{"as_of":"2026-08-20T13:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5681f17b3c95ddc927a54538288b82f50c3ed040916b9812cb4d2309f5e10ff4","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T01:17:15.502663Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2608.01040/citation-record","integrity":"/paper/2608.01040/integrity","json":"/paper/2608.01040/citation-record.json","paper":"/paper/2608.01040"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:17:16.378851Z","title":"Ambro and A","venue":null,"work_id":"c03c2be1-3557-4f09-92d5-81b727c4f496","year":2020},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.560827Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:4622dc5f542c77c86ee32cddf8a1c6cd2232a522482c67b6391f3fb9684af8ba","observation_id":"e0abfea0-7e35-4eab-b833-639eb93b56ef","resolution":{"observed_at":"2026-08-07T01:17:16.445467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T01:17:16.308795Z","title":"Ambro and A","venue":null,"work_id":"37eaa0c5-b857-4224-b867-8adbcdf1f365","year":2020},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.622614Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:aaa15f6ce3012e091ddedd0ad8693ab6891d78a742c927c1644d59a688ea1810","observation_id":"f5b7fbf6-b862-43ea-aea2-0d7b07d5b8be","resolution":{"observed_at":"2026-08-07T01:17:16.315646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T01:17:13.661577Z","title":"Beresnevich, L","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.661577Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:b20a984c61c0342f8e329f93c6408a81c6e7205fc2d394c36409cbbd1e160b2d","observation_id":"d4e2d521-b020-4406-b527-57fab56d981f","resolution":{"observed_at":"2026-08-07T01:17:13.661577Z","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":"2026-08-07T01:17:13.739684Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.739684Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:912d443ec8e48fb147baad6ca293e0a55fd094805524228bdb6922c5199478c9","observation_id":"736047bc-aca8-4745-8f13-5f4735d69555","resolution":{"observed_at":"2026-08-07T01:17:13.739684Z","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":"2026-08-07T01:17:13.812479Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.812479Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:b8ec901cbbfb9515656194e876c24024abbfe50c557ee971a9b844ad1d6fd685","observation_id":"904d407a-a78a-4d43-94ac-a37c55313940","resolution":{"observed_at":"2026-08-07T01:17:13.812479Z","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":"2026-08-07T01:17:13.865386Z","title":"Berndtsson, Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains, Ann","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.865386Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:969d40e022f299665875b277f53bb01ded86ed324ae76ca020283b3a715d9567","observation_id":"dc8539e0-5321-4725-b303-6c863be12c4f","resolution":{"observed_at":"2026-08-07T01:17:13.865386Z","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":"2026-08-07T01:17:13.947029Z","title":"Boucksom and H","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:13.947029Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:53dfe4e73d45a5e4c0897f2d49acb8a917d4726a9f55950b81221182c8bc7c4a","observation_id":"111dd2a9-0db0-477e-adea-b9ca3f53fae6","resolution":{"observed_at":"2026-08-07T01:17:13.947029Z","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":"2026-08-07T01:17:14.011475Z","title":"Campos, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.011475Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:ac2856c9ceb34085e620fbaff40b01e2b5eb85818950e021ce317ebcde60a3df","observation_id":"65f9404b-8f44-4fa9-9139-733c42a96303","resolution":{"observed_at":"2026-08-07T01:17:14.011475Z","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":"2026-08-07T01:17:14.091612Z","title":"Cordero-Erausquin and B","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.091612Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:4259cab07405394e58359cf1be146e062e11431a0d4376cf772866db41680707","observation_id":"ac73e065-8f69-4e62-b50e-edee28bfcf89","resolution":{"observed_at":"2026-08-07T01:17:14.091612Z","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":"2026-08-07T01:17:14.132326Z","title":"Dubuc, Crit\\`eres de convexit\\'e et in\\'egalit\\'es int\\'egrales, Ann","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.132326Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:8647031b717c0f149671a8490c6a6be0a322b52d6015a6dc32f0b2073aacd985","observation_id":"8171011e-21b4-4aa7-8b2e-012a6de7fee3","resolution":{"observed_at":"2026-08-07T01:17:14.132326Z","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":"2026-08-07T01:17:14.195810Z","title":"Ehrhart, Une g\\'en\\'eralisation du th\\'eor\\`eme de Minkowski, C","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.195810Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:e5ffb2c3bcaf4afea9e7e9ee6c2e3526e29623c4a9b33dd04aae35f8b5d2ba2b","observation_id":"2e30507a-c7fb-4d3e-9eef-4dd8cebed643","resolution":{"observed_at":"2026-08-07T01:17:14.195810Z","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":"2026-08-07T01:17:14.260497Z","title":"Ehrhart, Propri\\'et\\'es arithmog\\'eom\\'etriques des polygones, C","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.260497Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:4912da11333c0e2f9afb83aa972d1d1615e82851300d97d5af574a5f4efed117","observation_id":"d6d0cd24-f994-4e35-a993-9cbc4011224e","resolution":{"observed_at":"2026-08-07T01:17:14.260497Z","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":"2026-08-07T01:17:14.315969Z","title":"Ehrhart, Une