{"as_of":"2026-08-09T05:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c0f5fe09ee6ca6388c8b89d8fcbc8b1318f53bd7d11798b5cf01d379663f663e","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:39:26.271721Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T17:33:15.611899Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2012.09815","last_updated":"2020-12-17T18:33:32Z","snapshot_observed_at":"2026-07-06T10:25:35.721396Z","submitted_at":"2020-12-17T18:33:32Z","title":"The characteristic 2 anisotropicity of simplicial spheres","version":1},"cited_work":{"arxiv_id":"2012.09815","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.09815","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"40 [PP23] Roberto Pagaria and Gian Marco Pezzoli,Hodge theory for polymatroids, Int","venue":null,"work_id":"e9288330-e8df-4680-be14-93041bc0a874","year":2023},"citing_paper":{"arxiv_id":"2411.04070","last_updated":"2026-05-05T07:25:04Z","snapshot_observed_at":"2026-07-06T19:46:15.364468Z","submitted_at":"2024-11-06T17:45:35Z","title":"Chow functions for partially ordered sets","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-23T17:32:25.270727Z"},"links":{"cited_paper":"/paper/2012.09815","citing_paper":"/paper/2411.04070"},"observation_digest":"sha256:c8237ebcd38dffa6a0f3d10d54ee1e1e4a40585b0245d893dcbf53e07e10d8e1","observation_id":"674d4643-64e2-45d2-baec-4175acc27707","resolution":{"observed_at":"2026-05-23T17:33:15.614893Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.09815","last_updated":"2020-12-17T18:33:32Z","snapshot_observed_at":"2026-07-06T10:25:35.721396Z","submitted_at":"2020-12-17T18:33:32Z","title":"The characteristic 2 anisotropicity of simplicial spheres","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.09815","snapshot_observed_at":"2026-08-07T10:39:26.271721Z","title":"The characteristic 2 anisotropicity of simplicial spheres, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.05193","last_updated":"2026-07-02T12:40:07Z","snapshot_observed_at":"2026-08-09T04:18:23.695721Z","submitted_at":"2025-06-05T16:05:45Z","title":"On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T10:39:26.271721Z"},"links":{"cited_paper":"/paper/2012.09815","citing_paper":"/paper/2506.05193"},"observation_digest":"sha256:50839ddc91b7529e0b9ead99129ac8e99597e9e75cb682077ee2d555a168ba59","observation_id":"72d92b10-8cc4-43d4-bb80-655f21783231","resolution":{"observed_at":"2026-08-07T10:39:26.271721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.09815","last_updated":"2020-12-17T18:33:32Z","snapshot_observed_at":"2026-07-06T10:25:35.721396Z","submitted_at":"2020-12-17T18:33:32Z","title":"The characteristic 2 anisotropicity of simplicial spheres","version":1},"cited_work":{"arxiv_id":"2012.09815","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.09815","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"40 [PP23] Roberto Pagaria and Gian Marco Pezzoli,Hodge theory for polymatroids, Int","venue":null,"work_id":"e9288330-e8df-4680-be14-93041bc0a874","year":2023},"citing_paper":{"arxiv_id":"2604.04550","last_updated":"2026-07-10T19:42:33Z","snapshot_observed_at":"2026-07-16T23:17:50.051852Z","submitted_at":"2026-04-06T09:20:51Z","title":"Matroid analogues of Gal's conjecture","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-10T20:04:31.783706Z"},"links":{"cited_paper":"/paper/2012.09815","citing_paper":"/paper/2604.04550"},"observation_digest":"sha256:a55cba01907e50dbcddc42b8c33f5a60f0892db351f1722c5887ab63d6bd92a4","observation_id":"18bcf91e-f98e-4d0e-b554-a186f2844bcf","resolution":{"observed_at":"2026-05-10T22:15:50.267586Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.09815","last_updated":"2020-12-17T18:33:32Z","snapshot_observed_at":"2026-07-06T10:25:35.721396Z","submitted_at":"2020-12-17T18:33:32Z","title":"The characteristic 2 anisotropicity of simplicial spheres","version":1},"cited_work":{"arxiv_id":"2012.09815","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2012.09815","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"40 [PP23] Roberto Pagaria and Gian Marco Pezzoli,Hodge theory for polymatroids, Int","venue":null,"work_id":"e9288330-e8df-4680-be14-93041bc0a874","year":2023},"citing_paper":{"arxiv_id":"2604.16905","last_updated":"2026-04-18T08:32:37Z","snapshot_observed_at":"2026-07-06T23:04:05.813982Z","submitted_at":"2026-04-18T08:32:37Z","title":"Lower bounds on the $g$-numbers of spheres without large missing faces","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-10T06:58:18.071465Z"},"links":{"cited_paper":"/paper/2012.09815","citing_paper":"/paper/2604.16905"},"observation_digest":"sha256:ba554c42ecebbd7828d6aa9ff9eb5759399998bea6e030a7e32523ee156d1807","observation_id":"139e9e70-0a22-4394-b6c8-f9700bd917e9","resolution":{"observed_at":"2026-05-10T07:01:49.332571Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2012.09815/citation-record","integrity":"/paper/2012.09815/integrity","json":"/paper/2012.09815/citation-record.json","paper":"/paper/2012.09815"},"outbound":[],"paper":{"arxiv_id":"2012.09815","last_updated":"2020-12-17T18:33:32Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-07-06T10:25:35.721396Z","submitted_at":"2020-12-17T18:33:32Z","title":"The characteristic 2 anisotropicity of simplicial spheres"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2012.09815."}