finite.works: releases

An explicit nonlocal game of quantum value one that needs exponential entanglement, version 1.1.0

2026-11-02T07:05:16Z

Version 1.1.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23878232. Adds a formal verification in Lean 4: Theorem A, conditional on the published implication from perfect tensor-product strategies, and Theorems C, D, E and F, with only the standard axioms. The release was rebuilt from scratch and replayed by two independent kernel checkers. The mathematics is unchanged.

Band edges of the almost Mathieu operator at Liouville scales, version 2.0.0

2026-11-02T06:12:18Z

Version 2.0.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23877075. Adds the other side of the Liouville threshold: for 0 < x < 1 the gap-decay rate satisfies ρ ≤ 1 − x, and with the theorem of Liu and Shi, 1/C ≤ ρ ≤ 1 − x for 0 < x ≤ 2/C. New sections and appendices give the proof; the Numerical Record gains three independent checks, archived with their code and certified outputs in the release's verification folder.

Houghton’s group H₃ has superpolynomial sofic profile, version 1.2.0

2026-11-02T04:44:50Z

Version 1.2.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23875978. Adds a sweep form of the counting criterion: a quadratic Dehn function for H3, or a quadratic bound for block coherence, would give a lower exponent of 1/2, matching the upper exponent up to a logarithm. The unconditional bounds are unchanged, and the open problem is sharpened.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.2.0

2026-11-02T04:44:46Z

Version 1.2.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23875973. Adds a sweep form of the counting criterion; for the dyadic lamplighter of Section 8.1 the lower bound rises from exp(c r1/3) to exp(c r1/2). The discussion of Thompson’s groups cites the recent soficity preprint of Chaudkhari, Juschenko and Muliarchyk (arXiv:2610.25415), on which the soficity of the subgroup L relies.

Where the quantum capacity sits in the arithmetical hierarchy, version 1.0.0

2026-11-02T04:37:22Z

Version 1.0.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23875900.

Worst-case transport and light cones for quasi-periodic operators, version 2.0.0

2026-11-02T04:28:23Z

Version 2.0.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23875774. The worst-case law of the almost Mathieu operator is now exact for every finite β = βe greater than (log λ)/2 (version 1.0.0: at least log λ), with a new proof in new sections and appendices.

Band edges of the almost Mathieu operator at Liouville scales, version 1.0.0

2026-11-02T01:16:55Z

Version 1.0.0, archived on Zenodo, 2 Nov 2026. DOI 10.5281/zenodo.23873797.

Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic, version 1.0.3

2026-11-02T01:16:49Z

Version 1.0.3, archived on Zenodo, 1 Nov 2026. DOI 10.5281/zenodo.23873781. Records an independent rebuild and kernel replay of the Lean formalization, attaches the PDF to the Zenodo record, and makes two wording changes (the scope of Kaplansky's Problem 6; the universe of the fields in the Lean statement). No mathematical statement changes.

Exact transport and spectral dimensions for the almost Mathieu operator, version 2.0.1

2026-11-01T17:40:00Z

Version 2.0.1, archived on Zenodo, 1 Nov 2026. DOI 10.5281/zenodo.23864352. The phase set of Jitomirskaya, Liu and Tcheremchantsev is contained in the paper's, with proof; Remark 9.11's table corrected; precision fixes and two citation locators.

Exact transport and spectral dimensions for the almost Mathieu operator, version 2.0.0

2026-11-01T00:00:00Z

Version 2.0.0, archived on Zenodo, 1 Nov 2026. DOI 10.5281/zenodo.23848977. Theorem B strengthened (almost all of the packet moves); a larger phase set; a correction to the outer-barrier lemma.

Worst-case transport and light cones for quasi-periodic operators, version 1.0.0

2026-10-31T20:54:20Z

Version 1.0.0, archived on Zenodo, 31 Oct 2026. DOI 10.5281/zenodo.23845228.

Universality of the transport law for supercritical quasi-periodic operators, version 1.0.0

2026-10-31T06:08:09Z

Version 1.0.0, archived on Zenodo, 31 Oct 2026. DOI 10.5281/zenodo.23830333.

