Paper Citation Record · LEDGER

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend

As of 19 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2607.07939.

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

pith.paper-citation-record.v1
2607.07939 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-10T15:04:27.445849Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T05:36:34.254346Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

verified exact3
verified fuzzy19
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9a55223b-406d-432b-86ca-5c1bfe934e53 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.731307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2d79443f-10eb-4dc1-93f0-8c7b71264ab8 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.742651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 86c4ed0f-9337-4765-8315-6a953daae5e4 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.759004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5a2b8bc0-5d78-4410-bd38-b0a590ff9c4e · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.755845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ffa7d15d-7763-4790-890f-19f8f03e66ad · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.763655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7773afd8-f2e5-4713-a3c9-e146e9ef7aa9 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.757411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 91891a9f-80e8-40f6-a04b-d35400e8e6a0 · outbound

This paper cites Wilkeit, Isometric embeddings in Hamming graphs, J.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Wilkeit, Isometric embeddings in Hamming graphs, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.752804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3a41f308-8ed5-4cf0-ad07-f9c8ae4b6ae6 · outbound

This paper cites Aurenhammer, J.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Aurenhammer, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.754404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 59b3f3c6-1e32-49d8-a4f0-8769759de57c · outbound

This paper cites Imrich, S.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Imrich, S

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.741027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 26820c3e-1eee-4f0b-a09d-b762b0f0d540 · outbound

This paper cites Ovchinnikov, Partial cubes: structures, characterizations, and con- structions, Discrete Math.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Ovchinnikov, Partial cubes: structures, characterizations, and con- structions, Discrete Math

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.744303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 070bed94-69d0-4c13-9135-f4b93c4fe4f1 · outbound

This paper cites Eppstein, The lattice dimension of a graph, European J.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Eppstein, The lattice dimension of a graph, European J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.737814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d3786738-a982-4305-8b7e-54166719f492 · outbound

This paper cites Imrich, S.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Imrich, S

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.739479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 244137ff-c552-44e2-b02b-21d080bb82af · outbound

This paper cites Hammack, W.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Hammack, W

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.746161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a7235951-03c1-4ac3-b0d3-6b00e80e6d68 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.747817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation be9280f3-a358-4626-9c5f-85d674cd6d59 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.749441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 24c2f491-0489-4111-a930-25948fe1ce5b · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.734497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 94f04237-fd6d-4ffb-8f8e-710ef1e5e4f4 · outbound

This paper cites Laurent, Hypercube embedding of distances with few values, in: H.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Laurent, Hypercube embedding of distances with few values, in: H

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.736159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d7dc8903-0f81-4b09-9188-8b9571819619 · outbound

This paper cites Bandelt, V.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Bandelt, V

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.732942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9be0fb06-219a-4958-8d1e-d0bd2ef06fc3 · outbound

This paper cites Bandelt, Retracts of hypercubes, J.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Bandelt, Retracts of hypercubes, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.727938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3230dffc-0491-4ccc-bb9e-262adb97d5b4 · outbound

This paper cites Bandelt, H.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Bandelt, H

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.724678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 93f821b9-a59e-4a80-a091-e93cef293baf · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.726342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 00ffd010-4b09-4bab-b7bc-c199f7f208cf · outbound

This paper cites Factorization and pseudofactorization of weighted graphs.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Factorization and pseudofactorization of weighted graphs

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-07-10T15:07:19.374751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 399b59c9-75eb-4ac0-9b44-b3b5b235c8e9 · outbound

This paper cites Ebrahimi Boroojeni, M.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Ebrahimi Boroojeni, M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.721486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 11d16eea-8b15-484e-8fbc-29a5468e9149 · outbound

This paper cites Green, I.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Green, I

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.723082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f47a0874-873b-4a5e-b928-a57c1062f03e · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.729581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 181b5896-9643-46c2-9bf1-0d49917526ca · outbound

This paper cites Smith Normal Form in Combinatorics.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Smith Normal Form in Combinatorics

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-07-10T15:07:19.371751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation be462e31-d4ed-453b-a873-f8ec8333bc85 · outbound

This paper cites Godsil, G.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Godsil, G

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.718310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 939e24fa-212a-4ce0-9a85-5e004efbfbee · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.711913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aa418bd8-6b08-41c9-9519-4aa9f469d491 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.713550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 98c992ed-9fb5-4d3f-a87b-a53be7041c70 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.715189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2a7a4a92-5b80-4021-8f26-1a4ef7d46260 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.719951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7af4f64e-a2b5-459a-801b-bd6928f85afa · outbound

This paper cites Sandryhaila, J.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Sandryhaila, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.716783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 474c1e34-4e2d-4c67-8615-68cfd75c031e · outbound

This paper cites Ortega, P.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Ortega, P

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.708661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dc80af35-f6be-4d7b-8b50-d408cbea08b1 · outbound

This paper cites an unresolved cited work.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-07-10T15:07:19.710269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6d6f9045-89e2-4742-ad5e-983d7e390080 · outbound

This paper cites Fokam Souop, L.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Fokam Souop, L

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.751091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9f4843d7-5cd7-4ef4-b621-a9e0b3bf41a5 · outbound

This paper cites Fokam Souop, L.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Fokam Souop, L

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.760552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5eaaa011-4d43-4c88-b447-12a9fde4bc46 · outbound

This paper cites Signal Process., 2026.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Signal Process., 2026

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T15:07:19.762097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cf67c885-821b-4599-b743-6e91618ec6b4 · outbound

This paper cites Minimal Isometric Embeddings of Graphs into Abelian Groups: Theory, Algorithms, and Applications to Signal Processing over Networks.

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend Minimal Isometric Embeddings of Graphs into Abelian Groups: Theory, Algorithms, and Applications to Signal Processing over Networks

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-07-10T15:07:19.377418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 5c5fd503-5bd4-41aa-826f-94467c8c7265 · inbound

Harmonic Analysis on Graphs via Isometric Group Embedding: A Canonical Fourier Transform, Shift, and Convolution for Network Signals cites this paper.

Harmonic Analysis on Graphs via Isometric Group Embedding: A Canonical Fourier Transform, Shift, and Convolution for Network Signals Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T05:36:34.254346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a50ae1fd-74a3-479f-854e-be51946658bf · inbound

Tight Wavelet Frames on Graphs via Isometric Group Embedding cites this paper.

Tight Wavelet Frames on Graphs via Isometric Group Embedding Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T04:55:15.689583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.