Library

Correction round · released August 14, 2026
D. Kirtchakov, Independence-claim round: every “shares no code” sentence in the corpus measured against the files it describes. A checker is only worth what its independence from the thing it checks is worth, and this program had asserted that independence in prose without ever measuring it. Every such sentence was tested by clone detection — verbatim line overlap, longest identical run, syntax-tree equivalence under renaming, shared string literals, and an import scan — and twelve of them, across eight deposited papers, were false. In the worst case the checker for a published upper bound ran the same dynamic program that produced the bound, so it could not have detected an error in it; that number was then recomputed by a different method and matched exactly, as rationals, at all five certificates. No certified value, theorem, certificate, or checker logic changed anywhere in the round. The corrections state what is shared and what independence survives, rather than withdrawing the claim. Two sentences written by this round were themselves false and were caught by its own gates before release. corrections index · doi:10.5281/zenodo.21933031

Correction round · released August 13, 2026
D. Kirtchakov, Documentation-correction round: every released part's prose re-derived against its own artifacts. No certified value changed and no checker's verification logic changed; every checker passes as before and every mathematical result of Parts A through M stands. What changed is documentation — artifact inventories listing files the deposit does not contain, replay instructions that did not run as written, counts and labels contradicted by the shipped artifacts, and several claims the artifacts refute. Found by cross-examining every build-log decision against the prose of its own paper, then by seven independent gates; nine blockers in all, six of them written by the passes repairing earlier findings. The index is generated from the diff, not written. corrections index · doi:10.5281/zenodo.21922469

Note · released August 12, 2026
D. Kirtchakov, Certified ZEFOZ brackets for ¹⁶⁷Er³⁺:Y₂SiO₅: existence, curvature and stationary-point type of every published clock transition, 8 pp. For each of the twenty published nonzero-field ZEFOZ points of a leading quantum-memory platform, across both crystallographic sites: transition brackets of width 4×10⁻¹⁰ MHz, a certified gradient bound, two-sided brackets on all three eigenvalues of the frequency Hessian with certified signature, and Krawczyk existence and local uniqueness of an exact stationary point within 2.9×10⁻¹⁴ mT of the stated field. The completeness question is reported dead under a pre-registered kill condition, with the measured statistics that fired it. Three errata in the reference are documented and versioned. PDF · certificates · prior-art record · doi:10.5281/zenodo.21898996

Note · released August 12, 2026
D. Kirtchakov, Certified demagnetization-tensor reference tables, and where double-precision micromagnetics loses its digits, 7 pp. Two-sided rational enclosures of the Newell tensor entries that every finite-difference micromagnetic simulator evaluates, computed in outward-rounded interval arithmetic. Against them the naive double-precision evaluation is measured rigorously: about six correct decimal digits lost per decade of cell separation, no correct significant figure near 300 cells, and at ten thousand cells a value of the wrong sign and nine orders of magnitude too large. The breakdown radius is mapped for fifty geometry and component pairs. Erratum v0.12.1 (August 12) corrects the gold-value anchor sentence from containment to agreement — the enclosures are far tighter than the 50-digit check values, so agreement with the midpoints to at least 49.6 digits is the certified statement; no enclosure, certificate or checker changed. PDF · certificates · prior-art record · doi:10.5281/zenodo.21910159

Note · released August 12, 2026
D. Kirtchakov, The exact logical error probability of the rotated surface code under a lookup-table decoder, 7 pp. A character-sum identity over the syndrome space returns the complete spectrum of uncorrectable fault sets in a single pass, replacing the two-sided bracket of the August 11 note with the exact rational value of the logical error probability at distances 3 and 5. The weight-7 enumeration barrier that the earlier note named as its own frontier is removed for these configurations; the exact values fall strictly inside the published brackets, at 0.36 and 0.51 of their widths. PDF · certificates · prior-art record · doi:10.5281/zenodo.21898343