Exact transport and packing dimension for the almost Mathieu operator, version 1.0.0

2026-10-31T06:06:46Z

Version 1.0.0, archived on Zenodo, 31 Oct 2026. DOI 10.5281/zenodo.23830305.

A finite game that normal hyperfinite strategies approach but never win, version 1.0.0

2026-10-30T19:00:00Z

Version 1.0.0, archived on Zenodo, 30 Oct 2026. DOI 10.5281/zenodo.23816141.

Galilean Covariance Almost Fixes the Quantum Probability Current

2026-10-30T18:00:00Z

Archived on Zenodo, 30 Oct 2026. DOI 10.5281/zenodo.23815695.

Finitely presented infinite p-groups for every prime, version 1.0.1

2026-10-30T04:06:09Z

Version 1.0.1, archived on Zenodo, 30 Oct 2026. DOI 10.5281/zenodo.23791059. Correction: Credit: a “Note added” in the introduction cites Kenta Kitamura’s independent, concurrent work (manuscript 13 October 2026, Lean 16 October 2026), which also proves the every-prime result; in the paper’s words, “the extension to every prime listed above is shared with it.”

The price of keeping time, version 1.1.1

2026-10-30T03:54:19Z

Version 1.1.1, archived on Zenodo, 30 Oct 2026. DOI 10.5281/zenodo.23790746. Correction: Version 1.1.0 said, in the batch-law appendix, that a minimizing Y need not exist. The infimum is attained (Rockafellar, Convex Analysis, Theorem 28.2). No result depended on the sentence.

Finite games that read the type of a von Neumann algebra, version 1.0.0

2026-10-30T00:50:43Z

Version 1.0.0, archived on Zenodo, 30 Oct 2026. DOI 10.5281/zenodo.23787124.

A beginning is worth one limit: robust unlearnable laws in noisy cellular automata, version 1.0.0

2026-10-29T22:03:59Z

Version 1.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23782039.

Uncomputable critical exponents, version 2.1.0

2026-10-29T21:10:01Z

Version 2.1.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23780285. Correction: Packaging: version 2.0.0 stored text files with line-ending conversion, so some checksum-manifest entries did not verify from a fresh clone. Version 2.1.0 stores files byte for byte.

The price of unreachable perfection: dimension laws at every regular scale, version 1.0.1

2026-10-29T18:14:29Z

Version 1.0.1, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23774171. Correction: Packaging: version 1.0.0 omitted the recorded check outputs listed in its checksum manifests, and one manifest entry was stale. The paper is unchanged.

Perfect play in a binary-scoring nonlocal game requires infinite dimension but only finite energy, version 2.0.0

2026-10-29T17:40:52Z

Version 2.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23772890. Correction: Packaging: versions 1.0.0 and 1.1.0 omitted the recorded outputs of the finite checks. Version 2.0.0 includes them.

Matter that pays the price of perfection, version 1.0.0

2026-10-29T16:42:55Z

Version 1.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23771444.

Uncomputable critical exponents, version 2.0.0

2026-10-29T07:21:35Z

Version 2.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23757361.

Perfect play in a binary-scoring nonlocal game requires infinite dimension, version 1.1.0

2026-10-29T06:52:16Z

Version 1.1.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23756753.

Perfect play in a binary-scoring nonlocal game requires infinite dimension, version 1.0.0

2026-10-29T05:15:35Z

Version 1.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23754447.

The price of unreachable perfection: dimension laws at every regular scale, version 1.0.0

2026-10-29T04:56:44Z

Version 1.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23754199.

Uncomputable finite-size gap exponents, version 1.0.0

2026-10-29T04:36:49Z

Version 1.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23753840.

The uncomputable price of precision, version 4.0.0

2026-10-29T04:31:05Z

Version 4.0.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23753741.

The price of precision: usable entanglement in nonlocal games and the geometry of groups, version 1.1.0

2026-10-29T04:09:23Z

Version 1.1.0, archived on Zenodo, 29 Oct 2026. DOI 10.5281/zenodo.23753349.

The uncomputable price of precision, version 3.0.0

2026-10-28T15:59:40Z

Version 3.0.0, archived on Zenodo, 28 Oct 2026. DOI 10.5281/zenodo.23736188.

