{"as_of":"2026-08-11T14:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d46af9b72b4bdf6eaae53dde9815d1deb590ec8cb47033d0689d58b76fcd4beb","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":"2026-08-01T07:05:35.610394Z","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":"2026-08-11T06:34:44.6726+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/2607.27488/citation-record","integrity":"/paper/2607.27488/integrity","json":"/paper/2607.27488/citation-record.json","paper":"/paper/2607.27488"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:05:34.002708Z","title":"Aigner, The Penrose polynomial of a plane graph , Mathematische Annalen, 307, 173-189, 1997","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.002708Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:e0a0abb2b9a3bd646ee5ed552a61259e2b39159f7153ea4af5a82aedc9b89862","observation_id":"ccb76422-b9fc-4e90-bf4f-7c34497ea016","resolution":{"observed_at":"2026-08-01T07:05:34.002708Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.07302","last_updated":"2023-03-13T18:31:03Z","snapshot_observed_at":"2026-08-11T00:47:52.376481Z","submitted_at":"2018-10-16T22:49:52Z","title":"A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.07302","snapshot_observed_at":"2026-08-01T07:05:34.083876Z","title":"Baldridge, A new cohomology theory for planar trivalent graphs with perfect matchings","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.083876Z"},"links":{"cited_paper":"/paper/1810.07302","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:ff7388d9f307856db5e68d3bd690e6c84f71fea6de55393e8542a95dbb310b9b","observation_id":"9e992e71-6ef0-4c74-9f62-143e58f02215","resolution":{"observed_at":"2026-08-01T07:05:34.083876Z","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":"2026-08-01T07:05:34.202209Z","title":"Baldridge, L","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.202209Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:100cdcac5a4e7c655f51b680e91bf399c9573ece34445c3e99999e3a4134e3f8","observation_id":"439b05cb-daa2-4dff-a4aa-296413578850","resolution":{"observed_at":"2026-08-01T07:05:34.202209Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.10346","last_updated":"2020-05-30T12:19:24Z","snapshot_observed_at":"2026-07-06T07:23:30.538397Z","submitted_at":"2018-12-26T15:45:05Z","title":"The 2-Factor Polynomial Detects Even Perfect Matchings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.10346","snapshot_observed_at":"2026-08-01T07:05:34.260171Z","title":"Baldridge, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.260171Z"},"links":{"cited_paper":"/paper/1812.10346","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:8bfe994336ef6dcbf2bc7d44b31dd428ee563e464864f97b1a1aa57f171601ad","observation_id":"dd42bdd6-7869-4447-aa5d-8d6097d990ff","resolution":{"observed_at":"2026-08-01T07:05:34.260171Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.12010","last_updated":"2023-03-21T16:47:00Z","snapshot_observed_at":"2026-08-11T00:42:55.384307Z","submitted_at":"2023-03-21T16:47:00Z","title":"A topological quantum field theory approach to graph coloring","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.12010","snapshot_observed_at":"2026-08-01T07:05:34.352491Z","title":"Baldridge and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.352491Z"},"links":{"cited_paper":"/paper/2303.12010","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:d976d9696fd77303f91233ec7296518d9d3c1673b4e87a902624163b57586b3a","observation_id":"fa89b0e7-cbc2-4801-b701-a7ad60660ec5","resolution":{"observed_at":"2026-08-01T07:05:34.352491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.18558","last_updated":"2024-12-24T17:21:07Z","snapshot_observed_at":"2026-08-11T11:39:29.484506Z","submitted_at":"2024-12-24T17:21:07Z","title":"A new way to prove configuration reducibility using gauge theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.18558","snapshot_observed_at":"2026-08-01T07:05:34.438569Z","title":"Baldridge and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.438569Z"},"links":{"cited_paper":"/paper/2412.18558","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:cd8afe387008f82b8b7e5e5da58f16215502146d969a612b31b637349b4c7fdc","observation_id":"667062df-c424-476b-8f7b-86c7315ca69b","resolution":{"observed_at":"2026-08-01T07:05:34.438569Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.07939","last_updated":"2024-01-15T19:58:49Z","snapshot_observed_at":"2026-07-06T17:15:50.649358Z","submitted_at":"2024-01-15T19:58:49Z","title":"Quantum state systems that count perfect matchings","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.07939","snapshot_observed_at":"2026-08-01T07:05:34.531248Z","title":"Baldridge and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.531248Z"},"links":{"cited_paper":"/paper/2401.07939","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:0c5684dfd9fa2550197c1b96d84a6fc83e13a44b1f45948334fb5c29df5a7385","observation_id":"e5d3e01b-76d7-423a-b4eb-f65a715c5708","resolution":{"observed_at":"2026-08-01T07:05:34.531248Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.06643","last_updated":"2026-06-04T18:49:10Z","snapshot_observed_at":"2026-08-11T00:43:25.120944Z","submitted_at":"2026-06-04T18:49:10Z","title":"New relations for the Penrose polynomial","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.06643","snapshot_observed_at":"2026-08-01T07:05:34.601623Z","title":"Baldridge and