{"as_of":"2026-08-09T06:53:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b4e1756d44cc8b48960326dc77a1ef93b3e2a048fe630d893397b1da926ba54f","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T16:55:15.764733Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2607.17895/citation-record","integrity":"/paper/2607.17895/integrity","json":"/paper/2607.17895/citation-record.json","paper":"/paper/2607.17895"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T16:55:15.711471Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.711471Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:ac2ec3f6900ab0323b5628f2140f62ae1673950f22a349cc8dbed7eb325e1f47","observation_id":"eeb0a15f-61a6-47c8-9315-456d747a95e1","resolution":{"observed_at":"2026-08-01T16:55:15.711471Z","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":"2026-08-01T16:55:15.715221Z","title":"Angel, J","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.715221Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:0a41120b944f85b2adb24518f55b77a0304fb5e7ec49e3c1ec896c95ae14c39b","observation_id":"e4867c5a-86bd-413f-95d1-0ca854e9558d","resolution":{"observed_at":"2026-08-01T16:55:15.715221Z","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":"2026-08-01T16:55:15.717902Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.717902Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:aaf25a83b55c6e43adf5e826a663241b8932fb48fb7432146ecb737f3b6f3065","observation_id":"96f763b3-07bb-4d4c-8124-c928b90c392b","resolution":{"observed_at":"2026-08-01T16:55:15.717902Z","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":"2026-08-01T16:55:15.720468Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.720468Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:81d2faafcda1c4159149dbf003c4269720f3b9ebe355e7fdd83a14c1edcd4fcd","observation_id":"6f62a635-09f9-4c31-b739-146bc5e58e81","resolution":{"observed_at":"2026-08-01T16:55:15.720468Z","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":"2026-08-01T16:55:15.723181Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.723181Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:1215df14cb3b641885da5aad05e62cdadbb14186c7c5be7f4ef8eaed664cf664","observation_id":"05e6db73-b59d-49e7-926e-ebc42ec137a3","resolution":{"observed_at":"2026-08-01T16:55:15.723181Z","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":"2026-08-01T16:55:15.725665Z","title":"Burda, J","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.725665Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:b58a0ab3f03a3c8a5d3abd7bf4289498f9e0dc5dd2abd3b90584f07e24ba892d","observation_id":"849789d3-8ca0-455b-84ee-23742fd6b59f","resolution":{"observed_at":"2026-08-01T16:55:15.725665Z","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":"2026-08-01T16:55:15.728334Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.728334Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:ad8a142385453e0f28a21964c869e0e189a2f3e907ebcf1f11cd854cbab8e7e4","observation_id":"adbb8aff-1eff-4cdf-b507-1411bb1b71ae","resolution":{"observed_at":"2026-08-01T16:55:15.728334Z","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":"2026-08-01T16:55:15.730552Z","title":"Cvetkovi´ c, P","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.730552Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:309e6b91cec4a7b4b6f76a8366e544762d53c317a5ecfa84d426e7d94add6c25","observation_id":"64773321-31d0-40ce-98e3-2e7a31afcfc0","resolution":{"observed_at":"2026-08-01T16:55:15.730552Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.10337","last_updated":"2026-04-30T07:05:57Z","snapshot_observed_at":"2026-08-02T20:35:02.949836Z","submitted_at":"2024-10-14T09:49:01Z","title":"Entropy and the growth rate of universal covering trees","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.10337","snapshot_observed_at":"2026-08-01T16:55:15.732753Z","title":"Eisner and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.732753Z"},"links":{"cited_paper":"/paper/2410.10337","citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:3b18abc1738fbc9e7aabb40b24d45fbf421f5468930c395b5311ebc44fdcca51","observation_id":"91458ee8-4f64-4965-8837-85e6d4ca21c1","resolution":{"observed_at":"2026-08-01T16:55:15.732753Z","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":"2026-08-01T16:55:15.735333Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.735333Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:84ffe8e01a1b9423ec65620a766cb5db9279cf7643b1e1d7aa5f54b4b533bda0","observation_id":"9eb3616a-8762-4d43-8b22-cd6e148a75ac","resolution":{"observed_at":"2026-08-01T16:55:15.735333Z","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":"2026-08-01T16:55:15.737641Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.737641Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:2299f1b2f85a79aee32bd07e4c85ea382bbbde44f0cf26efcdb53d85fb07bb7c","observation_id":"2d577214-1481-40de-a97c-c35c57465b24","resolution":{"observed_at":"2026-08-01T16:55:15.737641Z","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":"2026-08-01T16:55:15.739860Z","title":"Hong, J.