The thermodynamics of deadlines: one law for the work cost of acting in time, version 1.0.0

2026-10-28T03:31:42Z

Version 1.0.0, archived on Zenodo, 28 Oct 2026. DOI 10.5281/zenodo.23719180.

The uncomputable price of precision, version 2.0.0

2026-10-28T01:59:31Z

Version 2.0.0, archived on Zenodo, 28 Oct 2026. DOI 10.5281/zenodo.23717986.

A nonlocal game whose dimension exponent is uncomputable, version 1.0.0

2026-10-27T19:47:12Z

Version 1.0.0, archived on Zenodo, 27 Oct 2026. DOI 10.5281/zenodo.23701734.

The heat price of precision, version 1.0.0

2026-10-27T19:47:10Z

Version 1.0.0, archived on Zenodo, 27 Oct 2026. DOI 10.5281/zenodo.23701732.

The price of precision: usable entanglement in nonlocal games and the geometry of groups, version 1.0.0

2026-10-27T17:07:29Z

Version 1.0.0, archived on Zenodo, 27 Oct 2026. DOI 10.5281/zenodo.23697346.

An explicit nonlocal game of quantum value one that needs exponential entanglement, version 1.0.0

2026-10-27T17:00:10Z

Version 1.0.0, archived on Zenodo, 27 Oct 2026. DOI 10.5281/zenodo.23697255.

Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic, version 1.0.2

2026-10-26T18:42:03Z

Version 1.0.2, archived on Zenodo, 26 Oct 2026. DOI 10.5281/zenodo.23673698. Correction: A sentence of the introduction attributed the zero-divisor conjecture to all cubulated groups; Agol’s theorem gives it for cubulated hyperbolic groups. No mathematical statement changes.

The Resource Theory of Complexness References in Real Quantum Networks, version 1.0.4

2026-10-18T19:04:54Z

Version 1.0.4, archived on Zenodo, 18 Oct 2026. DOI 10.5281/zenodo.23457692. Correction: A remark expected asymptotic equivalence at rate one; it is false, because the unit reference copies itself exactly. Version 1.0.4 adds the exact-replication lemma and corrects the remark.

Finitely presented infinite p-groups for every prime, version 1.0.0

2026-10-15T16:53:32Z

Version 1.0.0, archived on Zenodo, 15 Oct 2026. DOI 10.5281/zenodo.23401291.

The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs, version 1.2.1

2026-10-14T17:58:52Z

Version 1.2.1, archived on Zenodo, 14 Oct 2026. DOI 10.5281/zenodo.23375704. Correction: Credit added to Oufkir, Yao and Berta for the data-processing inequality behind non-signalling simulation, and to Wang and Duan (2018); Shariat, Hoogsteder-Riera and Tomamichel are described as giving an alternative proof. Section 1.1 said “the first three” terms of the Duan–Winter chain are radii, which would have included S_NS; corrected. A verification section that printed a number matching no statement of the paper is removed.

Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic, version 1.0.1

2026-10-14T16:50:09Z

Version 1.0.1, archived on Zenodo, 14 Oct 2026. DOI 10.5281/zenodo.23374592. Correction: Version 1.0.0 gave the author order wrongly. Version 1.0.1 lists Nidhal Mghirbi, Seth Douglas.

Non-soficity of OpenAI's torsion-free hyperbolic group, version 1.1.0

2026-10-14T16:31:07Z

Version 1.1.0, archived on Zenodo, 14 Oct 2026. DOI 10.5281/zenodo.23374284. Correction: Alongside new results: the note of Sandhu and Thom is described correctly and credited with its authors; Ivanov (arXiv:2610.17662) is credited for torsion-free zero divisors in odd characteristic; credit added for Ozawa and Pestov, Kun, Kun and Thom, Elek and Szabó, Alon, Hall, Knauer, Pinchasi and Yuster, and others; a corollary now states only its new part. The non-soficity argument is unchanged.

Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic, version 1.0.0

2026-10-14T16:29:33Z

Version 1.0.0, archived on Zenodo, 14 Oct 2026. DOI 10.5281/zenodo.23374264.

