{"as_of":"2026-08-15T19:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9ee2adb30539c1eb8f79af90fe6810b8c4bfe2bf8d3db374d4a83ec89b5119f8","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:36:07.681414Z","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":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T11:14:51.495182Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.13153","snapshot_observed_at":"2026-08-03T11:14:51.495182Z","title":"Matherne , and Anna Shapiro , Syzygies of polymatroidal ideals , arXiv e-prints (2025), arXiv:2507.13153","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2601.07697","last_updated":"2026-07-20T21:27:44Z","snapshot_observed_at":"2026-08-09T06:21:03.947298Z","submitted_at":"2026-01-12T16:30:28Z","title":"Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T11:14:51.495182Z"},"links":{"cited_paper":"/paper/2507.13153","citing_paper":"/paper/2601.07697"},"observation_digest":"sha256:627075ac41ec9c8801496f8f5de2e0feccfb6b8fd0c8412663f41a699c556a7d","observation_id":"3d2e3cf3-a9fd-43cc-8dc4-fcd08aa1026e","resolution":{"observed_at":"2026-08-03T11:14:51.495182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.13153/citation-record","integrity":"/paper/2507.13153/integrity","json":"/paper/2507.13153/citation-record.json","paper":"/paper/2507.13153"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:36:10.677025Z","title":null,"venue":null,"work_id":"d0d27bd2-82d8-40f3-8d89-339cb2b040d1","year":2010},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:05.612678Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:f7359b669078b3cceb763229218b450f63e0993bc210b52548aa4e015765e4d7","observation_id":"304e7a51-8c66-4331-a480-c47dad0479ca","resolution":{"observed_at":"2026-08-06T16:36:10.736496Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:10.558604Z","title":null,"venue":null,"work_id":"b56a54cc-5ce2-4b79-93a4-e2e1a5178dac","year":2018},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:05.718103Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:96d580275532684c0b24178ec45835239a8da00686e03a0d35959b22439247cc","observation_id":"99ea1e14-194a-436d-9e59-55372288e8c1","resolution":{"observed_at":"2026-08-06T16:36:10.612419Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:10.463822Z","title":null,"venue":null,"work_id":"a9c95a8e-1b96-4c56-b3a3-33e0ac10c4ef","year":2020},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:05.844153Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:8fb53bc40f346b84aeff1c237c7c6144f50869e061a66c848574ef606fff58f0","observation_id":"5d82d279-0c23-4f70-a7ef-07a87ccf1d78","resolution":{"observed_at":"2026-08-06T16:36:10.526640Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:10.349200Z","title":"Math., vol","venue":null,"work_id":"7313bf64-90e7-49c7-9711-b81ef40ddef5","year":2001},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:05.911803Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:b5c1ff97c6a9029adc17375ae2ca7d12f716619966d47eb7ad5e8d9d88b4132e","observation_id":"85b40790-69a2-4d6e-a3c7-4a557a470ba3","resolution":{"observed_at":"2026-08-06T16:36:10.407548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:10.248015Z","title":null,"venue":null,"work_id":"f7363047-e38c-4424-980c-9b5acf126df9","year":2023},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.115048Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:5b4920ded297f2942c84ad49db1292ea8d7eab7c0eb1f952e6aa0f546f98e0ff","observation_id":"b1192183-e514-405f-a58c-55c010f3654b","resolution":{"observed_at":"2026-08-06T16:36:10.282158Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.13091","last_updated":"2025-06-12T10:13:54Z","snapshot_observed_at":"2026-08-13T23:19:06.000062Z","submitted_at":"2022-12-26T11:23:37Z","title":"K-polynomials of multiplicity-free varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2212.13091","snapshot_observed_at":"2026-08-06T16:36:06.219709Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.219709Z"},"links":{"cited_paper":"/paper/2212.13091","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:719943422a45d3ede939a547742855f470c704cbc00690ef0ee6494c285fd1ea","observation_id":"df173e6d-63fd-4ddf-b865-3eea1ff9399d","resolution":{"observed_at":"2026-08-06T16:36:06.219709Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.08764","last_updated":"2024-01-18T15:40:38Z","snapshot_observed_at":"2026-08-13T15:02:02.192807Z","submitted_at":"2022-07-18T17:13:21Z","title":"The Bergman fan of a polymatroid","version":2},"cited_work":{"arxiv_id":"2207.08764","doi":null,"metadata_source":"pith","pith_arxiv_id":"2207.08764","snapshot_observed_at":"2026-08-06T16:36:08.397998Z","title":"The Bergman fan of a