimensions not assessed
10 October 2026
Three people can always share up to eight indivisible items under pairwise maximin share fairness; nine is the smallest number of items where it can fail.
availability and archiving · internal replay · 5 dimensions not assessed
10 October 2026
A centred Gaussian and a three-component Gaussian mixture pass every one-dimensional convex-order test, yet an explicit joint convex function separates them.
availability and archiving · internal replay · 5 dimensions not assessed
9 October 2026
An explicit classification gives 11 centrally nilpotent right Bol loops at order eight and p + 10 at every odd prime-cube order, including groups.
availability and archiving · internal replay · 5 dimensions not assessed
9 October 2026
A cyclotomic generating function has strictly positive coefficients, yet its largest parameters break a conjectured ordering—even while every lower-prefix inequality holds.
availability and archiving · internal replay · 5 dimensions not assessed
9 October 2026
For a sufficiently weak repulsive interaction, the ball is the unique energy-minimising shape at fixed volume, up to translation and the stated negligible-set convention.
availability and archiving · 5 dimensions not assessed
8 October 2026
For two yes-or-no signals, four exact inequalities decide whether every partial disclosure preserves a specified diminishing-returns property.
availability and archiving · internal replay · 5 dimensions not assessed
8 October 2026
Any nine indivisible chores can be shared among three agents with a strong fairness guarantee—even when their additive costs disagree and some chores cost nothing.
availability and archiving · internal replay · 5 dimensions not assessed
7 October 2026
Exact rational certificates for how far an optimal transport map on a polygon can move when the coefficients of the comparison potential are only known to lie in a box: a possible-winner envelope valid for every realisation, a proof that its gap is linear in the box radius, and a convergent bisection that brackets the true worst case with a lower bound reached by an explicit realisation.
availability and archiving · internal replay · 5 dimensions not assessed
6 October 2026
A constructive local uniqueness theorem links erosion, diffusion and drainage on nonradial domains, with a separate radial theory and channel audit.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
A smooth, strictly convex body gains four centroidal equilibria under inward curvature flow: 22 become 26.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
A matched elastic interface removes the leading normal–tangential coupling and gives a three-dimensional incremental contact existence theorem—even when lower-order coupling remains.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
Exact conditioning reveals order fluctuations in one random-tree model; a positive prefactor sharpens the branching law in another.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
A minimum-principle argument raises the guaranteed heat loss through the base of an internally heated fluid, with different scaling laws for rigid and stress-free plates.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
Two reticulations can leave exactly the same complete pattern probabilities as a tree—even with continuous-time, transition-biased mutation.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
An exact periodic arrangement of convex cells has harmonic degree 468/115—strictly above the proposed three-dimensional ceiling of four.
availability and archiving · internal replay · 5 dimensions not assessed
5 October 2026
An exact finite exclusion narrows the independence-number interval to 108–112; the precise answer remains open.
availability and archiving · internal replay · 5 dimensions not assessed
4 October 2026
An explicit mass-action realization reaches the positive-equilibrium bound, with a construction in every dimension.
availability and archiving · internal replay · 5 dimensions not assessed
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 gives structural restrictions and finite certificates for Seymour's conjecture, and refutes DeVos's printed strengthening; a dated note addresses the subsequent general-proof claim.
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 candidate computer-assisted proof, released with its full certificate chain, claims to settle the first open case of an Erdős–Gimbel problem.
availability and archiving · internal replay · 6 dimensions not assessed