Non-soficity of OpenAI's torsion-free hyperbolic group, version 1.0.1

2026-10-13T15:33:29Z

Version 1.0.1, archived on Zenodo, 13 Oct 2026. DOI 10.5281/zenodo.23345877. Correction: Incomplete credit in version 1.0.0. Version 1.0.1 cites Chapman and Peled’s conditional construction, Soulé’s torsion bound and Thom’s independent note based on Sandhu’s construction. No mathematical change.

The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs, version 1.2.0

2026-10-12T23:50:24Z

Version 1.2.0, archived on Zenodo, 13 Oct 2026. DOI 10.5281/zenodo.23328355.

The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs, version 1.1.1

2026-10-12T23:42:44Z

Version 1.1.1, archived on Zenodo, 13 Oct 2026. DOI 10.5281/zenodo.23328240. Correction: Credit and precision, after an attribution audit and a referee audit that found no false result: θ0 = θ is credited to Schrijver (as Dalai’s Theorem 8), to Duan and Winter, and to Cabello, Severini and Winter; Wang and Duan’s answer to Duan and Winter’s question, Vrana’s continuum on C5 in the ordinary spectrum, Li and Zuiddam, and others are credited; a figure caption’s witness radius had been rounded in the unsafe direction. No theorem changes.

Order, not speed: the work price of letting go, version 1.1.0

2026-10-12T20:24:13Z

Version 1.1.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23325747.

The price of keeping time, version 1.1.0

2026-10-12T20:23:30Z

Version 1.1.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23325723.

Order, not speed: the work price of letting go, version 1.0.0

2026-10-12T18:24:20Z

Version 1.0.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23323809.

The price of keeping time, version 1.0.2

2026-10-12T17:31:39Z

Version 1.0.2, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23323046.

The work cost of answering in real time, version 1.0.2

2026-10-12T17:31:38Z

Version 1.0.2, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23323045.

Only quantum channels save work by waiting, version 1.0.2

2026-10-12T17:31:37Z

Version 1.0.2, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23323044.

The price of time order, version 1.0.2

2026-10-12T17:31:36Z

Version 1.0.2, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23323043. Correction: The four thermodynamics papers of 11 October cited Thompson et al. with a DOI that did not resolve. Version 1.0.2 of each paper gives the correct DOI, 10.1103/dryx-l5rt.

The price of keeping time, version 1.0.1

2026-10-12T06:03:45Z

Version 1.0.1, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310740.

The work cost of answering in real time, version 1.0.1

2026-10-12T06:03:43Z

Version 1.0.1, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310737.

Only quantum channels save work by waiting, version 1.0.1

2026-10-12T06:03:42Z

Version 1.0.1, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310736.

The price of time order, version 1.0.1

2026-10-12T06:03:38Z

Version 1.0.1, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310735.

The price of keeping time, version 1.0.0

2026-10-12T05:55:23Z

Version 1.0.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310633.

The work cost of answering in real time, version 1.0.0

2026-10-12T05:55:20Z

Version 1.0.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310629.

Only quantum channels save work by waiting, version 1.0.0

2026-10-12T05:55:17Z

Version 1.0.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310625.

The price of time order, version 1.0.0

2026-10-12T05:55:15Z

Version 1.0.0, archived on Zenodo, 12 Oct 2026. DOI 10.5281/zenodo.23310623.

No algorithm can tell how much memory a repeated quantum channel needs, version 1.1.0

2026-10-07T05:46:05Z

Version 1.1.0, archived on Zenodo, 7 Oct 2026. DOI 10.5281/zenodo.23204398.

Non-soficity of OpenAI's torsion-free hyperbolic group, version 1.0.0

2026-10-07T03:59:59Z

Version 1.0.0, archived on Zenodo, 7 Oct 2026. DOI 10.5281/zenodo.23202475.

No algorithm can tell how much memory a repeated quantum channel needs, version 1.0.0

2026-10-06T23:23:30Z

Version 1.0.0, archived on Zenodo, 7 Oct 2026. DOI 10.5281/zenodo.23199341.

The memory and purity cost of immediate delivery, version 1.0.0

2026-10-06T22:38:03Z

Version 1.0.0, archived on Zenodo, 7 Oct 2026. DOI 10.5281/zenodo.23198907.