polymatroid","venue":"math.CO","work_id":"03dcfbc5-00b3-4e54-b939-805f46a6a4ef","year":2022},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.287175Z"},"links":{"cited_paper":"/paper/2207.08764","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:3bb07561329ac550656cfd6a738c74cf04a57f988a2a7d39dbb7e947b6eed399","observation_id":"10f38ca2-b40e-403c-8efa-c678677c8db9","resolution":{"observed_at":"2026-08-06T16:36:08.436052Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:10.129664Z","title":null,"venue":null,"work_id":"7cc69242-3c8c-492e-af9f-8582754340b9","year":2010},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.366903Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:b3386e6f334eb5f2ca572f9d8d3509b1b07abc7083b7b3a1c4d6a0c80c3f398a","observation_id":"b6cb8143-483d-470b-b6e2-82fb1164bcbe","resolution":{"observed_at":"2026-08-06T16:36:10.171473Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.11996","last_updated":"2024-09-19T13:45:15Z","snapshot_observed_at":"2026-08-13T05:21:01.345946Z","submitted_at":"2023-11-20T18:26:59Z","title":"K-theoretic positivity for matroids","version":2},"cited_work":{"arxiv_id":"2311.11996","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.11996","snapshot_observed_at":"2026-08-06T16:36:08.239333Z","title":"K-theoretic positivity for matroids","venue":"math.AG","work_id":"f997f735-2ff8-4b23-9977-41e46aa85b0b","year":2023},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.451713Z"},"links":{"cited_paper":"/paper/2311.11996","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:df5d327879706baf0b0cb701fed1c77f9769534149c62ebf195895168fa67f2f","observation_id":"a1c1d5f0-b38d-4083-9940-79132e98ef5c","resolution":{"observed_at":"2026-08-06T16:36:08.319708Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.988216Z","title":null,"venue":null,"work_id":"f72a778e-2485-44c3-b226-26dbe53497d3","year":2024},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.514270Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:f5d9a82f7c234252349b171ee8f0785227743f4c1e0e4366ec48458d5ade2724","observation_id":"284f40c9-2153-429b-8df0-074aa4d6ef72","resolution":{"observed_at":"2026-08-06T16:36:10.035696Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.854994Z","title":null,"venue":null,"work_id":"52b51c09-6fd6-453d-bc67-53beaf152c6c","year":2023},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.602073Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:1de84eb174cc23de05f83ba18a7da81c901419474bf388238d8272fbdce881eb","observation_id":"21a4da80-a745-4073-a2c7-78beaf5aa6a3","resolution":{"observed_at":"2026-08-06T16:36:09.893819Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2205.04163","last_updated":"2025-01-14T09:16:01Z","snapshot_observed_at":"2026-08-14T09:53:25.273035Z","submitted_at":"2022-05-09T10:17:32Z","title":"Homological shifts of polymatroidal ideals","version":3},"cited_work":{"arxiv_id":"2205.04163","doi":null,"metadata_source":"pith","pith_arxiv_id":"2205.04163","snapshot_observed_at":"2026-08-06T16:36:08.068100Z","title":"Homological shifts of polymatroidal ideals","venue":"math.AC","work_id":"377359ad-5746-4272-ad87-aa77bd7640df","year":2022},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.672687Z"},"links":{"cited_paper":"/paper/2205.04163","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:d433554abb9db0cf9b060dc287ccc5b6652f79eaeb7011c152eaf108d78e03f7","observation_id":"1f4b1a7a-d64e-46bf-b25c-f2f4725c017c","resolution":{"observed_at":"2026-08-06T16:36:08.151455Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.746008Z","title":"260, Springer-Verlag London, Ltd., London, 2011","venue":null,"work_id":"9c17d1ac-50c9-473e-8bcf-358d3160b274","year":2011},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.775397Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:a0dd51ffaa06fa8c4d8fa700d013d8a3629a831b2ec528e15d84133a677945f4","observation_id":"4b4dd174-ae1d-4932-8ee9-e6ba74ff13d6","resolution":{"observed_at":"2026-08-06T16:36:09.799371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.636509Z","title":null,"venue":null,"work_id":"ec7db6d7-4b68-48d9-8ae2-b2dae02b00f7","year":2021},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.853858Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:900f3507959d01d120f2942e10541f8a6f082bb1cfc6cadf2ad3bb4fb9882630","observation_id":"95ccc52b-9c29-483d-8cd4-20731b09ad01","resolution":{"observed_at":"2026-08-06T16:36:09.687936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.521129Z","title":"3, 1245--1318","venue":null,"work_id":"d87db868-74b5-4f05-8921-0d116a6e838b","year":2005},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:06.962587Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:b0f8d4bf2d79b1e84860a1d109d98eb639caffbc09565d9425f6011684e16821","observation_id":"90f1ddce-6d26-4d0e-a51f-6e3cc94e8da1","resolution":{"observed_at":"2026-08-06T16:36:09.578074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0902.1930","last_updated":"2009-02-11T16:25:41Z","snapshot_observed_at":"2026-08-15T05:55:14.600344Z","submitted_at":"2009-02-11T16:25:41Z","title":"Frobenius splitting and M\\\"obius inversion","version":1},"cited_work":{"arxiv_id":"0902.1930","doi":null,"metadata_source":"pith","pith_arxiv_id":"0902.1930","snapshot_observed_at":"2026-08-06T16:36:07.921141Z","title":"Frobenius