B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.601623Z"},"links":{"cited_paper":"/paper/2606.06643","citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:437b80c31cabc8fb934100b04ceb95a9701f04bbae2c482697d640a994157e2d","observation_id":"35f0bd7b-39d8-439f-b19f-d183c841e05a","resolution":{"observed_at":"2026-08-01T07:05:34.601623Z","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":"2026-08-01T07:05:34.687658Z","title":"Baldridge, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.687658Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:d7f742282a460099bbfd9e03d2fd138fa5cc7a57d3118a3e2beec8e28e74b44f","observation_id":"54c4e7df-ef23-4e3e-84e4-62bba6ff513b","resolution":{"observed_at":"2026-08-01T07:05:34.687658Z","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":"2026-08-01T07:05:34.780431Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.780431Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:5729da15e5b057ee03eeb8b40e991137b7e070974caaae45e60a3ec145df16aa","observation_id":"12f9b343-1845-4b4b-81b1-19a941b9a819","resolution":{"observed_at":"2026-08-01T07:05:34.780431Z","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":"2026-08-01T07:05:34.871352Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.871352Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:9d26f2e3e8577a4ebfadb8c4ea99a116753877b97518bae9f96a9c38ed00fcc5","observation_id":"b80e99cb-0030-4db2-b942-a3a8fdaf11d9","resolution":{"observed_at":"2026-08-01T07:05:34.871352Z","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":"2026-08-01T07:05:34.952944Z","title":"Snarks, boojums, and other conjectures related to the four-color-map theorem","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:34.952944Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:37fde2b2128f3b0b8605d4cc135dc311a32368a1c37a8dfb13b97a4d200d30c7","observation_id":"60423e55-d79a-47b8-a89c-2bc090138da6","resolution":{"observed_at":"2026-08-01T07:05:34.952944Z","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":"2026-08-01T07:05:35.019247Z","title":"American Mathematical Monthly , vol","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.019247Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:a442dc248af390a6493524c6d563c1bee5156fa80048d5da0622aca446ff3178","observation_id":"098608fa-ee76-47e2-8e64-1922700ce30f","resolution":{"observed_at":"2026-08-01T07:05:35.019247Z","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":"2026-08-01T07:05:35.101579Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.101579Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:c28b5030877e051283b41394c27c60f579e5a29c3d7f003b6f5042d97f193226","observation_id":"c3e6d825-864d-4dab-ad6d-3748892a9e30","resolution":{"observed_at":"2026-08-01T07:05:35.101579Z","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":"2026-08-01T07:05:35.192767Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.192767Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:595a1cf17015f46cc5c5aa9d1ce1ac2e31323e446438618f71654c3a711d5757","observation_id":"39d1c990-64e5-430f-bdc3-a4b6b7385392","resolution":{"observed_at":"2026-08-01T07:05:35.192767Z","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":"2026-08-01T07:05:35.258570Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.258570Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:802eea0dd396ba2290bff173f3ae1fe1a6c86d0c6d19d1ed3e0e41720c486fd6","observation_id":"cc336285-8c7c-4699-8f88-ab532ce6821a","resolution":{"observed_at":"2026-08-01T07:05:35.258570Z","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":"2026-08-01T07:05:35.341442Z","title":"Khovanov, A categorification of the Jones polynomial, Duke Math","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.341442Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:18ee252d21b142fff6f3d0c127bb223ede1ff656e3d32e3336975df600fa29e4","observation_id":"316d6a88-ccf6-4a64-b1b6-0b05147df0ce","resolution":{"observed_at":"2026-08-01T07:05:35.341442Z","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":"2026-08-01T07:05:35.408390Z","title":"Lee, An endomorphism of the Khovanov invariant, Adv","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.408390Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:e7498b456e6a0d630e84b525786691c24d92fcb4ae86510229567933a73ee051","observation_id":"a4ef087c-348c-44e9-a2cd-cba62f443c63","resolution":{"observed_at":"2026-08-01T07:05:35.408390Z","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":"2026-08-01T07:05:35.473248Z","title":"Thesis, Grenoble 1977","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.473248Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:d7438533a97fe696ff24dcefad7ec1e729f381f6789e056030e9d762e9f9f43a","observation_id":"a698da00-d83d-467d-8413-ee0187dcdf9e","resolution":{"observed_at":"2026-08-01T07:05:35.473248Z","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":"2026-08-01T07:05:35.512441Z","title":"Penrose, ``Applications of negative dimensional tensors,'' in Combinatorial Mathematics and Its Applications , Academic Press (1971)","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.512441Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:e4d8436c7523458bea4d6359cbc3a807fa460a48b11ecc257e6aa77d9b5fae6d","observation_id":"70cd1637-60fb-4364-bcfb-b1d2b7923dad","resolution":{"observed_at":"2026-08-01T07:05:35.512441Z","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":"2026-08-01T07:05:35.546295Z","title":"Sur le th\\'eor\\`me de Tait","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.546295Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:793d87dfe56481b520fa4eb18dc60404b0857a384a95d196a873195b27d0413f","observation_id":"e5198919-d5da-4023-be2f-52174ee6aa9b","resolution":{"observed_at":"2026-08-01T07:05:35.546295Z","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":"2026-08-01T07:05:35.578361Z","title":"Combin.TheorySer.B 70 (1997),no.1, 166-183","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.578361Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:136d142edd6bfee54d33df991c09ad2e1b625e341231ed04666f1073489238c9","observation_id":"37f78dd5-2545-4c78-ae9f-669933027804","resolution":{"observed_at":"2026-08-01T07:05:35.578361Z","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":"2026-08-01T07:05:35.610394Z","title":"T., On the algebraic theory of graph colorings , J","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-01T07:05:35.610394Z"},"links":{"citing_paper":"/paper/2607.27488"},"observation_digest":"sha256:c655af315feae9b6b3ef88f55bd3d981071eb9263ae293cf9c1ef0dfab669ae6","observation_id":"a10bda48-7860-44b0-9fff-6140ef7dcf24","resolution":{"observed_at":"2026-08-01T07:05:35.610394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.27488","last_updated":"2026-07-29T22:06:33Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-11T00:48:18.794423Z","submitted_at":"2026-07-29T22:06:33Z","title":"New relations for the vertex polynomial"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.27488."}