{"as_of":"2026-08-21T13:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:883582795dd892d14017b49172ce53a6cd59617d84351757112dfb2fe890667f","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T10:07:18.492343Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2510.11991/citation-record","integrity":"/paper/2510.11991/integrity","json":"/paper/2510.11991/citation-record.json","paper":"/paper/2510.11991"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.25560/28115","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Spiral (Imperial College London)","work_id":"7c91efc0-c128-41b7-8b0d-e9a47faf5e54","year":2015},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:15.474648Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:bbed6f670d5bc86a10183ce3d5beff6b84bfd2cca71cc5c232cc5d7ae9a0a7d5","observation_id":"8bc7c9f8-11ca-49f0-adfc-1b8cc86616e6","resolution":{"observed_at":"2026-08-04T10:08:28.816629Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T10:07:15.600680Z","title":"Altmann and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:15.600680Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:3b3d09ba40627e53383f5d65d77404c46cbac43da2ce168433b0db13b78f0bae","observation_id":"12e19ea7-1d50-4cd0-842b-c5b7c4d9a3be","resolution":{"observed_at":"2026-08-04T10:07:15.600680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00208-012-0880-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Anderson","venue":"Mathematische Annalen","work_id":"25bafcf5-9b3d-451f-bf93-af7b4d529578","year":2013},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:15.944551Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:8c80359ac1e3c3105b9aae5d5fb61f1ffd74698f2ccd9c5674f283cc36642fff","observation_id":"2aee9f85-e9e0-4786-936b-c944f6d23d88","resolution":{"observed_at":"2026-08-04T10:08:28.571958Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T10:07:16.085260Z","title":"Birkar, P","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.085260Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:8d7f1195c77eef560f314fd5ef5abeafbf68190653809bf33f139e65937b8286","observation_id":"f956962e-bb22-4046-9844-e27a64c4cafb","resolution":{"observed_at":"2026-08-04T10:07:16.085260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.01788","last_updated":"2024-08-03T14:00:21Z","snapshot_observed_at":"2026-08-21T12:52:41.538153Z","submitted_at":"2024-08-03T14:00:21Z","title":"Gorenstein-Fano polytopes and compactifications of rank 2 polyptych lattices","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.01788","snapshot_observed_at":"2026-08-04T10:07:16.302210Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.302210Z"},"links":{"cited_paper":"/paper/2408.01788","citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:1a098fd0c2d43d2855a375c741a18d985fc591c142081c4c96fb1fa859599024","observation_id":"f6564354-7eef-4ce0-b80e-1998d877e15d","resolution":{"observed_at":"2026-08-04T10:07:16.302210Z","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":"2026-08-04T10:07:16.462287Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.462287Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:b3e9ef9fb936dde68dc8e248c1e18c0f7bc3f82371648f725b020116fa1d5583","observation_id":"615cfd88-1c01-4315-9761-aa6150acf168","resolution":{"observed_at":"2026-08-04T10:07:16.462287Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.05878","last_updated":"2024-04-08T21:21:31Z","snapshot_observed_at":"2026-08-16T14:02:35.260807Z","submitted_at":"2024-04-08T21:21:31Z","title":"Log Calabi-Yau pairs of birational complexity zero","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.05878","snapshot_observed_at":"2026-08-04T10:07:16.602629Z","title":"Enwright, F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.602629Z"},"links":{"cited_paper":"/paper/2404.05878","citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:f0429cf155f88ffd7ea308c8d912cdb38890134a7c7895c13503640ee604a551","observation_id":"b11c15f4-5369-46fd-aaf5-f912db1fabf7","resolution":{"observed_at":"2026-08-04T10:07:16.602629Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.17369","last_updated":"2026-08-03T16:09:36Z","snapshot_observed_at":"2026-08-17T19:04:18.196253Z","submitted_at":"2025-04-24T08:40:45Z","title":"Complexity one varieties are cluster type","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.17369","snapshot_observed_at":"2026-08-04T10:07:16.735313Z","title":"Enwright, J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.735313Z"},"links":{"cited_paper":"/paper/2504.17369","citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:5bb8752a6b9fbd6c2da2d47dee00f74e4fa3b371fad4b3efb7de0259b3d87e2a","observation_id":"3f49e448-f627-4bab-aa89-2a7f9aafe1f2","resolution":{"observed_at":"2026-08-04T10:07:16.735313Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.01785","last_updated":"2024-12-29T01:09:06Z","snapshot_observed_at":"2026-08-16T13:28:46.396052Z","submitted_at":"2024-08-03T13:43:29Z","title":"Geometric