Factorizable Rational Quantum Channels at an Explicit Distance from Finite Tracial Baths, version 2.0.0

2026-10-06T19:49:41Z

Version 2.0.0, archived on Zenodo, 6 Oct 2026. DOI 10.5281/zenodo.23196593.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.1.2

2026-10-02T22:33:38Z

Version 1.1.2, archived on Zenodo, 3 Oct 2026. DOI 10.5281/zenodo.23111927. Correction: Credit added in the introduction: Gromov and Weiss; OpenAI’s announcement, Fournier-Facio, and Kun and Thom on non-sofic groups; Slofstra and Vidick, and Slofstra; Arzhantseva and Cherix; and work on channel simulation, memory costs and collision models.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.1.1

2026-10-02T18:32:41Z

Version 1.1.1, archived on Zenodo, 2 Oct 2026. DOI 10.5281/zenodo.23108312. Correction: Precision: a step in an appendix’s Choi-rank count is corrected (the bound is unchanged), and a set of coefficients is corrected from {±1, ±2^−1/2} to {1, ±2^−1/2}.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.1.0

2026-10-02T16:59:07Z

Version 1.1.0, archived on Zenodo, 2 Oct 2026. DOI 10.5281/zenodo.23107117.

A rational quantum channel beyond finite tracial baths, version 1.0.0

2026-10-02T02:53:01Z

Version 1.0.0, archived on Zenodo, 2 Oct 2026. DOI 10.5281/zenodo.23093839.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.0.2

2026-09-30T21:30:26Z

Version 1.0.2, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23070871. Correction: Credit made precise: Cornulier’s dichotomy and his facts on local embeddability, Lee’s Dehn function, Johnson’s presentation, and Brown, Brin, and Hennig and Matucci for finite presentation are cited where they are used, as are the lemmas taken from the companion papers.

Causal quantum-channel simulation: memory beyond entropy, version 1.1.2

2026-09-30T21:30:18Z

Version 1.1.2, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23070870. Correction: Credit and scope: that the cost vanishes on the closure of finite tracial factorizations is credited to the closed-device preprint, and this paper proves the converse; “polynomial memory at every exchange rate” is scoped to purity limited to O(log n); Watrous is credited for a relative-interior fact.

Houghton’s group H₃ has superpolynomial sofic profile, version 1.1.2

2026-09-30T21:30:10Z

Version 1.1.2, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23070869. Correction: Credit made precise: Cornulier’s linear lower bound and bounded cases, Lee’s reduction of the Dehn function, Elek and Szabó’s construction, Arzhantseva and Cherix, Röver, and the known birational consequences are credited where they are used; Slofstra’s earlier chunk is described exactly, with its exponent, near 1/4, larger than ours. The mathematics is unchanged.

The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs, version 1.1.0

2026-09-30T16:57:39Z

Version 1.1.0, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23066485. Correction: Version 1.0.0 stated that both pentagon geometries in Figure 4 are nonoptimal throughout 0 < α < 1/2; the displayed bounds do not show this. Version 1.1.0 states only the proved regimes. The package also corrects a SHA-256 digest in the certificate README.

Causal quantum-channel simulation: memory beyond entropy, version 1.1.1

2026-09-30T16:19:30Z

Version 1.1.1, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23065791.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.0.1

2026-09-30T16:19:01Z

Version 1.0.1, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23065778.

Houghton’s group H₃ has superpolynomial sofic profile, version 1.1.1

2026-09-30T16:18:23Z

Version 1.1.1, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23065750.

Amenable groups with nearly exponential sofic profile, and quantum channels that need nearly linear memory, version 1.0.0

2026-09-30T02:24:41Z

Version 1.0.0, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23050303.

Causal quantum-channel simulation: memory beyond entropy, version 1.1.0

2026-09-29T23:58:18Z

Version 1.1.0, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23048998.

Houghton’s group H₃ has superpolynomial sofic profile, version 1.1.0

2026-09-29T23:49:42Z

Version 1.1.0, archived on Zenodo, 30 Sep 2026. DOI 10.5281/zenodo.23048875.

