{"as_of":"2026-08-19T04:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cfd356a32c432f535421bc6efd0950eb6a20bd7e78fef878fc02837de23d16dc","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":"2026-08-11T12:35:39.901993Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T16:32:56.232536Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-08T17:17:07.063858Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"cited_work":{"arxiv_id":"2412.14310","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.14310","snapshot_observed_at":"2026-08-08T17:17:07.063858Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","venue":"math.SG","work_id":"1b916356-dbff-4a8a-928d-61d25c725c45","year":2024},"citing_paper":{"arxiv_id":"2502.05983","last_updated":"2025-04-29T13:50:35Z","snapshot_observed_at":"2026-08-18T11:30:00.480931Z","submitted_at":"2025-02-09T18:28:05Z","title":"Boundary framings for locally conformally symplectic four-manifolds","version":5},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T17:17:06.739901Z"},"links":{"cited_paper":"/paper/2412.14310","citing_paper":"/paper/2502.05983"},"observation_digest":"sha256:794d63dd25c7174a4a325f19fdcb71c30c96afba513c897e2a3cf0ce37c2adaa","observation_id":"eb86129c-a767-475a-94fb-ba13702ca3ac","resolution":{"observed_at":"2026-08-08T17:17:07.067619Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.14310","snapshot_observed_at":"2026-08-15T16:32:56.232536Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.04890","last_updated":"2025-09-05T08:12:50Z","snapshot_observed_at":"2026-08-18T15:15:21.896766Z","submitted_at":"2025-09-05T08:12:50Z","title":"On the equivariant cohomological rigidity of semi-free Hamiltonian circle actions","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T16:32:56.232536Z"},"links":{"cited_paper":"/paper/2412.14310","citing_paper":"/paper/2509.04890"},"observation_digest":"sha256:8e124e2993bdc3c4e7604bd82668f82ba8d9632ffe529456f4fcaf8b1a845e32","observation_id":"a2880589-4a2c-410b-b257-a2e9da7f586e","resolution":{"observed_at":"2026-08-15T16:32:56.232536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.14310/citation-record","integrity":"/paper/2412.14310/integrity","json":"/paper/2412.14310/citation-record.json","paper":"/paper/2412.14310"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:35:40.400341Z","title":"Ahara and A","venue":null,"work_id":"9f662595-a479-47d1-afee-ebd8b3fc2d51","year":1991},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.780705Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:78b0081bfbbee4c21e8e5e216313af520b26089c503ff02e0dcff764052c3acd","observation_id":"7dc6ac58-9ae5-45b0-ad5d-1c8015b95230","resolution":{"observed_at":"2026-08-11T12:35:40.405314Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.384022Z","title":"Atiyah, Convexity and commuting Hamiltonians , Bull","venue":null,"work_id":"0a54e010-e3d1-4158-914c-174f073b6a68","year":1982},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.787399Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:ff3e718d6373b5275b7a4d97e929a2272ce95bcc27c41650bf7ff3e1bdbb59db","observation_id":"9dd4aaac-b337-41c8-93d7-1b570258b86d","resolution":{"observed_at":"2026-08-11T12:35:40.389500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.366884Z","title":null,"venue":null,"work_id":"24c672ae-a664-4f6b-aa5b-1ebf27b433c3","year":1984},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.792657Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:7c9dcab45b2d1ea950f45edb9d539c87c204aa101f57da7ddca6e6e82a20e4eb","observation_id":"0cbdc27d-c35c-488d-9a5a-7b2f740886fe","resolution":{"observed_at":"2026-08-11T12:35:40.372299Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.348298Z","title":null,"venue":null,"work_id":"005154ca-d0e7-4b30-b4e0-a601b6c5d080","year":1988},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.798177Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:c4576512eb5b837310bd5f20bf4020c17fd75a9c5492b7ce47089981b16cde07","observation_id":"665b5940-9873-4ab3-ad3d-2733cab64e98","resolution":{"observed_at":"2026-08-11T12:35:40.354264Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.329121Z","title":"Berline and