families of degenerations from mutations of polytopes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.01785","snapshot_observed_at":"2026-08-04T10:07:16.865145Z","title":"Escobar, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:16.865145Z"},"links":{"cited_paper":"/paper/2408.01785","citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:1d218b6a4b6fbfed9c1b775643734ffdf76da7d491f8620e3ed22f90678a884d","observation_id":"178d50f1-f3e5-426b-8689-14658656762f","resolution":{"observed_at":"2026-08-04T10:07:16.865145Z","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":"2026-08-04T10:07:17.005323Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.005323Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:0ce4d4ef5110ce3386cc2abf5ef0cb99e48dc29d0b27896f135dfc330ed6ee54","observation_id":"dc128ca9-f548-493a-8f46-778457bd2e89","resolution":{"observed_at":"2026-08-04T10:07:17.005323Z","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":"2026-08-04T10:07:17.070925Z","title":"Gross, P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.070925Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:0ac4cabecbc19cdb7530d07bc7d072ef00b6b3e0a6c76376139d67f58025ed57","observation_id":"91e18b45-35ed-4391-bea4-453a75d9717b","resolution":{"observed_at":"2026-08-04T10:07:17.070925Z","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":"2026-08-04T10:07:17.170305Z","title":"Hartshorne","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.170305Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:3114fe186d04298fbd74ffc7706f8dab3c6499f1f383ae7e9f1a9328a82fc4b5","observation_id":"2ba0dafb-d553-4b0d-9ecc-0ef57c142ac8","resolution":{"observed_at":"2026-08-04T10:07:17.170305Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.aim.2010.03.010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hausen and H","venue":"Advances in Mathematics","work_id":"c0a1cb84-7c60-4f69-940c-0a96eaddd417","year":2010},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.282689Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:b1068d55882e65f5d0dc4663436a5f2ae272548e73830915374146cf454577e5","observation_id":"30b8c1a4-7670-43d7-96a8-7e8ff60adc2b","resolution":{"observed_at":"2026-08-04T10:08:28.463799Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3842/sigma.2012.047","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Symmetry Integrability and Geometry Methods and Applications","work_id":"a29c525a-8990-4ed0-af59-1169b06703c2","year":2012},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.377338Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:b673481c6966c1af19a9b70dd65e8ca79529d3f7b05d3d697f831d8de4c058a3","observation_id":"479808f1-e5fc-48ce-a44d-78aafe65a453","resolution":{"observed_at":"2026-08-04T10:08:28.375966Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s1056-3911-2011-00585-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Algebraic Geometry","work_id":"f9048b5b-598d-4df1-bed0-e091c6410ca2","year":2012},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.441447Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:fbfc68a77ee4ac1d2697d1ababf32ccd76c23443c02aeae583a9010f24e46540","observation_id":"2a5ecd46-a8a1-42b7-91cf-6c867e2fddbb","resolution":{"observed_at":"2026-08-04T10:08:28.299458Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T10:07:17.500461Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.500461Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:c4761d29b1f9b746a5d294803f112dd50da1c3a276aaa495c131bbb7015ed331","observation_id":"e7e76b66-be19-44d4-8979-65b8cac869c8","resolution":{"observed_at":"2026-08-04T10:07:17.500461Z","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":"2026-08-04T10:07:17.564509Z","title":"Ji and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.564509Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:e9e5b62b3b90d3087cd22d0a9adb839f7ba04b2888c2ee266e1a3bbd9b7855c6","observation_id":"e54bd75f-f862-4359-9925-bb5488d9439a","resolution":{"observed_at":"2026-08-04T10:07:17.564509Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/fms.2017.10","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kasprzyk, B","venue":"Forum of Mathematics Sigma","work_id":"c04b3aa8-c10e-420d-8fe5-9c762f7fdb8e","year":2017},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.655241Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:6b0c158b4e75d3ce8c57f1d192fa648682e83f96b7c9c92fffb18840bee6e818","observation_id":"7de16cd5-b9fb-4a1e-8b5c-1128388f3eab","resolution":{"observed_at":"2026-08-04T10:08:28.190258Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T10:07:17.737372Z","title":"Kaveh