Causal quantum-channel simulation: memory beyond entropy, version 1.0.0

2026-09-29T01:08:25Z

Version 1.0.0, archived on Zenodo, 29 Sep 2026. DOI 10.5281/zenodo.23027627.

Houghton’s group H₃ has superpolynomial sofic profile, version 1.0.0

2026-09-29T01:08:23Z

Version 1.0.0, archived on Zenodo, 29 Sep 2026. DOI 10.5281/zenodo.23027625.

The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs, version 1.0.0

2026-09-26T22:02:46Z

Version 1.0.0, archived on Zenodo, 27 Sep 2026. DOI 10.5281/zenodo.22983499.

How much dimension does an epsilon-approximation to a non-attained quantum correlation cost? A Diophantine answer for K_5, version 1.0.2

2026-09-24T17:53:46Z

Version 1.0.2, archived on Zenodo, 24 Sep 2026. DOI 10.5281/zenodo.22944181. Correction: An open lemma of versions 1.0.0 and 1.0.1 conjectured that marginal drift δ costs δ^−1/2. It is false: an explicit two-block carrier has deficit exactly zero with drifted marginals. Version 1.0.2 proves the cost Θ(min(ε^−1/4, δ^−1/4)).

Bath dimension and initial entropy for closed repeated use of a quantum channel, version 1.1.0

2026-09-16T07:00:14Z

Version 1.1.0, archived on Zenodo, 16 Sep 2026. DOI 10.5281/zenodo.22788806. Correction: A displayed lower bound, 0.045566, had been rounded up from 0.0455659970, and a growth remark failed at r = 0. Version 1.1.0 uses a stronger exact witness and restates the remark.

Closed Mixed-Apparatus Compression of Schur Channels: Exact-Approximate Separation and Scheduled Delivery, version 1.0.0

2026-09-16T04:51:40Z

Version 1.0.0, archived on Zenodo, 16 Sep 2026. DOI 10.5281/zenodo.22785669.

Bath dimension and initial entropy for closed repeated use of a quantum channel, version 1.0.0

2026-09-15T22:51:20Z

Version 1.0.0, archived on Zenodo, 16 Sep 2026. DOI 10.5281/zenodo.22779673.

Quantum recovery from finitely many sharp questions, version 1.0.0

2026-09-15T22:51:17Z

Version 1.0.0, archived on Zenodo, 16 Sep 2026. DOI 10.5281/zenodo.22779671.

Observable Quantum Equilibrium under Controlled Measurements

2026-09-15T00:00:00Z

Archived on Zenodo, 15 Sep 2026. DOI 10.5281/zenodo.22778741.

The Clean Two-Query Threshold for Unitary Synthesis, version 1.0.4

2026-09-14T04:09:22Z

Version 1.0.4, archived on Zenodo, 13 Sep 2026. DOI 10.5281/zenodo.22740995.

The I3322 quantum value is attained spatially but not in finite dimension, version 4.1.0

2026-09-10T23:33:22Z

Version 4.1.0, archived on Zenodo, 11 Sep 2026. DOI 10.5281/zenodo.22698978. Correction: Proof correction to version 4.0.0. The lower bound had identified paired components without justification; it now uses a weighted flow over all retained edges. The limiting-weld justification, an endpoint-gap constant, the spatial amplitude notation, the mixed-state argument and two upper-rate constants were also corrected. Concurrent independent work by Pauwels and by Coladangelo is credited. The main statements and the upper coefficient are unchanged.

Alternating Bellman–Jacobi duality for three-setting binary Bell functionals

2026-09-10T00:00:00Z

Archived on Zenodo, 10 Sep 2026. DOI 10.5281/zenodo.22688911.

Critical Bellman–Jacobi dynamics for reversible Bell functionals

2026-09-10T00:00:00Z

Archived on Zenodo, 10 Sep 2026. DOI 10.5281/zenodo.22688831.

How much dimension does an epsilon-approximation to a non-attained quantum correlation cost? A Diophantine answer for K_5, version 1.0.1

2026-08-25T15:43:35Z

Version 1.0.1, archived on Zenodo, 25 Aug 2026. DOI 10.5281/zenodo.22099141. Correction: Credit: version 1.0.0 said that Coladangelo’s embezzlement proof of non-closure (arXiv:1904.02350) comes with no rate; its abstract states an explicit dimension lower bound, 2^Ω(ε^−1/8). The priority statement is now scoped to the K5 witness. The theorem and constants are unchanged.

