Paper Citation Record · LEDGER

Improved lower bounds for the Shannon capacity of odd cycles

As of 8 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:2607.21517.

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

pith.paper-citation-record.v1
2607.21517 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T07:17:10.846036Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T00:05:40.061043Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

17 of 17 outbound references displayed

verified exact0
verified fuzzy0
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 47a68f9e-506d-488b-8aae-23c888229b4c · outbound

This paper cites The Shannon capacity of a graph and the independence numbers of its powers.IEEE Transactions on Information Theory, 52(5):2172–2176, 2006.

Improved lower bounds for the Shannon capacity of odd cycles The Shannon capacity of a graph and the independence numbers of its powers.IEEE Transactions on Information Theory, 52(5):2172–2176, 2006

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.344909Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdc0382b-7a8e-4bee-b279-5fb2e40e3027 · outbound

This paper cites A combinatorial packing problem.

Improved lower bounds for the Shannon capacity of odd cycles A combinatorial packing problem

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.427567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b439689d-c1eb-43f4-bb04-224ab48c7bbe · outbound

This paper cites A limit theorem for the Shannon capacities of odd cycles I.Proceedings of the American Mathematical Society, 131(11):3559–3569, 2003.

Improved lower bounds for the Shannon capacity of odd cycles A limit theorem for the Shannon capacities of odd cycles I.Proceedings of the American Mathematical Society, 131(11):3559–3569, 2003

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.486262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1ac3a0f-3b17-4d97-ab0c-cc1030f62488 · outbound

This paper cites On the inde- pendence numbers of the cubes of odd cycles.The Electronic Journal of Combinatorics, page P10, 2013.

Improved lower bounds for the Shannon capacity of odd cycles On the inde- pendence numbers of the cubes of odd cycles.The Electronic Journal of Combinatorics, page P10, 2013

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.564995Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2098612f-3f71-47a0-954a-1e3e5d97b4e3 · outbound

This paper cites Some remarks on the Shannon capacity of odd cycles.Ars Combinatoria, 66:243–258, 2003.

Improved lower bounds for the Shannon capacity of odd cycles Some remarks on the Shannon capacity of odd cycles.Ars Combinatoria, 66:243–258, 2003

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.623193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7727ef33-45b1-4a06-bd00-5a26bd359f48 · outbound

This paper cites The asymptotic spec- trum distance, graph limits, and the Shannon capacity.arXiv preprint arXiv:2404.16763, 2024.

Improved lower bounds for the Shannon capacity of odd cycles The asymptotic spec- trum distance, graph limits, and the Shannon capacity.arXiv preprint arXiv:2404.16763, 2024

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.758222Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d388c7f-d26c-48e9-b0ad-79527da148a2 · outbound

This paper cites Linear Shannon capacity of Cayley graphs.

Improved lower bounds for the Shannon capacity of odd cycles Linear Shannon capacity of Cayley graphs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.846491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8c4e2e1-b9cd-45ee-bfa0-cb609d9374b0 · outbound

This paper cites Cliqueishardtoapproximatewithin n1−ε.Acta Mathematica, 182(1):105–142, 1999.

Improved lower bounds for the Shannon capacity of odd cycles Cliqueishardtoapproximatewithin n1−ε.Acta Mathematica, 182(1):105–142, 1999

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:09.987641Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69fae594-fef9-4f7f-95ec-88d7e52509b2 · outbound

This paper cites Advances in the Shannon capacity of graphs.

Improved lower bounds for the Shannon capacity of odd cycles Advances in the Shannon capacity of graphs

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.131326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dcfb4874-6d1f-4f35-a7b5-46f3ce92d6aa · outbound

This paper cites On the Shannon capacity of a graph.IEEE Transactions on Information theory, 25(1):1–7, 1979.

Improved lower bounds for the Shannon capacity of odd cycles On the Shannon capacity of a graph.IEEE Transactions on Information theory, 25(1):1–7, 1979

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.266217Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b62cb53d-a054-4c5b-834a-f158501f95e1 · outbound

This paper cites New lower bounds for the Shannon capacity of odd cycles.Designs, Codes and Cryptography, 84(1):13– 22, 2017.

Improved lower bounds for the Shannon capacity of odd cycles New lower bounds for the Shannon capacity of odd cycles.Designs, Codes and Cryptography, 84(1):13– 22, 2017

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.387356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a2ad0a6-936d-4acd-be39-1873e21a7370 · outbound

This paper cites New lower bound on the Shannon capacity of C7 from circular graphs.Information Processing Letters, 143:37– 40, 2019.

Improved lower bounds for the Shannon capacity of odd cycles New lower bound on the Shannon capacity of C7 from circular graphs.Information Processing Letters, 143:37– 40, 2019

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.465714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 367eb8ef-1340-4b78-90ac-c16eb144fcdf · outbound

This paper cites Mathemati- cal discoveries from program search with large language models.Nature, 625(7995):468–475, 2024.

Improved lower bounds for the Shannon capacity of odd cycles Mathemati- cal discoveries from program search with large language models.Nature, 625(7995):468–475, 2024

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.545803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f218138-a712-4ec1-bb41-59768e675d55 · outbound

This paper cites Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems.

Improved lower bounds for the Shannon capacity of odd cycles Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.629745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ceafe3e2-042c-429a-9f11-f6bf4adfa218 · outbound

This paper cites The zero error capacity of a noisy channel.IRE Transac- tions on Information Theory, 2(3):8–19, 1956.

Improved lower bounds for the Shannon capacity of odd cycles The zero error capacity of a noisy channel.IRE Transac- tions on Information Theory, 2(3):8–19, 1956

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.709694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59c60cd4-b504-4844-a373-c73fe44a4d4d · outbound

This paper cites Improved lower bound on the Shannon capacity of C7.Information processing letters, 81(5):277–282, 2002.

Improved lower bounds for the Shannon capacity of odd cycles Improved lower bound on the Shannon capacity of C7.Information processing letters, 81(5):277–282, 2002

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.769945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bf3c529-5ba0-44fb-a133-6046adb07f8c · outbound

This paper cites $X$-evolve: Solution space evolution powered by large language models.

Improved lower bounds for the Shannon capacity of odd cycles $X$-evolve: Solution space evolution powered by large language models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T07:17:10.846036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation ec526226-364e-4a2b-8b8d-934c67a303cc · inbound

A Recursive Construction Improving the Lower Bound on the Shannon Capacity of $C_7$ cites this paper.

A Recursive Construction Improving the Lower Bound on the Shannon Capacity of $C_7$ Improved lower bounds for the Shannon capacity of odd cycles

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T00:05:40.061043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.