and C","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.737372Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:9c6d374e78401580b2499980e6e22468c978974b11aa9b4ed7ed700d1dc7b525","observation_id":"5df89f14-6cbf-4a5f-84b7-962eecda3391","resolution":{"observed_at":"2026-08-04T10:07:17.737372Z","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":"2026-08-04T10:07:17.819080Z","title":"Keel and J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.819080Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:e034ae3ad0c6328e701dcac183fb15377cd22bdc600343ac467bd77e8347a4d6","observation_id":"8ff9ab0d-df68-4d3c-964d-25b144aad0ed","resolution":{"observed_at":"2026-08-04T10:07:17.819080Z","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":"2026-08-04T10:07:17.907985Z","title":"Koll´ ar","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.907985Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:79e5859d8fa23895defb46da3b6c0d932974e3ee614d0cfb2e34051bb10e1294","observation_id":"18d42c13-2b68-4032-b3c9-20a9b18acd1e","resolution":{"observed_at":"2026-08-04T10:07:17.907985Z","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":"2026-08-04T10:07:17.996050Z","title":"Koll´ ar, K","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:17.996050Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:a884bec4846ed43ed2dbc4125d544295e756a52dcdeec05e39b3ca85809f33ef","observation_id":"2c3e22a7-9051-4e29-ac95-f10f59cb9130","resolution":{"observed_at":"2026-08-04T10:07:17.996050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1971295","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Looijenga","venue":"Annals of Mathematics","work_id":"edb62882-b47c-4bb0-b00c-ce4b0b3ac39a","year":1981},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:18.102010Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:b234561f8cef37ce18d9f3614122c6fe9d4d0ca2ef764f638b2680844e021d17","observation_id":"3041423d-8844-4fc2-be5d-db69e979ab7c","resolution":{"observed_at":"2026-08-04T10:08:28.065763Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T10:07:18.214843Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:18.214843Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:df07cba25a19702e3492d1ae213e45fb6fc411718354ea5d8e88a339d15a8163","observation_id":"301fe528-bf42-4e02-a321-121087a25103","resolution":{"observed_at":"2026-08-04T10:07:18.214843Z","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":"2026-08-04T10:07:18.371359Z","title":"Rosenlicht","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:18.371359Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:34eda9ed5aaacb35e76445ac68d495ac63ce5843f6e784139c12699cb5af8ff0","observation_id":"3a38d6aa-d044-4202-ab6e-b8786abd8a1f","resolution":{"observed_at":"2026-08-04T10:07:18.371359Z","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":"2026-08-04T10:07:18.492343Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:18.492343Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:2a9d1b34f256ec4bc7c538af1dc835ef3e925844fbdfe6660da605e16b43038f","observation_id":"48a4df77-8bb3-4f9a-8057-37da008525e1","resolution":{"observed_at":"2026-08-04T10:07:18.492343Z","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":"2026-08-04T10:07:18.272197Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:18.272197Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:87e0609a8981e0ea78e18e77be66066adf21e15fbb0678368732b405612717bd","observation_id":"819f22c3-0813-4ef9-bd7a-34ee317fa16c","resolution":{"observed_at":"2026-08-04T10:07:18.272197Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jpaa.2011.12.018","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Pure and Applied Algebra","work_id":"c8e80d00-4130-43c6-9a70-b0fd86506a44","year":2011},"citing_paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation","version":3},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-04T10:07:15.777155Z"},"links":{"citing_paper":"/paper/2510.11991"},"observation_digest":"sha256:04d175487c82974eb6916b18d5f8d70f4db9c253c0ce6c57d0e8432866b502c3","observation_id":"8fa1cc40-313c-439b-b42b-4ac51a303b7d","resolution":{"observed_at":"2026-08-04T10:08:28.713084Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2510.11991","last_updated":"2026-06-09T18:21:09Z","latest_version":3,"primary_category":"math.AG","snapshot_observed_at":"2026-08-09T17:23:00.634845Z","submitted_at":"2025-10-13T22:34:19Z","title":"Geometry of tropical mutation surfaces with a single mutation"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":7,"verified_fuzzy":0},"total_outbound_references":28},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2510.11991."}