g\\'en\\'eralisation probable du th\\'eor\\`eme fondamental de Minkowski, C","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.315969Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:42304d43d9f6937ea80caff7f65e4318dbd56b4c783228135940139b6b562ffb","observation_id":"d93940c4-d61c-452b-8290-87fe858de3b6","resolution":{"observed_at":"2026-08-07T01:17:14.315969Z","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":"2026-08-07T01:17:14.400333Z","title":"Ehrhart, Volume r\\'eticulaire critique d'un simplexe, J","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.400333Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:9eebf71123b92cf146342b5fa2573e9ea64f2d26814f6872909cf82634f40e2f","observation_id":"1f0c938e-63d9-4cbe-982f-073ea7f41a9d","resolution":{"observed_at":"2026-08-07T01:17:14.400333Z","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":"2026-08-07T01:17:14.452687Z","title":"Fujita, Optimal bounds for the volumes of K\\\"ahler--Einstein Fano manifolds, Amer","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.452687Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:f61856ec61546c2aed7e4fe6e527f06c0bdc517ab26191dd246e1f3d213c180f","observation_id":"4e6c3446-50fd-4b72-8447-468e6f31f5f7","resolution":{"observed_at":"2026-08-07T01:17:14.452687Z","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":"2026-08-07T01:17:14.532837Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.532837Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:4a2b34e845779aada3349fbbf94c082ba76654abd13d5e54f861ae54457048cb","observation_id":"1211f64f-ed46-4f1a-82ab-ef96ec0059ed","resolution":{"observed_at":"2026-08-07T01:17:14.532837Z","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":"2026-08-07T01:17:14.580698Z","title":"Gr\\\"unbaum, Partitions of mass-distributions and of convex bodies by hyperplanes, Pacific J","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.580698Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:922f9bbfd19475dd86ab3aa0f74223ce532c1dbc87b2552d612485cab8772b13","observation_id":"1f300ec4-16be-4541-9200-bd9000990515","resolution":{"observed_at":"2026-08-07T01:17:14.580698Z","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":"2026-08-07T01:17:14.622661Z","title":"Uber einfache und mehrfache Bedeckung des n -dimensionalen Raumes mit einem W\\","venue":null,"work_id":null,"year":1941},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.622661Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:9602df6cfbf9db4a96f2d9633cf308193615eb8694c6b769ae5aac2bdc98a868","observation_id":"9b811b4b-d2fc-4627-a08a-65fcdeec736c","resolution":{"observed_at":"2026-08-07T01:17:14.622661Z","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":"2026-08-07T01:17:14.684660Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.684660Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:816844223e5d2692e09dfa643fe3286ae573fb0a098e4dc6487f1acb409cf5c8","observation_id":"f17c763e-3428-4140-a2d3-ed8b53556f27","resolution":{"observed_at":"2026-08-07T01:17:14.684660Z","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":"2026-08-07T01:17:14.729306Z","title":"Huang, B","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.729306Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:6e309ee0bed2e4335d9dbbdab03a86e5798d3b2c1650c861ceec495d732a6999","observation_id":"6ba62d83-c61e-4f9f-86db-a13cbdfaadd4","resolution":{"observed_at":"2026-08-07T01:17:14.729306Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.03789","last_updated":"2026-05-30T05:07:37Z","snapshot_observed_at":"2026-07-13T12:18:08.261894Z","submitted_at":"2026-04-04T16:35:16Z","title":"Automated Conjecture Resolution with Formal Verification","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.03789","snapshot_observed_at":"2026-08-07T01:17:14.813042Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.813042Z"},"links":{"cited_paper":"/paper/2604.03789","citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:5c579b5c21c090f9d12f2884cde1aaa96b85950879a861e9ec759cf4df9f3da1","observation_id":"10005d64-fe27-4faf-977e-7ff1fcc274c3","resolution":{"observed_at":"2026-08-07T01:17:14.813042Z","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":"2026-08-07T01:17:14.866646Z","title":"Klartag and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.866646Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:0ef7c114f0a0959ae924cb7c9151cae769574371441062b2f9fc3c127f99dd07","observation_id":"1cdcc343-ef31-4985-8876-7b2ff58a1a5b","resolution":{"observed_at":"2026-08-07T01:17:14.866646Z","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":"2026-08-07T01:17:14.900515Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.900515Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:314224c18d67b5dfbe1dc667b26056d670203f1241948b223e1d48d0b2f11d9c","observation_id":"e51c2382-136d-40f1-bb2f-21b1d599da39","resolution":{"observed_at":"2026-08-07T01:17:14.900515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.17420","last_updated":"2026-05-20T18:47:24Z","snapshot_observed_at":"2026-08-17T21:46:14.082522Z","submitted_at":"2025-06-20T18:35:27Z","title":"On the volume of K-semistable Fano manifolds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.17420","snapshot_observed_at":"2026-08-07T01:17:14.977108Z","title":"Li