The I3322 quantum value is attained spatially but not in finite dimension, version 4.0.0

2026-08-25T15:42:32Z

Version 4.0.0, archived on Zenodo, 25 Aug 2026. DOI 10.5281/zenodo.22099128. Correction: Alongside merging the rate note into the paper: Theorem (S) restated with its locality constraint, which the earlier statement did not formally require; the orbit structure of Section 4 corrected; Pál and Vértesi’s conjecture positioned against their paper; the minimality argument completed; the priority claim for the rate narrowed and sourced; an endpoint-mass bound stated correctly; one displayed constant corrected from 0.9197272 to 0.91972725.

The Resource Theory of Complexness References in Real Quantum Networks, version 1.0.3

2026-08-13T04:05:27Z

Version 1.0.3, archived on Zenodo, 13 Aug 2026. DOI 10.5281/zenodo.21911918. Correction: Packaging: the verification suite of version 1.0.2 had a machine-local import path and a missing module, so it did not run from a clean clone. Version 1.0.3 repairs it and scopes a footnote to Corollary 7.3 to the surviving sector.

The Resource Theory of Complexness References in Real Quantum Networks, version 1.0.2

2026-08-13T03:38:08Z

Version 1.0.2, archived on Zenodo, 13 Aug 2026. DOI 10.5281/zenodo.21911717. Correction: The general clause of Corollary 7.3 was false for arbitrary frame codes; explicit counterexamples are given. The corollary now states the exact alignment and disjointness condition, and the guarantee for the target pair is unaffected.

The Frame Bus: Exact Amplification and Catalysis of Complexness References in Real Quantum Networks, version 1.0.0

2026-08-13T01:55:26Z

Version 1.0.0, archived on Zenodo, 13 Aug 2026. DOI 10.5281/zenodo.21911081.

The Resource Theory of Complexness References in Real Quantum Networks, version 1.0.1

2026-08-12T23:12:15Z

Version 1.0.1, archived on Zenodo, 13 Aug 2026. DOI 10.5281/zenodo.21910329. Correction: Version 1.0.0 called the accounting of the auxiliary descent unit-neutral at best; the paper’s own protocol is nondemolition, so each descent is net positive and catalytic. The corollary is corrected; no other statement is affected.

The Resource Theory of Complexness References in Real Quantum Networks, version 1.0.0

2026-08-12T16:33:01Z

Version 1.0.0, archived on Zenodo, 12 Aug 2026. DOI 10.5281/zenodo.21907063.

Critical Bellman–Jacobi dynamics for reversible Bell functionals

2026-08-12T00:00:00Z

Archived on Zenodo, 12 Aug 2026. DOI 10.5281/zenodo.21910041.

Exact rational certification of upper and lower quantum bounds for the 𝐼3322 Bell inequality

2026-08-11T00:00:00Z

Archived on Zenodo, 11 Aug 2026. DOI 10.5281/zenodo.21891897.

A repair price for contextuality, and its identity with Min-Rep, version 1.0.0

2026-08-10T17:26:30Z

Version 1.0.0, archived on Zenodo, 10 Aug 2026. DOI 10.5281/zenodo.21876901.

How much dimension does an epsilon-approximation to a non-attained quantum correlation cost? A Diophantine answer for K_5, version 1.0.0

2026-08-10T17:26:30Z

Version 1.0.0, archived on Zenodo, 10 Aug 2026. DOI 10.5281/zenodo.21876899.

