{"as_of":"2026-08-08T14:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:908626961126cdc53a56ed9cca91c61e6bf06cf8d8a76670df133025e1fed9fc","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T00:30:29.377408Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.26271/citation-record","integrity":"/paper/2607.26271/integrity","json":"/paper/2607.26271/citation-record.json","paper":"/paper/2607.26271"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/rsa.20872(cit","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:57.142925Z","title":"On connectivity, conductance and bootstrap percolation for a random k-out, age-biased graph","venue":null,"work_id":"f648d5d6-ffae-473f-a5ca-5e7e1e28e4a9","year":2020},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.315473Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:8991955c95ba650eb8dc1232372c8f8e0f4035d022398e32edba4306b50c71f7","observation_id":"d1fbee73-a909-44d6-9393-87f98d4f1158","resolution":{"observed_at":"2026-08-01T00:30:57.214491Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:26.403199Z","title":"Coloring graphs with sparse neighborhoods","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.403199Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:2d0534bc6f37b716c93b33b938a252fc4d8f60b1ba91db559680d68f5baaea65","observation_id":"e85bc71f-41df-4e93-be65-3fc4e6a7871e","resolution":{"observed_at":"2026-08-01T00:30:26.403199Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0963548322000104(cit","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.982099Z","title":"Coloring graphs with forbidden bipartite sub- graphs","venue":null,"work_id":"dbed8f95-d629-4065-aa3a-d3bb701ad583","year":2023},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.489045Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:b38b7d7be18919f441a9fac080b531bb112b878674a72dc449bf7fcc334f3316","observation_id":"03162214-5faa-48cd-8547-0719d2e2320b","resolution":{"observed_at":"2026-08-01T00:30:57.129291Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/rsa.20811.url:https://doi.org/10.1002/rsa","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.888983Z","title":"The Johansson-Molloy theorem for DP-coloring","venue":null,"work_id":"3179c32b-0dee-40d3-ad57-b09c7e395665","year":2019},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.575790Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:18d3f91ebc0433455924cea2ea38e2f83b1b5df3642557f4de88a7a14ec398c6","observation_id":"7e419f0d-15e2-404a-bdd6-99c8fad4df6c","resolution":{"observed_at":"2026-08-01T00:30:56.965652Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:26.659572Z","title":"Counting colorings of triangle-free graphs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.659572Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:74b44bb7d4423b22fbfd43e10d3f3e8bf90a93ffdd48cf117f6d34caf2a26164","observation_id":"038a32af-9eba-489d-a9ad-81230b5efa47","resolution":{"observed_at":"2026-08-01T00:30:26.659572Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/rsa.20973.url:https://doi","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.728883Z","title":"Dynamic concentration of the triangle-free process","venue":null,"work_id":"2b3112c3-41a5-4426-892d-8309982662a0","year":2021},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.722230Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:c2e4883d58df7d956915ae716100c718cd70d9a463eda0894f6d266db9734260","observation_id":"59551f3d-24b4-4b26-950b-74813d3b13b0","resolution":{"observed_at":"2026-08-01T00:30:56.864429Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:26.796889Z","title":"Bradaˇ c, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.796889Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:fc83681f14a0a947e9e626a5c67ce993052da04099f5981801f2ac1fdfbb8854","observation_id":"1d20cf2d-caf1-46dd-b038-a85e5c8155ce","resolution":{"observed_at":"2026-08-01T00:30:26.796889Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.16818","last_updated":"2025-09-08T12:49:30Z","snapshot_observed_at":"2026-08-05T17:11:30.711701Z","submitted_at":"2025-08-22T22:37:22Z","title":"Toward Vu's conjecture","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.16818","snapshot_observed_at":"2026-08-01T00:30:26.866426Z","title":"Bradshaw, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.866426Z"},"links":{"cited_paper":"/paper/2508.16818","citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:843401e8f23d953226146ee1134ffb7a1df428ac677f7bd2a6a745f52716e77e","observation_id":"78da1a6b-c977-4034-9d3e-d24c9fa6f4d5","resolution":{"observed_at":"2026-08-01T00:30:26.866426Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:26.903683Z","title":"Campos, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.903683Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:7f988270564fbc2880a7d62f6dd30ca028ac671e2916f162626a429b5ad08484","observation_id":"98523e40-2a18-40fa-9964-1a7c121371c4","resolution":{"observed_at":"2026-08-01T00:30:26.903683Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.14361","last_updated":"2020-03-31T16:42:57Z","snapshot_observed_at":"2026-07-06T09:08:48.961436Z","submitted_at":"2020-03-31T16:42:57Z","title":"Graph structure via local occupancy","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.14361","snapshot_observed_at":"2026-08-01T00:30:27.051185Z","title":"Graph structure via local