splitting and M\\\"obius inversion","venue":"math.AG","work_id":"74f0a4f2-c700-466b-af59-8cd41ff7b285","year":2009},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.042361Z"},"links":{"cited_paper":"/paper/0902.1930","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:971518812d4b5ba8e46bd87e91e58b566b10ee0140197bfd625cec62e13d296c","observation_id":"8987eb5b-cfb9-49e5-a557-3768e9396e7f","resolution":{"observed_at":"2026-08-06T16:36:07.985178Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.430328Z","title":null,"venue":null,"work_id":"9eb268b0-588e-47af-ada4-452fae22e4b3","year":2024},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.139225Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:694b5a88b6dac32f7749a8634faa68b923b76c14cb6a5821699e53a51934397a","observation_id":"723652a7-4788-4ca9-b693-0bfdc94da0fa","resolution":{"observed_at":"2026-08-06T16:36:09.464234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.250139Z","title":"227, Springer-Verlag, New York, 2005","venue":null,"work_id":"58839a23-d7ee-43cf-8de9-ea65a16b4aa8","year":2005},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.207115Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:e8116db13144030425a101fad6f20c414a4eef7590618999e41010b57c8d0a6a","observation_id":"40341a0f-0e2c-4df1-89d2-bc0118ffe16a","resolution":{"observed_at":"2026-08-06T16:36:09.344268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:09.096841Z","title":null,"venue":null,"work_id":"bc21d8fc-f442-4590-8174-5b1381d2bba7","year":2003},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.298623Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:f4fd0b1cc3b5afd6268e7e9479f5930b76595275847988306569be13fed6c36a","observation_id":"39929c5d-551f-4219-85d0-ac203652cc8e","resolution":{"observed_at":"2026-08-06T16:36:09.184430Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:08.972203Z","title":null,"venue":null,"work_id":"b717a351-6762-400a-960a-ef8c1739a6df","year":2002},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.370053Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:6bb566ec7322fcc4fbfefd3727fb7ea538582986238e63340721f085e565f451","observation_id":"9a8e9a10-68c5-4c64-ad29-1684351b1522","resolution":{"observed_at":"2026-08-06T16:36:09.042327Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:08.784689Z","title":null,"venue":null,"work_id":"6742a9bc-2a1b-4b09-9f29-6fc11b84d678","year":2023},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.399205Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:fea6b2bab03c4649f6409c65af72131205d9a62e14e8ddca1ca097027fa31ea6","observation_id":"bcdea516-a445-417d-95f8-fa0a9d01fe16","resolution":{"observed_at":"2026-08-06T16:36:08.890848Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.08399","last_updated":"2023-05-30T13:48:15Z","snapshot_observed_at":"2026-08-13T12:00:49.383823Z","submitted_at":"2023-04-17T16:06:28Z","title":"Dually Lorentzian Polynomials","version":3},"cited_work":{"arxiv_id":"2304.08399","doi":null,"metadata_source":"pith","pith_arxiv_id":"2304.08399","snapshot_observed_at":"2026-08-06T16:36:07.777514Z","title":"Dually Lorentzian Polynomials","venue":"math.CO","work_id":"bff2cf4b-2768-4088-b8d0-79b18ad8eaed","year":2023},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.495399Z"},"links":{"cited_paper":"/paper/2304.08399","citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:f1b060ff100d6d6619c3eec351e76dc51f7272e604a1be0001db5b7070435851","observation_id":"6fc81920-52e6-4256-842c-f62285f7e2e1","resolution":{"observed_at":"2026-08-06T16:36:07.852211Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:08.644743Z","title":null,"venue":null,"work_id":"b7ac6107-05e4-40d0-9613-25370806057d","year":2025},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.564306Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:216f8e82a5fd8ca3e08b3d2e6bd1e5437fc0f1db3355cd7499cd232903e10b8b","observation_id":"77145acc-14ec-4086-88a4-2bd8364dce71","resolution":{"observed_at":"2026-08-06T16:36:08.716010Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-06T16:36:08.545021Z","title":"P olyhedra and efficiency","venue":null,"work_id":"fd96723e-4911-484c-adc5-3db3840ed7cc","year":2003},"citing_paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T16:36:07.681414Z"},"links":{"citing_paper":"/paper/2507.13153"},"observation_digest":"sha256:d1d18841ede230a93e773a0bdcc9d3f26d750412ec590914024c53cb83854b43","observation_id":"668c9b0e-a985-4365-a814-79e60f0c59a3","resolution":{"observed_at":"2026-08-06T16:36:08.566203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.13153","last_updated":"2025-07-17T14:16:02Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-10T15:09:42.336138Z","submitted_at":"2025-07-17T14:16:02Z","title":"Syzygies of polymatroidal ideals"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":5,"verified_fuzzy":5},"total_outbound_references":24},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2507.13153."}