-L","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.739860Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:7dfd16ac5c2c70303a39a87cc3efbd9fbe7c0fbb91fe573bedba93d809ac2890","observation_id":"eb99a684-3f0f-4677-9a23-eb79cca9d7f0","resolution":{"observed_at":"2026-08-01T16:55:15.739860Z","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":"2026-08-01T16:55:15.742287Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.742287Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:5a9639362693833bbd3f46f0183cfb1bccf28c167d7ddf80205c43ee38484db4","observation_id":"1ffdc4b5-3cd9-4982-8fc6-c0db01dfe8f4","resolution":{"observed_at":"2026-08-01T16:55:15.742287Z","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":"2026-08-01T16:55:15.744410Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.744410Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:093b5c2529131e8fe743b9898c7d442e36623e3c468cbdba723d1468dd22015f","observation_id":"4ced9f3f-756b-4dc5-8a70-7fbfa0e19112","resolution":{"observed_at":"2026-08-01T16:55:15.744410Z","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":"2026-08-01T16:55:15.746526Z","title":"Liu and C.-w","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.746526Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:8266dfe7f738cf2bab8605379f6f0221df7ec3bd0fa12259bdc14053dab3c638","observation_id":"6bd542ff-4e6f-4023-ba06-756ec2afdaa4","resolution":{"observed_at":"2026-08-01T16:55:15.746526Z","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":"2026-08-01T16:55:15.748679Z","title":"Nikiforov","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.748679Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:474dc9d0eb850d151530710882938bffa615a8d6f50d9e5229dafd288b0aedfc","observation_id":"53b88f27-01e7-42e0-af21-3041200c5ae6","resolution":{"observed_at":"2026-08-01T16:55:15.748679Z","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":"2026-08-01T16:55:15.750838Z","title":"Nikiforov","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.750838Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:913f23884f8743ff8ae1765861598aefbe0477e1f2b47dca5b1d12531bf61b80","observation_id":"d8905506-b873-47ec-a8fd-750163348c2f","resolution":{"observed_at":"2026-08-01T16:55:15.750838Z","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":"2026-08-01T16:55:15.753013Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.753013Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:963a10e27401f76609c0b23401164c8b14f1ec5118c5c85c1666497ba6bef847","observation_id":"d3624af3-c0c4-4765-81eb-2cd9e78e53db","resolution":{"observed_at":"2026-08-01T16:55:15.753013Z","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":"2026-08-01T16:55:15.755306Z","title":"Shu and Y","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.755306Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:9507e0de5faaf4dc6760b69e1ce043680859aa2365cb413217bda390f2c1be1b","observation_id":"b728066d-5115-40f1-adb3-6c59bc81988d","resolution":{"observed_at":"2026-08-01T16:55:15.755306Z","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":"2026-08-01T16:55:15.757575Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.757575Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:c5559e8841a4b4653dd8a78e2ee59ecc8ff2fc1802d9cf57bd1625c0957f1310","observation_id":"967b7566-99ac-4112-b8ea-53a439ea01a1","resolution":{"observed_at":"2026-08-01T16:55:15.757575Z","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":"2026-08-01T16:55:15.759978Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.759978Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:7d0acf1d022157ba6fcc008ccbf049ef89c45a973105718ad778ec7ab4819814","observation_id":"91f11563-6bba-47bd-86aa-ad304c9de021","resolution":{"observed_at":"2026-08-01T16:55:15.759978Z","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":"2026-08-01T16:55:15.762400Z","title":"Tripathi and S","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.762400Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:8244e731818e4361cac7bc1662991e52ea017c2ce6ce041cc859a48debf70e23","observation_id":"24e3e72b-29c7-4503-9a54-317db43a15d2","resolution":{"observed_at":"2026-08-01T16:55:15.762400Z","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":"2026-08-01T16:55:15.764733Z","title":"Von Collatz and U","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T16:55:15.764733Z"},"links":{"citing_paper":"/paper/2607.17895"},"observation_digest":"sha256:8f5e256207e523727f6cf17f36ecca0582d18d425f3204e3a18439797766a59e","observation_id":"8647b1d5-8b44-4fc4-81e4-dc4b2894f860","resolution":{"observed_at":"2026-08-01T16:55:15.764733Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.17895","last_updated":"2026-07-20T12:43:12Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T14:46:54.575134Z","submitted_at":"2026-07-20T12:43:12Z","title":"A New Lower Bound on the Spectral Radius of Graphs with Prescribed Average Degree"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":23,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":23},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.17895."}