occupancy","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.051185Z"},"links":{"cited_paper":"/paper/2003.14361","citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:8d29e975f659e8b8b91988dd8bcb528d74ea28e98802bda9d53b17f3fae9e7e8","observation_id":"3ba8d04e-623f-43e0-8c20-2402a03930aa","resolution":{"observed_at":"2026-08-01T00:30:27.051185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2603.17730","last_updated":"2026-04-13T22:28:19Z","snapshot_observed_at":"2026-07-06T22:49:33.482934Z","submitted_at":"2026-03-18T13:54:23Z","title":"Fractional coloring via entropy","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2603.17730","snapshot_observed_at":"2026-08-01T00:30:27.111303Z","title":"Dhawan.Fractional coloring via entropy","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.111303Z"},"links":{"cited_paper":"/paper/2603.17730","citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:fc554cf3193ac879dd1ea4019df01fc882f3899affd5ad5bb1c8d75d219d2f57","observation_id":"821ecb09-fae1-4668-b147-3725af3bf93e","resolution":{"observed_at":"2026-08-01T00:30:27.111303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:27.195735Z","title":"Dhawan, O","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.195735Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:9ef7bc764fbd0313f3b68d34a61aebb93017ac5cb95d954ccc19ba224cc08381","observation_id":"ae46fc08-d555-404f-aa9c-743914d61dcc","resolution":{"observed_at":"2026-08-01T00:30:27.195735Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0963548319000026(cit","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.583340Z","title":"Separation choosability and dense bipartite induced subgraphs","venue":null,"work_id":"722b8678-00e0-41b5-a352-859926a1d517","year":2019},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.256675Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:c19e87810cba829785731dac5ed0a6eb6aae75496be5e64cb30e278689c5468d","observation_id":"aa7101d0-8e13-4cd3-830c-2bc6026bf1f3","resolution":{"observed_at":"2026-08-01T00:30:56.720512Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/memo/1274.url:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.494173Z","title":"The triangle-free process and the Ramsey number R(3, k)","venue":null,"work_id":"920d6ede-eb3c-42e5-ba43-96d825f3994d","year":2020},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.336187Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:cfbd30bc08e1bbe594ee167256c29028176b1a9409d1a6523a21a8a4af57c8de","observation_id":"662e5f0c-37c0-4bbe-b552-72bb26b941f8","resolution":{"observed_at":"2026-08-01T00:30:56.569120Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/rsa.20778.url:https://doi.org/10.1002/rsa.20778(cit","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.348978Z","title":"Perfect matchings and Hamiltonian cycles in the preferential attachment model","venue":null,"work_id":"b9beb4ee-b1f6-467f-b1f7-c1c359328d0f","year":2019},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.423107Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:074e4e6671f00c2f195656bc50f4f4f7c2498e9cc24c1f02d09a155f2cd2875d","observation_id":"2e32554c-1b6d-4c21-ba97-8319facc772d","resolution":{"observed_at":"2026-08-01T00:30:56.490514Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:27.580287Z","title":"On the independence and chromatic numbers of random regular graphs","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.580287Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:a93be8d868d3dc10e4381addf877403a6162a159e15b2f177ec8ac550309fb8a","observation_id":"735435c4-874f-4080-a408-3ec509063f11","resolution":{"observed_at":"2026-08-01T00:30:27.580287Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/17m115918x.url:https:","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.169718Z","title":"Some results on chromatic number as a function of triangle count","venue":null,"work_id":"f61a3d0d-5e3c-4ade-b328-02da1bc2f828","year":2019},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.693633Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:50e5c6e0e5a6dc32646cc7fc448fe7bdf3df11bdeea5e13ae69f369e922bd99a","observation_id":"778ce0b7-a79c-4af6-a169-73c22bd87b19","resolution":{"observed_at":"2026-08-01T00:30:56.312888Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:27.758044Z","title":"Hefty, P","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.758044Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:9b954ad8d377a899611526b98e218cefe1455f0ef556b3622d63ea1d8aaf0a18","observation_id":"08285408-3729-4f48-a400-447115a9513e","resolution":{"observed_at":"2026-08-01T00:30:27.758044Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:27.851536Z","title":"Uniformly random colourings of sparse graphs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.851536Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:997dd3735173c10c10cb95fe4513640dab0bc476f54c40983ae7e52c340ef9b3","observation_id":"62b0942d-0580-4279-a746-b491d1cd6dd5","resolution":{"observed_at":"2026-08-01T00:30:27.851536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:27.945309Z","title":"Johansson.Asymptotic choice number for triangle free graphs","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:27.945309Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:a241a12b759b82fd21d1956a327d4a0a79b8ff29c8653f790d68a1067fea9e88","observation_id":"54718058-09f8-4ada-ada1-4423734e14c0","resolution":{"observed_at":"2026-08-01T00:30:27.945309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:28.060156Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.060156Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:2579c84ef65548eb63ad7de9d17a797b24f36d3fcb8103a500fc895b62ea7b0e","observation_id":"80a5477c-e980-4c96-9b1d-cb0d3a17fe49","resolution":{"observed_at":"2026-08-01T00:30:28.060156Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0963548300001528.url:https://doi.org/10.1017/s0963548300001528","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:56.096505Z","title":"On