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Paper Citation Record · LEDGER

Quantum chromatic numbers of some graphs in Hamming schemes

As of 12 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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.776898Z digest=sha256:649096a7b33fbb70bf31a70699be9680f29fe5adf5ef20865f25e3111e18d672

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.781977Z digest=sha256:75e70e3b4d5b6a5a8461401a6eb79b182dd3a838cb87eff24a3bfc1637921439

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.786815Z digest=sha256:3d44e4e5ad2650ae0fb5a1523a4ff4446a45acdd9d025966da13b2b18118b429

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.791608Z digest=sha256:4092458136b6a490fc6616d03cf93b1c113826ce663ce2545ac00bcaf3c9d2f1

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.796288Z digest=sha256:bd22da5f7fb0153094ad56420ee3b2ae8fbdbc51dcc723cf06fb44c7dd46c11b

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.801362Z digest=sha256:cb093dc62feb8d101600beea207eb93fa1b0db945a2f1f5488befa6e13a53293

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.806465Z digest=sha256:cf97916af7fde49f5a0b3fdfece58f13b3ebe11c71e27a286c94afa2abc2af80

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.811244Z digest=sha256:7a95cb214a70c67235d741449fa82a9a2bc2cc489243227784e890fc716b7273

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.

source=pdf_text observed=2026-08-11T16:45:47.815688Z digest=sha256:f74cd70e20aa3208170908607f3aa04b5de06903563a2183dd059ddaf1735fa5

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.820854Z digest=sha256:f7d2a11ba9a85c9360aec0705a07fb593d7696febfd014c6f36c4166ba41e775

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.825289Z digest=sha256:e448c5f09b00cea9223c60b80625d8524c67c74d062b166407255d1cc200d744

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.829917Z digest=sha256:15183abba76caa15c3be707d783fcc18d44a690614059cf4adc5dd5c2154d407

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.834565Z digest=sha256:55013c646a59ebc467c155fd59bf895a1832ecdb4c74f630de5c8461afe1d328

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.839448Z digest=sha256:3129567d819c3fba1470dcf72f9113c4560cb25a8a2aa910f86fb90cc3784841

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.843972Z digest=sha256:e898f7c913158a8fc99c808328a66e9d4dcb278280b6cdef4517539770c6bce5

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.

source=pdf_text observed=2026-08-11T16:45:47.848253Z digest=sha256:f0a4a11b9ba0683ec3182363b469f8839fdc94b848fbbac15a517bedcba1cd60

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.852845Z digest=sha256:d9b0cf54be2c0dacd49969766205a6e3f1f875cab723db19dd13e52283c717da

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T16:45:47.857264Z digest=sha256:ba76670ab055c06582623b82ec37c52f765deaae4c4aa153b12eb8143f457fbf

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-09T19:08:25.325226Z digest=sha256:e3968106d00e55563b189334a84c652f9654523fd712afaf5223fc7192af938b

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-29T11:53:25.757324Z digest=sha256:b4c9f5143db509b0ee8de0e4e52d005c2f97d2b504c0949e328a3811a21f8aea