Note · released August 12, 2026
D. Kirtchakov, The extremal graph for k(3,4) = 21 is not unique: thirteen rigid witnesses and a forced Paley tournament, 4 pp. Question 8.1 of the August 11 note is answered in the negative. There are at least thirteen pairwise non-isomorphic oriented graphs on twenty vertices containing neither three mutually non-adjacent vertices nor four in transitive order, and every one of them is rigid, admitting only the identity automorphism. In any such graph a vertex has at most seven non-neighbours, and one with exactly seven has its non-neighbourhood equal to the Paley tournament on seven vertices. PDF · certificates · prior-art record · doi:10.5281/zenodo.21898266

Note · released August 12, 2026
D. Kirtchakov, Kelmans' 1984 problem on 3-vertex path packings in cubic 3-connected graphs, verified to 22 vertices, 10 pp. Every 3-connected cubic graph on at most 22 vertices — all 6,339,157 of them — admits the packing Kelmans conjectured in 1984, together with the applicable strong forms of his equivalence theorem. To our knowledge the first recorded computational verification of the problem at any order. Two pipelines sharing no code agree on every count; 43,580 certificates re-verify from graph6 strings by standard-library checkers. PDF · certificates · prior-art record · doi:10.5281/zenodo.21897011

Note · released August 11, 2026
D. Kirtchakov, Certified sub-threshold logical error rates: exact uncorrectable-set counts and a two-sided rational bracket for the rotated surface code, 7 pp. A quantum error-correcting code's failure rate in the low-noise regime that matters for real devices is too rare to measure by simulation — an industry group recently described it as not amenable to direct Monte Carlo. This note computes the exact integer counts of uncorrectable fault patterns and converts them into a guaranteed two-sided bound on the logical error probability, in exact arithmetic, re-derivable by a standard-library checker. Deep sub-threshold the certified bracket is far tighter than a 10⁷-shot Monte Carlo interval (about 18,500× at distance 3, 626× at distance 5). The bound is stated for the independent-mechanism noise model and a fixed lookup-table decoder, not the physical circuit. PDF · certificates & checker · prior-art record · doi:10.5281/zenodo.21895825

Note · released August 11, 2026
D. Kirtchakov, An Erdős–Rado oriented Ramsey number determined: k(3,4) = r(I₃,L₄) = 21, by explicit witness and certified exhaustion, 10 pp. A previously unknown value in Erdős Problem #112, where the published bounds were 9 ≤ k(3,4) ≤ 25: an explicit 20-vertex witness together with a 346-case LRAT-certified exhaustion at 21 vertices, completeness independently audited, every certificate replayed by a standard-library checker; the from-definition generator ships, so the chain is reproducible without trusting the authors' encodings. From the same campaign, 29 ≤ k(6,3) ≤ 33, the lower bound new. Ramsey-type values are permanent entries of the combinatorial record; the contribution is foundational. PDF · certificates · prior-art record · doi:10.5281/zenodo.21890619 · arXiv identifier to follow.

Note · released August 6, 2026
D. Kirtchakov, An explicit 5×25 circular Florentine rectangle establishing F_c(25) ≥ 5, 5 pp. An explicit array of five permutations of {0,…,24} in which every ordered pair at every circular distance is realized exactly once (3000 events, the maximum possible), verified exhaustively by a self-contained standard-library checker; exceeds the lower bound of 4 recorded in Table 62.27 of the Handbook of Combinatorial Designs, 2nd ed. (2006). No priority is claimed over H.-Y. Song's 2000 paper, which we could not access. Florentine rectangles arise in the design of frequency-hopping sequences for multiple-access radio, where the defining property bounds worst-case interference between transmitters. PDF · object & verifier · prior-art record · doi:10.5281/zenodo.21831896 · arXiv identifier to follow.

Note · released August 6, 2026
D. Kirtchakov, A bond-dimension-2 matrix-product state that is an exact zero-energy eigenstate at every length of the periodic chain H = −Σᵢ(I+Xᵢ)(Xᵢ₊₁+Zᵢ₊₁), 7 pp. The eigenstate property holds at every system size, proved by a sixteen-equation integer telescoping certificate (matrix-product-ansatz technique of Derrida–Evans–Hakim–Pasquier 1993, credited) and independently re-verified in exact arithmetic; the state has growing sublattice Schmidt rank. No claim is made about the remainder of the spectrum. Exact eigenstates of constrained chains of this type are studied as solvable reference points in the physics of thermalization and glassy relaxation. PDF · object & verifiers · prior-art record · doi:10.5281/zenodo.21832028 · arXiv identifier to follow.

