Paper Citation Record · LEDGER

Quantum chromatic numbers of some graphs in Hamming schemes

As of 23 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2412.09904.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.09904 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T16:45:47.857264Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T11:53:25.757324Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-06-29T12:03:24.501490Z

Reference resolution

18 of 18 outbound references displayed

verified exact1
verified fuzzy12
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 56c90747-3337-4be7-a894-d7ecd0c496c7 · outbound

This paper cites an unresolved cited work.

Quantum chromatic numbers of some graphs in Hamming schemes Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:45:48.151887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d2ab9315-386d-4dae-8fba-2276becb4611 · outbound

This paper cites Cameron, Ashley Montanaro, Michael W.

Quantum chromatic numbers of some graphs in Hamming schemes Cameron, Ashley Montanaro, Michael W

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.137644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9947c06d-45a4-417a-bca6-4e87ec7922ee · outbound

This paper cites Martin, Quantum isomorphism of graphs from association schemes, J.

Quantum chromatic numbers of some graphs in Hamming schemes Martin, Quantum isomorphism of graphs from association schemes, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.122463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 93de7fa0-29bc-4381-9074-941410651f00 · outbound

This paper cites an unresolved cited work.

Quantum chromatic numbers of some graphs in Hamming schemes Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:45:48.106898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 54ca6365-b03f-4d98-a20f-7f61c42b685d · outbound

This paper cites Hebei Normal Uni- versity (Natural Science), 17(5)(2023), 433-446.

Quantum chromatic numbers of some graphs in Hamming schemes Hebei Normal Uni- versity (Natural Science), 17(5)(2023), 433-446

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.092618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 393706f4-9a5b-4f72-87de-b07ccbc2161c · outbound

This paper cites an unresolved cited work.

Quantum chromatic numbers of some graphs in Hamming schemes Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:45:48.077682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation dba942ac-fcc3-4f11-bfbe-6caac0556586 · outbound

This paper cites 674(2023), 351-376.

Quantum chromatic numbers of some graphs in Hamming schemes 674(2023), 351-376

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.063398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e1272c84-2f2d-4740-becb-ffb5932c6ade · outbound

This paper cites I, Graphs Combin.

Quantum chromatic numbers of some graphs in Hamming schemes I, Graphs Combin

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.048901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 545aa8fd-5da5-4c57-a18b-3ed88f0c4665 · outbound

This paper cites Binary Constraint System Games and Locally Commutative Reductions.

Quantum chromatic numbers of some graphs in Hamming schemes Binary Constraint System Games and Locally Commutative Reductions

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T16:45:47.815688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9a8d50e-a86b-446a-a905-d02ccd560481 · outbound

This paper cites Klappenecker, M.

Quantum chromatic numbers of some graphs in Hamming schemes Klappenecker, M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.034481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e45bd6c6-60ff-4fef-9627-6b7d28e1fa84 · outbound

This paper cites Levenshtein, Krawtchouk polynomials and universal b ounds for codes and designs in Hamming spaces, IEEE Trans.

Quantum chromatic numbers of some graphs in Hamming schemes Levenshtein, Krawtchouk polynomials and universal b ounds for codes and designs in Hamming spaces, IEEE Trans

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.018655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8ad9e55d-6f20-487f-a9ee-844c9619c70d · outbound

This paper cites Menamara, ArXiv: 2410.

Quantum chromatic numbers of some graphs in Hamming schemes Menamara, ArXiv: 2410

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:48.002888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 94cfb240-54f7-4e77-a878-354c910392ff · outbound

This paper cites Murty, Ramanujan graphs, J.

Quantum chromatic numbers of some graphs in Hamming schemes Murty, Ramanujan graphs, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:47.987467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a829121d-786d-4af2-a315-b3ef5fa0ecc5 · outbound

This paper cites Nilsen and I.L.

Quantum chromatic numbers of some graphs in Hamming schemes Nilsen and I.L

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:47.972799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d908aacb-31d0-4db6-bf5c-fa5ee4dcdf4e · outbound

This paper cites Peres, Quantum Theory: Concepts and Methods.

Quantum chromatic numbers of some graphs in Hamming schemes Peres, Quantum Theory: Concepts and Methods

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:47.958384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 33324afb-e39c-4f1c-97b7-d65a02d17e29 · outbound

This paper cites Quantum chromatic numbers of products of quantum graphs.

Quantum chromatic numbers of some graphs in Hamming schemes Quantum chromatic numbers of products of quantum graphs

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T16:45:47.848253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34789c67-ce57-45f3-9baf-03b480c45d9a · outbound

This paper cites Steinberg, Representation Theory of Finite Groups: An Int roductory Approach.

Quantum chromatic numbers of some graphs in Hamming schemes Steinberg, Representation Theory of Finite Groups: An Int roductory Approach

Reference 17

Resolution: verified exact; doi, observed 2026-08-11T16:45:47.895061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 47de632c-a495-47c8-a1dd-cc4601358ab5 · outbound

This paper cites Note that if wt(a) = r, we denote by ρn ℓ (r)(= K n ℓ (r)) the eigenvalue of Hn,ℓ corresponding to a.

Quantum chromatic numbers of some graphs in Hamming schemes Note that if wt(a) = r, we denote by ρn ℓ (r)(= K n ℓ (r)) the eigenvalue of Hn,ℓ corresponding to a

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:45:47.942901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 7ef4fa23-feec-41ab-a17b-9e636f9170bd · inbound

Optimization and complexity of inertia-type bounds on the independence and chromatic numbers of graph powers cites this paper.

Optimization and complexity of inertia-type bounds on the independence and chromatic numbers of graph powers Quantum chromatic numbers of some graphs in Hamming schemes

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:51:43.273974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1a2a2a8c-921c-4abc-8aca-b145e5808238 · inbound

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations cites this paper.

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations Quantum chromatic numbers of some graphs in Hamming schemes

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-06-29T12:03:24.502677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.