M","venue":null,"work_id":"44c0fa8b-2e50-4c22-a344-b9969bc7699e","year":1982},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.803820Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:6be001b07c073ecea19d5dcd1642bf15519183e0150d1fe4b09fb4dccc215e56","observation_id":"4b1b5ef1-7863-457f-8366-cd0934501e9a","resolution":{"observed_at":"2026-08-11T12:35:40.334814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.307707Z","title":null,"venue":null,"work_id":"971a551c-2891-4499-92c7-ad1e01b4ce43","year":2011},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.809979Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:3cf250f5f1cfe8fcaf8186b13ae01ac1bfa83b8eddedb8071122185397bff0e7","observation_id":"381f55e8-1f9f-4b4d-92c1-a04c8408accd","resolution":{"observed_at":"2026-08-11T12:35:40.314803Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.288173Z","title":null,"venue":null,"work_id":"d15d1628-304e-423a-b6ce-30f898397f59","year":2014},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.816652Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:6a718d27d8f640d66e9ec77c2077ce2493c175a32e124403b51c50093f46f6ba","observation_id":"106a4905-174a-4e86-ad2c-7a5237cd8497","resolution":{"observed_at":"2026-08-11T12:35:40.293904Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.252684Z","title":"Delzant, Hamiltoniens p´ eriodiques et image convexe de l’application moment , Bulletin de la Soci´ et´ e Math´ ematique de France116 (1988), 315–339","venue":null,"work_id":"cc795fae-b334-4657-ac04-ae74f82b59d9","year":1988},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.821290Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:bc6ab6619d2f2bf11f2ebc3d9a8f17b895fb197005d10ec36cb5e72f92e6bb62","observation_id":"44364a35-c5ff-419b-b1fa-a9f4462f53f3","resolution":{"observed_at":"2026-08-11T12:35:40.259905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.229801Z","title":"Farb and D","venue":null,"work_id":"77bdfa1a-8bc3-4c04-8f2a-890f1ebf252b","year":2012},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.826579Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:f87a77894dddfa0204521a669278cb249bebb909451b96f88a1fede130d0bf7e","observation_id":"a7a921c2-b2dc-48a8-8bdb-1efd1076583e","resolution":{"observed_at":"2026-08-11T12:35:40.239552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.206855Z","title":"Fintushel, Circle actions on simply connected 4-manifolds, Trans","venue":null,"work_id":"06e71447-03bd-429d-bd2f-ef8dd7eada52","year":1977},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.831734Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:a3627b5817b7772e341001b65acbecf181613e8ece5e28c4a5b24caaf3f17565","observation_id":"ec6df02f-859c-4c79-b3c2-8ee01959b681","resolution":{"observed_at":"2026-08-11T12:35:40.213861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.184855Z","title":"Fintushel, Classification of circle actions on 4-manifolds, Trans","venue":null,"work_id":"82bc8f2a-36de-4c76-aa95-a3bf661f00f7","year":1978},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.836962Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:349496f64dc89ce83380776a9d5e3879789daa270eb03f290ce03216dbec27ff","observation_id":"d2ee9fd6-c95c-4c29-b5ca-45c814c5c157","resolution":{"observed_at":"2026-08-11T12:35:40.192446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.157719Z","title":"Guillemin and S","venue":null,"work_id":"8d21d9ee-b177-4b46-a4ec-7f746aa9511e","year":1982},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.842220Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:6cdb51ff2e9e79fac055af2e67b96dcdc90a54fd4227169f4638cffa687c7b45","observation_id":"66f97cf5-5c8a-4b03-acfa-7bab17472115","resolution":{"observed_at":"2026-08-11T12:35:40.169042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.128128Z","title":"Higashitani, K","venue":null,"work_id":"3683dd0d-8c3c-498d-a2ea-3b346b0e6158","year":2022},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.847687Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:8727b22c452247d2e5c56580ca521395eb113dd8ca2b499dba97ce31c901ccfc","observation_id":"bcc780fc-03a8-49ff-93a1-2ca85870fda7","resolution":{"observed_at":"2026-08-11T12:35:40.134600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1912.05647","last_updated":"2025-08-12T13:32:50Z","snapshot_observed_at":"2026-08-19T03:07:34.438246Z","submitted_at":"2019-12-11T21:35:42Z","title":"Equivariant cohomology of a complexity-one four-manifold is determined by combinatorial data","version":4},"cited_work":{"arxiv_id":"1912.05647","doi":null,"metadata_source":"pith","pith_arxiv_id":"1912.05647","snapshot_observed_at":"2026-08-11T12:35:39.943938Z","title":"Equivariant cohomology of a complexity-one four-manifold is determined by combinatorial data","venue":"math.SG","work_id":"4a17dc45-ccb9-46eb-bb04-3d29d08b8ed9","year":2019},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.853050Z"},"links":{"cited_paper":"/paper/1912.05647","citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:d9f5ca33f2b013e5f0ad52a9a098237841704f21c329392fe6b746aec06c7696","observation_id":"42f28930-ed63-46bd-ac67-73282484258e","resolution":{"observed_at":"2026-08-11T12:35:39.951782Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.109128Z","title":"Karshon, Periodic Hamiltonian flows on four dimensional manifolds , Memoirs of the Amer","venue":null,"work_id":"1cc49f0d-5d33-45e6-8b8a-8e3d627a29b3","year":1999},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.858630Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:a733f3b565e2220025316629d45a30b65304e548ac819e63354316cad7df83ad","observation_id":"de047c73-f640-43d2-b19a-8da5d4a071a3","resolution":{"observed_at":"2026-08-11T12:35:40.114872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.092064Z","title":"Karshon and E","venue":null,"work_id":"d7856b09-1473-4b17-ba2b-9d207dde31c7","year":2015},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.864602Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:bffcd006037f05d790cdac747dcffc0c4d9a63ec3ef7553312aab385579a73e9","observation_id":"400dde87-6a30-43a3-8d37-bd3ab4e4baf2","resolution":{"observed_at":"2026-08-11T12:35:40.097703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.075293Z","title":"Karshon and S","venue":null,"work_id":"fd9451ed-a17c-464a-bc6b-8758921a819d","year":2020},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.869350Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:ef096874db4105759a9cde06434111b7b2a97361a9733a7a2bdd819de57744f4","observation_id":"fb80f52f-4f06-454d-b8da-0fde9d898002","resolution":{"observed_at":"2026-08-11T12:35:40.080331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.056555Z","title":"Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry , Princeton University Press, Princeton, NJ, 1984","venue":null,"work_id":"07ec0d9b-4100-4bf7-a02d-302a3ba26038","year":1984},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.874657Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:fd3b8143e031286b9448e05b34282a55acb1df37a2e76b62592d288daa39df7e","observation_id":"0231231b-08fb-4ad0-91e6-613e03674b79","resolution":{"observed_at":"2026-08-11T12:35:40.062978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.036414Z","title":"Masuda, Equivariant cohomology distinguishes toric manifolds","venue":null,"work_id":"57a7cb5d-8f4a-4884-a529-abb07c3683a2","year":2008},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.880220Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:d3189a1eef12446048af3db9637ab0aabaea23864b5a0d28aa802a8ac270cab1","observation_id":"dc93f90f-6de0-4635-9595-e4287a46cba7","resolution":{"observed_at":"2026-08-11T12:35:40.042009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.019884Z","title":"Masuda and D.Y","venue":null,"work_id":"0ee005df-a931-4e77-9410-ef2a0bc927c0","year":2008},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.885383Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:95c75a637788b0d97fb595897353d916d3bca465831f0257a8da5c1e873bff87","observation_id":"18e96c37-4407-4675-a51f-877b42d18bc7","resolution":{"observed_at":"2026-08-11T12:35:40.025134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:40.001486Z","title":"S¨ uss,Orbit spaces of maximal torus actions on oriented Grassmannians of planes","venue":null,"work_id":"a5953fb1-d9be-4286-8509-614654375b36","year":null},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.890905Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:e0676a8b70cee287eb423f6972159e617aad312ac6077e5484f7bf6592ae272d","observation_id":"8a65b8ab-07ad-445e-9628-0b8f37cbcfdc","resolution":{"observed_at":"2026-08-11T12:35:40.006886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:39.982308Z","title":"McDuff and S","venue":null,"work_id":"0009f691-3371-4a81-981d-3fb4c3b88547","year":2006},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.896763Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:421a6edbf035c1db0ab15c9b2cf4e41af025d79ae1f9508b78b91b1fd3b7ba4a","observation_id":"6e781892-26cd-442c-87a5-ac7c8854e82a","resolution":{"observed_at":"2026-08-11T12:35:39.988461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T12:35:39.964023Z","title":"Tolman and J","venue":null,"work_id":"1ac21077-38d6-4119-a580-e4bffccbbce8","year":1999},"citing_paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T12:35:39.901993Z"},"links":{"citing_paper":"/paper/2412.14310"},"observation_digest":"sha256:d9fd2c59f557ad2dcf997a51856b5283c45d53fccac4422d073bbd04070ff00b","observation_id":"cd096156-5cc2-4de2-91b9-a9624078dea9","resolution":{"observed_at":"2026-08-11T12:35:39.969709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.14310","last_updated":"2024-12-18T20:23:55Z","latest_version":1,"primary_category":"math.SG","snapshot_observed_at":"2026-08-17T21:20:51.110253Z","submitted_at":"2024-12-18T20:23:55Z","title":"Equivariant cohomological rigidity for four-dimensional Hamiltonian $\\mathbf{S^1}$-manifolds"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":1,"verified_fuzzy":18},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2412.14310."}