Alternating Bellman–Jacobi duality for three-setting binary Bell functionals, version 1.0.0

2026-08-10T00:00:00Z

Version 1.0.0, archived on Zenodo, 10 Aug 2026. DOI 10.5281/zenodo.21879016.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.3.0

2026-08-07T19:48:41Z

Version 3.3.0, archived on Zenodo, 7 Aug 2026. DOI 10.5281/zenodo.21843326.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.2.3

2026-08-06T16:20:23Z

Version 3.2.3, archived on Zenodo, 6 Aug 2026. DOI 10.5281/zenodo.21826916. Correction: A fresh audit of the version 3.2.2 corrections found nine items, all fixed: the Mghirbi reference corrected to the right record, the 2018 attribution weakened to what the source says, other citations repaired, and stale withdrawn claims removed from the README and citation metadata. Nothing mathematical changed.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.2.2

2026-08-06T04:08:16Z

Version 3.2.2, archived on Zenodo, 6 Aug 2026. DOI 10.5281/zenodo.21817385. Correction: After three adversarial audits of the resolution paper: retitled to the statement it proves; two false decimal bounds fixed; credit added for N. Mghirbi’s earlier exact enclosures and for an implication in Dykema, Paulsen and Prakash (2018); the minimality claim scoped; attributions, definitions and bibliography corrected. The theorems are unchanged.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.2.1

2026-08-06T02:34:04Z

Version 3.2.1, archived on Zenodo, 6 Aug 2026. DOI 10.5281/zenodo.21816638. Correction: Packaging: version 3.2.0 shipped the resolution paper, but a tooling slip dropped the README and metadata edits that go with it. Version 3.2.1 restores them.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.2.0

2026-08-06T02:32:34Z

Version 3.2.0, archived on Zenodo, 6 Aug 2026. DOI 10.5281/zenodo.21816625.

The I3322 quantum value: certified window, spatial attainment, finite-dimensional nonattainment, and the Cqs/Cq separation, version 3.1.0

2026-08-05T22:09:36Z

Version 3.1.0, archived on Zenodo, 6 Aug 2026. DOI 10.5281/zenodo.21814777.

The I3322 quantum value: certified window, finite-dimensional nonattainment, and nonclosure of Cq(3,3;2,2), version 3.0.0

2026-08-05T20:39:43Z

Version 3.0.0, archived on Zenodo, 5 Aug 2026. DOI 10.5281/zenodo.21813360.

The I3322 quantum value: a certified two-sided window and correction record, version 2.0.0

2026-08-05T00:57:37Z

Version 2.0.0, archived on Zenodo, 5 Aug 2026. DOI 10.5281/zenodo.21799071. Correction: Versions 1.0.0 to 1.2.0 withdrawn. Our own exact audit after release found a nonzero mismatch in the construction behind their claims; both computation engines had inherited the same transcribed step. A rebuilt proof followed as version 3.0.0.

A rigorously characterized I3322 quantum wall, spatial attainment, and finite-dimensional nonattainment, version 1.2.0

2026-08-04T01:20:35Z

Version 1.2.0, archived on Zenodo, 4 Aug 2026. DOI 10.5281/zenodo.21782750.

A rigorously characterized I3322 quantum wall and finite-dimensional nonattainment, version 1.1.0

2026-08-04T00:50:09Z

Version 1.1.0, archived on Zenodo, 4 Aug 2026. DOI 10.5281/zenodo.21782527.

A rigorously characterized I3322 quantum wall and finite-dimensional nonattainment, version 1.0.0

2026-08-03T23:46:51Z

Version 1.0.0, archived on Zenodo, 4 Aug 2026. DOI 10.5281/zenodo.21782009.

Proof-carrying exact quantum bounds for the I3322 Bell inequality

2026-07-21T00:00:00Z

Archived on Zenodo, 21 Jul 2026. DOI 10.5281/zenodo.21477901.

Proof-Carrying Exact Bounds for the I3322 Bell Inequality, version 2.0.0

2026-07-20T00:00:00Z

Version 2.0.0, archived on Zenodo, 20 Jul 2026. DOI 10.5281/zenodo.21462892.

The Relativistic Necessity of the Born Rule: Uniqueness from Poincaré Symmetry and Dynamical Preservation

2025-11-09T00:00:00Z

Archived on Zenodo, 9 Nov 2025. DOI 10.5281/zenodo.17580489.

The Relativistic Necessity of the Born Rule: Uniqueness from Symmetry and Dynamics

2025-09-18T00:00:00Z

Archived on Zenodo, 18 Sep 2025. DOI 10.5281/zenodo.17153429.