and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:14.977108Z"},"links":{"cited_paper":"/paper/2506.17420","citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:b9953fb58a49cf7f9d1541769726c7cd9c30ca304053eec5f8585871f9e822a7","observation_id":"8d90297d-544c-4314-82b3-ed346f73ef7f","resolution":{"observed_at":"2026-08-07T01:17:14.977108Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:17:15.917424Z","title":"Liu, The volume of singular K\\\"ahler--Einstein Fano varieties, Compos","venue":null,"work_id":"6c7f1204-abbd-4d71-b4b1-a47dd61860a3","year":2018},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.035732Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:debd1e5fc2187b92a22a27c77acf0105378a4b0c928dfabd63b173df9ffa1e3a","observation_id":"408da443-b330-4441-b7d8-687ecd6383f6","resolution":{"observed_at":"2026-08-07T01:17:15.970335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T01:17:15.821700Z","title":"Liu and Z","venue":null,"work_id":"266a3703-a21b-4c26-a7d7-6225f7f46e49","year":2018},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.087445Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:5242e0de0e289339e98934071bef704e5ea52fc3aa58f1f4b9a5f8dbda190223","observation_id":"293851d9-152d-419b-9c21-c5dab77c9c2e","resolution":{"observed_at":"2026-08-07T01:17:15.873591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.06447","last_updated":"2026-07-08T12:23:39Z","snapshot_observed_at":"2026-08-15T08:43:37.020715Z","submitted_at":"2026-07-07T16:11:30Z","title":"Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.06447","snapshot_observed_at":"2026-08-07T01:17:15.144101Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.144101Z"},"links":{"cited_paper":"/paper/2607.06447","citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:5c3c79e1488fc9be93a9eea6be9e86822ea34ca6ce4f27c63a45c5897df1387f","observation_id":"eff3bfc5-fc39-46c8-82c0-c3a9403d43f5","resolution":{"observed_at":"2026-08-07T01:17:15.144101Z","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":"2026-08-07T01:17:15.210448Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.210448Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:be6c8d2c7d43cff68ef48f63c6e8b9c311f4da7a3cbe6c6368b08087bc6e57c2","observation_id":"2677a75f-4c77-4442-aa7f-2fd6eb5387e0","resolution":{"observed_at":"2026-08-07T01:17:15.210448Z","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":"2026-08-07T01:17:15.253633Z","title":"Nill and A","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.253633Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:e53ce20fdab58a7b9c14529633922b2ce35081fcb51a6ed33dbb23ba719f2f2d","observation_id":"9e25147e-cfd0-49e6-b6dd-fd838069f124","resolution":{"observed_at":"2026-08-07T01:17:15.253633Z","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":"2026-08-07T01:17:15.306584Z","title":"https://cdn.openai.com/pdf/ten-proofs-oai.pdf","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.306584Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:e37733890226b8b1c126586498462070bc45c103381f3b1ab739823dc432be6a","observation_id":"2fee6555-345c-4bfa-973c-8acca0b01065","resolution":{"observed_at":"2026-08-07T01:17:15.306584Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:17:15.665754Z","title":"Perkinson, Inflections of toric varieties, Michigan Math","venue":null,"work_id":"1cbd71a0-9067-43e7-980c-f8d42a29515c","year":2000},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.354610Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:d8e06a854ab730335708866e932858940bf35a1e3f9fcde186a52c4c8131c93f","observation_id":"d121a601-069f-4d45-bcd7-6d67503d0c43","resolution":{"observed_at":"2026-08-07T01:17:15.733554Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T01:17:15.385406Z","title":"Ross and D","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.385406Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:954fa3e8df50374097bc53ca36b05baa4ca5a805c22ef3f86e83a02dda5bb62a","observation_id":"6794bc1f-13b4-465c-a551-974ba381ff2d","resolution":{"observed_at":"2026-08-07T01:17:15.385406Z","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":"2026-08-07T01:17:15.470714Z","title":"Zhang, On the optimal volume upper bound for K\\\"ahler manifolds with positive Ricci curvature, with an appendix by Y","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.470714Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:83108815f7242d3da465cb550a01ac886f8b9a700fe63e9625611e59953295cd","observation_id":"41ea7572-7b04-4f41-ad85-bc0fe55b45ea","resolution":{"observed_at":"2026-08-07T01:17:15.470714Z","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":"2026-08-07T01:17:15.502663Z","title":"Zhang, Quantized volume comparison for Fano manifolds, Proc","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:15.502663Z"},"links":{"citing_paper":"/paper/2608.01040"},"observation_digest":"sha256:7d89fc754f7dfc3c47b315a6d02022039b39ec3ef1a53345c270b4d5ee9e7508","observation_id":"21491a92-97b6-4a0c-931a-1d73d3f8f01b","resolution":{"observed_at":"2026-08-07T01:17:15.502663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.01040","last_updated":"2026-08-06T08:48:26Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-20T08:56:29.604585Z","submitted_at":"2026-08-02T06:54:11Z","title":"The equality case of Ehrhart's volume conjecture"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":29,"verified_exact":0,"verified_fuzzy":5},"total_outbound_references":34},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2608.01040."}