Absolutely Maximally Entangled States in Five Open Cases

Five existence statements, all by explicit construction: $\mathrm{AME}(12,5)$ , $\mathrm{AME}(17,11)$ , $\mathrm{AME}(18,11)$ , $\mathrm{AME}(17,13)$ and $\mathrm{AME}(18,13)$ . The $[12,6,7]_{25}$ code came from a direct search with no symmetry imposed; its automorphism group turned out to have a regular $\mathbb{Z}_3^2$ coordinate orbit, and imposing that translation symmetry on two nine-coordinate orbits collapses an unrestricted $9 \times 9$ block to a nine-element kernel, which is what made the length-eighteen searches feasible. The symmetry is search scaffolding, not part of the proof: the three printed matrices and the two checks suffice on their own. The paper is explicit that the searches were not exhaustive, so it proves existence and classifies nothing - equivalence and classification for these parameters stay open. The length-twelve code is also shown not to be monomially equivalent to a generalized Reed-Solomon code.

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proved→proved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Absolutely Maximally Entangled States in Five Open Cases · AME states, five open cases

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Claude Fable 5
model · ai model contributor · Anthropic

ChatGPT 5.6 Sol
model · ai model contributor · OpenAI

Samuel Bevins
human · human collaborator

Yunus Bidav
human · human collaborator

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Named evidence

VibeMathed record: Absolutely Maximally Entangled States in Five Open Cases

specialist registry · passed

This site re-ran the certificate. The paper's logical content is three printed matrices and two checks on each, so verification means doing the checks again - here with field arithmetic built from the printed minimal polynomials and an independent determinant routine, nothing taken from the authors' code. All three matrices satisfy $A\overline{A}^{\mathsf T} = -I_k$ . Every nonempty square minor is nonzero: 923 for the $6 \times 6$ block and 48,619 for each $9 \times 9$ , 98,161 in total, matching the counts the paper states. The nine convolution equations that the paper says are equivalent to self-duality for the group-circulant blocks hold. And the Schur square of the length-twelve code has dimension 12, the paper's own argument that it is not monomially equivalent to a generalized Reed-Solomon code, since every GRS $[12,6]$ code has Schur-square dimension at most 11. The field conventions were checked first: Frobenius is an involution and norms land in the base field. What this does not settle is whether the five cases were open. The reachable copy of the Huber-Wyderka table (last updated February 2024) covers local dimensions up to 10, and $\mathrm{AME}(12,5)$ does sit in its unknown region, but it has no $q=11$ or $q=13$ axis, and the URL the paper cites for a newer version is dead. The paper's prior-art comparisons stand unchecked here.

Source ↗

Huber and Wyderka, Table of AME states - the existence table these cells come from

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Grassl, Tables of linear codes and quantum codes

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problem-record link supplied by the VibeMathed registry.

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Absolutely Maximally Entangled States in Five Open Cases

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

Corrects Absolutely Maximally Entangled States in Five Open Cases →

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Grassl, Tables of linear codes and quantum codes evidence for this event

This event attributed to Samuel Bevins

This event attributed to Yunus Bidav

This event attributed to ChatGPT 5.6 Sol

Absolutely Maximally Entangled States in Five Open Cases evidence for this event

Huber and Wyderka, Table of AME states - the existence table these cells come from evidence for this event

Absolutely Maximally Entangled States in Five Open Cases parent of this event

This event attributed to Claude Fable 5

VibeMathed record: Absolutely Maximally Entangled States in Five Open Cases evidence for this event

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