Note · released August 5, 2026
D. Kirtchakov, The minimum number of arc-disjoint transitive triples in a tournament: a first certified determination of ν₃(9) = 9 and ν₃(10) = 12, 8 pp. First certified determination of both values, confirming Yuster's 2004 formula at n = 9, 10 and extending the verified range from n ≤ 8, by certified lower bounds over all 191,536 + 9,733,056 tournament isomorphism classes with replayable optimality certificates, modulo one declared trust assumption (complete enumeration by nauty's gentourng, count-validated; see the note, §4); upper-bound constructions due to Yuster (2004), credited. The quantity is a basic extremal invariant of tournaments; the contribution is foundational, with no application claimed. PDF · certificates · prior-art record · doi:10.5281/zenodo.21816010 · arXiv identifier to follow.

Note · released August 5, 2026
D. Kirtchakov, If a [[14,3,5]] stabilizer code exists, its monomial automorphism group has order 2ᵃ3ᵇ5ᶜ, 9 pp. A certificate-backed exclusion of automorphism orders divisible by 7, 11, 13 for the [[14,3]] distance-5 existence question, open since 2005 (codetables.de); every nonzero symmetry class closed with pinned certificates and an exact-rational LP lemma. The existence question itself remains open; the CSS case is Koh et al., arXiv:2601.20927, credited. The [[14,3]] entry is the smallest unresolved case in the standard tables from which quantum error-correcting codes are selected; settling it either yields a better small code or a new impossibility. PDF · certificates · prior-art record · doi:10.5281/zenodo.21816018 · arXiv identifier to follow.

Preprint · released August 5, 2026
D. Kirtchakov, Replayable minimum-distance certificates for stabilizer codes, 22 pp. Certified distances for eleven codes through IBM's bivariate-bicycle family, with no solver and no proof assistant in the trusted base. Revised August 6 (v0.2.1): the interval 14 ≤ d ≤ 18 for [[288,12,18]] is closed to d = 18 exactly — the first machine-checkable determination of that code's distance, confirming the value asserted by Bravyi et al. by integer programming — together with a first lower bound 16 ≤ d for [[360,12,≤24]]. The codes and asserted values are IBM's, credited. A code's minimum distance is the number that determines how many physical faults it can correct — a load-bearing parameter of quantum hardware roadmaps, here made independently checkable for the first time. PDF · certificates · prior-art record · doi:10.5281/zenodo.21831995 (v0.2.1; the superseded v0.2.0 record is doi:10.5281/zenodo.21799780) · arXiv identifier to follow.

Preprint · released August 5, 2026
D. Kirtchakov, Degree minimality in the equivariant class of the Alpöge Keller map, and the moment-map structure of its cotangent lift, 20 pp. Proves degree 7 minimal in the map's symmetry class (strengthening Shaska, arXiv:2607.20210, Thm 10.10), with a no-go lemma and a moment-map identity; Dixmier/Poisson witnesses due to W. G. P. Mayner, credited. The equivariant reduction, the master equation, the S₃ cover and the image theorem were obtained independently but are anticipated by Shaska, by the anonymous ulam.ai note, and by Mayner; the Dixmier-witness route and the erratum are ours. The Jacobian conjecture is among the oldest open problems of algebraic geometry; this work is foundational, and no application is claimed. Erratum v0.1.2 (August 6) corrects the Theorem D fiber count over {Δ₂ = 0} from two to three distinct points; no other statement was affected — see the erratum. PDF · repository & certificates · prior-art record · doi:10.5281/zenodo.21799112 · arXiv identifier to follow.

Repository · public
certify — one repository holding every body of work listed above under a single method: each claim maps to a certificate a skeptic can replay without trusting the tool that produced it. Among the forms in use: Gröbner unit-ideal certificates; LRAT proofs replayable in pure Python; exhaustive sweeps with optimality certificates; exact-rational LP lemmas; graph6 packing witnesses; outward-rounded interval enclosures. github.com/05oz/certify — each result ships as a tagged release carrying its certificates, its checkers and a dated prior-art sweep, most also carrying an independent adversarial audit log.