{"as_of":"2026-08-16T16:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ed78f452c42f3da45db336c0d9efd892f166b7d05ca72fd99dace9122142fd2a","coverage":[{"denominator":6,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-12T02:24:31.059515Z","state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-11T19:43:41.049552Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.09798","snapshot_observed_at":"2026-07-11T19:43:41.049552Z","title":"Attwa, M","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.04368","last_updated":"2026-07-05T15:54:44Z","snapshot_observed_at":"2026-08-16T10:57:44.716386Z","submitted_at":"2026-07-05T15:54:44Z","title":"Paths of even length with equal-degree endpoints","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-11T19:43:41.049552Z"},"links":{"cited_paper":"/paper/2605.09798","citing_paper":"/paper/2607.04368"},"observation_digest":"sha256:b181bf53f479e46b0a8caf447f4f1209c4c88e2762bd99df120bddcc705b1c8f","observation_id":"bff62a62-fa79-4952-ae52-fab32ac0e231","resolution":{"observed_at":"2026-07-11T19:43:41.049552Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2605.09798/citation-record","integrity":"/paper/2605.09798/integrity","json":"/paper/2605.09798/citation-record.json","paper":"/paper/2605.09798"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Ma, J","venue":null,"work_id":"69ea0a61-cc41-4465-acf2-5c3d84308f95","year":2026},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:b1a60f78ecaddc7a3895b817abfbb9d8e31165e76a9a07466f70653d30021fa1","observation_id":"51158570-95c9-4191-886d-ab851fc062de","resolution":{"observed_at":"2026-05-12T22:51:56.365149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Zeng, Q","venue":null,"work_id":"e21c1f91-225d-429a-b00c-db6116ef2d3b","year":null},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:aef274acf5b33ce6f40697f1953aeba40a09fc5b81b11f0df71e406196d5906b","observation_id":"a4f9293f-c1ee-4adf-9289-5c24dd67d547","resolution":{"observed_at":"2026-05-12T22:51:56.360381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Springer , year=","venue":null,"work_id":"d0a77c6b-9d97-4450-b323-66719ae4569c","year":null},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:9c6a9dc5a125ec0cbba660ce3d6fdf19ebe2cb145405f443eabeec839b3ef4fd","observation_id":"372ca85d-3ced-44fc-83d6-20821c8cf4c5","resolution":{"observed_at":"2026-05-12T22:51:56.353002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.11664","last_updated":"2026-04-13T16:12:16Z","snapshot_observed_at":"2026-07-31T18:51:55.791892Z","submitted_at":"2026-04-13T16:12:16Z","title":"Paths of length five with equal-degree endpoints","version":1},"cited_work":{"arxiv_id":"2604.11664","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.11664","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Paths of length five with equal-degree endpoints","venue":"math.CO","work_id":"b31ed2e7-386f-459e-a599-f813c6a4ff30","year":2026},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"cited_paper":"/paper/2604.11664","citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:32dd433d885ebde87a181b0771de36f15e14345bbc7d2df64072d8b5f639855b","observation_id":"7cbf79c8-58f0-4814-82d3-e1b58724d2e6","resolution":{"observed_at":"2026-05-12T07:41:25.270392Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Wang, Y","venue":null,"work_id":"a770bc08-65e6-4253-83fe-bf9c7c34833a","year":null},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:bd80ff75b9e50febcb115ad8b421f9790df5244544d570153f7bd8a77e409cbf","observation_id":"d839ddec-524e-483a-b06d-9a75fa5dbe24","resolution":{"observed_at":"2026-05-12T22:51:56.348952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Graph theory, combinatorics, and applications, Vol","venue":null,"work_id":"ad4e1eef-abea-4645-a000-3ee796345119","year":null},"citing_paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-12T02:24:31.059515Z"},"links":{"citing_paper":"/paper/2605.09798"},"observation_digest":"sha256:87398ad250c8de8161ed2fa60bb89a88f81e94154abd0139d287f1b35d316fb1","observation_id":"cc4e76f5-c391-417d-8f61-1c1bedff9a86","resolution":{"observed_at":"2026-05-12T22:51:56.356633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.09798","last_updated":"2026-05-10T22:35:08Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-04T16:03:57.117163Z","submitted_at":"2026-05-10T22:35:08Z","title":"The density of graphs with no $\\ell$-path connecting equal-degree vertices: a short proof"},"reference_resolution":{"displayed":6,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":5},"total_outbound_references":6},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 6 of 6 outbound references and 1 inbound Pith citation observation for arXiv:2605.09798."}