Brooks’ theorem for sparse graphs","venue":null,"work_id":"32f8748d-7854-4872-8ea1-c13eff793e3a","year":1995},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.205814Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:d1e938bfcc2acfd46e9323cd702f3f2a5b9957b7794542c59d4beb84d53d5362","observation_id":"3b9f1fc8-3154-440a-806d-73461adb2c36","resolution":{"observed_at":"2026-08-01T00:30:56.160550Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:28.389253Z","title":"γ-variable first-order logic of uniform attachment random graphs","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.389253Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:d5d8f6e07a4950b7971605a45c4725989c380ef455943d9d6d60e99eb069a8fd","observation_id":"afe76488-99d7-4b87-ad0f-9c8fde063fd9","resolution":{"observed_at":"2026-08-01T00:30:28.389253Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:28.497804Z","title":"Random independent sets in triangle-free graphs","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.497804Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:71a6038f6ae1c157379c39324732a0fb0a3bc9d123c0e704606cb61ffb9e1e09","observation_id":"74005da2-0b6b-4367-808d-f7726d983d47","resolution":{"observed_at":"2026-08-01T00:30:28.497804Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:28.610295Z","title":"Mitzenmacher and E","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.610295Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:5c73883c9d951fbac66475a2a52bbdbd5b5d8078ccd660e8e4171fdb60b79782","observation_id":"8df59f38-2d25-493b-b68e-d527adc44eb1","resolution":{"observed_at":"2026-08-01T00:30:28.610295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2018.06.007.url:https://doi.org/10","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:55.964178Z","title":"The list chromatic number of graphs with small clique number","venue":null,"work_id":"acd41264-9a02-4e0f-9193-89ab4aa29c64","year":2019},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.733974Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:ecbf72656cbdd3dc885faa62b9740a80a4260546c5c5ed2b832145ed908df074","observation_id":"95e7ea50-3b51-44aa-8c03-0bda743f0b5a","resolution":{"observed_at":"2026-08-01T00:30:56.080314Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:28.906736Z","title":"Molloy and B","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:28.906736Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:7430347e1004222a44f3d2e4456c2eb595b06a2fc278d0c69c21a41fef694254","observation_id":"25a518b5-669f-4642-b527-b2bc0a49469d","resolution":{"observed_at":"2026-08-01T00:30:28.906736Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:29.083573Z","title":"The spectral density of Hardy kernel matrices","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:29.083573Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:f40e23398cdb2c738bd08c1723a0f2ca4c1d60bf71c395ba20ed6e3e2220469b","observation_id":"ca1804f4-26f2-47ad-95bf-113bb87b1a6a","resolution":{"observed_at":"2026-08-01T00:30:29.083573Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0012-365x(83)90273-x.url:https://doi.org/","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:55.772353Z","title":"A note on the independence number of triangle-free graphs","venue":null,"work_id":"6853d87a-55cb-4da1-8d1d-3541d3fba6d9","year":1983},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:29.200727Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:2b59efc6ba65e15c573971300a103191041a3d1579e49c242b9964319c75dea6","observation_id":"ea667817-d85c-4ca3-a5a6-e5387477c3d4","resolution":{"observed_at":"2026-08-01T00:30:55.843549Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/cbo9781139871495(cit","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:30:55.604508Z","title":null,"venue":null,"work_id":"fb8ac494-694e-4982-951f-973599993838","year":2015},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:29.377408Z"},"links":{"citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:df322e429696c5651598de1d0c4c0099803b4000faad21b1927b54a202de0e18","observation_id":"cdabec45-5a7a-44df-9266-998b348a7e11","resolution":{"observed_at":"2026-08-01T00:30:55.673305Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.10026","last_updated":"2023-12-15T18:46:48Z","snapshot_observed_at":"2026-07-06T17:03:02.786273Z","submitted_at":"2023-12-15T18:46:48Z","title":"A new lower bound for sphere packing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.10026","snapshot_observed_at":"2026-08-01T00:30:26.989506Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-01T00:30:26.989506Z"},"links":{"cited_paper":"/paper/2312.10026","citing_paper":"/paper/2607.26271"},"observation_digest":"sha256:6b2e263b18673fa8536920a5fee3fa1774bee737bb7c96880d0d96c869129fb9","observation_id":"bfc1164f-c9ee-43de-849d-405453be8264","resolution":{"observed_at":"2026-08-01T00:30:26.989506Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.26271","last_updated":"2026-07-28T21:02:45Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T00:27:01.146926Z","submitted_at":"2026-07-28T21:02:45Z","title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":6,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":11,"verified_fuzzy":0},"total_outbound_references":31},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2607.26271."}