{"as_of":"2026-08-16T20:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:185b70cc1227019573de34bfacdf618353d674a1082e7a2a8dcb5308d6db44e7","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:56:44.138182Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:56:42.653575Z","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":"2026-07-04T00:59:20.134115Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.19889","snapshot_observed_at":"2026-08-12T05:56:42.653575Z","title":"Tropical representations and valuated matroids","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.19883","last_updated":"2025-02-14T18:24:17Z","snapshot_observed_at":"2026-08-12T05:40:42.463146Z","submitted_at":"2024-11-29T17:48:59Z","title":"Representation theory over semifields","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.653575Z"},"links":{"cited_paper":"/paper/2411.19889","citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:77d0a0d64277920f0b302986db40b74633e62df3b58efd6ccefe69c02955bdc9","observation_id":"2ce816aa-fe43-44b8-a894-beda42f2253c","resolution":{"observed_at":"2026-08-12T05:56:42.653575Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"cited_work":{"arxiv_id":"2411.19889","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.19889","snapshot_observed_at":"2026-07-04T00:59:20.134115Z","title":"Tropical representations and valuated matroids","venue":null,"work_id":"ae57f695-1d70-4047-9414-45fba2ce5eff","year":2024},"citing_paper":{"arxiv_id":"2606.18562","last_updated":"2026-06-17T00:28:44Z","snapshot_observed_at":"2026-08-01T10:21:56.953399Z","submitted_at":"2026-06-17T00:28:44Z","title":"Closure operators and geometric modules of valuated matroids","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-26T20:49:43.897662Z"},"links":{"cited_paper":"/paper/2411.19889","citing_paper":"/paper/2606.18562"},"observation_digest":"sha256:6bbb6c33f95a4f4457837233b9bba15cd4f1ae2d1f4bef9f5a0371a78bfab193","observation_id":"5d5f62af-b41d-4eb6-98ca-090155b2cdbb","resolution":{"observed_at":"2026-07-04T00:59:20.137301Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.19889/citation-record","integrity":"/paper/2411.19889/integrity","json":"/paper/2411.19889/citation-record.json","paper":"/paper/2411.19889"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.18645","last_updated":"2025-06-30T03:18:35Z","snapshot_observed_at":"2026-08-16T13:48:24.418911Z","submitted_at":"2024-05-28T23:07:16Z","title":"Facets of module theory over semirings","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.18645","snapshot_observed_at":"2026-08-12T05:56:44.059918Z","title":"Facets of module theory over semirings","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.059918Z"},"links":{"cited_paper":"/paper/2405.18645","citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:4808c0c5ba27dbc8e36c74b6a077c90344379bab35edcc73b2ce05ff37b9ae73","observation_id":"4eeca2ab-dbfe-4af2-a2b2-2ae4109b2ae4","resolution":{"observed_at":"2026-08-12T05:56:44.059918Z","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":"2026-08-12T05:56:44.064438Z","title":"Cohomology of groups , volume 87","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.064438Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:5db28b486dde96e9e26635dc7b08acba3f3277c409dca2ae0488804a94202f21","observation_id":"d0d91701-2116-4f61-8e42-428b62fe1722","resolution":{"observed_at":"2026-08-12T05:56:44.064438Z","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":"2026-08-12T05:56:44.356774Z","title":"Valuated matroids","venue":null,"work_id":"7a28e3a8-272e-4531-bb6b-0d0af0cb6a83","year":1992},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.068289Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:1be5274d50f7d7c2879f8b59b3e9105e37f86db428fb7ac4340545fa502f08b4","observation_id":"f85efa93-9971-4f1a-8585-b5e792805bd6","resolution":{"observed_at":"2026-08-12T05:56:44.360809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.344587Z","title":"Tropical cycles and C how polytopes","venue":null,"work_id":"90bb692c-4aec-4596-bcc1-61ce8c6bce5b","year":2013},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.071891Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:a2fd7330b8e7bf25119f4cec3d0c7f428e77f0839746b7d0a751e907644d1e65","observation_id":"bec0cffe-ecc9-4463-a068-fb78475755bd","resolution":{"observed_at":"2026-08-12T05:56:44.348592Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.077090Z","title":"Tropical varieties, maps and gossip","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.077090Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:c16f3114642be4d2e8621421713d52c2644b2f63626f95ef98fa2ad0b19e89a0","observation_id":"467c05a8-caf8-4a2e-8154-fc8798c23ac3","resolution":{"observed_at":"2026-08-12T05:56:44.077090Z","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":"2026-08-12T05:56:44.081695Z","title":"Equations of tropical varieties","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.081695Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:a6c999cab650ddac5d8d2e00e140bb9d5bc0b7658b4fafdf655f2f044963ba47","observation_id":"3afd422f-1aa8-412d-bcd9-2e0d0103764d","resolution":{"observed_at":"2026-08-12T05:56:44.081695Z","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":"2026-08-12T05:56:44.085749Z","title":"A G rassmann algebra for matroids","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.085749Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:bfd9bf4c78f086b49114c759c19dd9387ddb22bcce39fb6eea13e0f407aae4ea","observation_id":"0f66c70e-7b07-45d0-9003-c11ab0c22294","resolution":{"observed_at":"2026-08-12T05:56:44.085749Z","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":"2026-08-12T05:56:44.090184Z","title":"Matroidal representations of groups","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.090184Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:2658f3f4c26aa973a4deb6c5a4527e84651b0e4e56abf989946afabe8de6d0c5","observation_id":"3ac770a3-5235-477a-9b2c-3f5a61bd58ab","resolution":{"observed_at":"2026-08-12T05:56:44.090184Z","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":"2026-08-12T05:56:44.305293Z","title":"Methods and applications of (max,+) linear algebra","venue":null,"work_id":"d7f5baaa-bdd8-4bb2-ae29-649b0294ae9c","year":1997},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.093892Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:77801eafd996ca349e6ee355cc3d173ca9b5b6088fcc528439ed258afb93b31a","observation_id":"0d5fc0bf-5e23-42dc-94cb-def88984321f","resolution":{"observed_at":"2026-08-12T05:56:44.310035Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.293474Z","title":"On the automorphism group of a cone","venue":null,"work_id":"f5d8c5a0-7161-41f0-9dda-ba92d4a8fcf9","year":1978},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.097928Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:29a6463865d81ef9916736d12039f8df4916578f55fb280bc7e6a9f1eb2bad2f","observation_id":"8c97f2be-d94b-4f40-bd9b-bd3f7b2049bd","resolution":{"observed_at":"2026-08-12T05:56:44.297821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.18648","last_updated":"2023-11-30T15:57:16Z","snapshot_observed_at":"2026-08-16T14:38:47.526290Z","submitted_at":"2023-11-30T15:57:16Z","title":"Tropical Quiver Grassmannians","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.18648","snapshot_observed_at":"2026-08-12T05:56:44.102315Z","title":"Tropical quiver G rassmannians","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.102315Z"},"links":{"cited_paper":"/paper/2311.18648","citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:f50318e9dc80b2f271ad7118843c10f54d8759d49a9c0ab8c3aeb1757d4e28cf","observation_id":"e3b031a4-0911-499b-8aa5-1f03fadf73c9","resolution":{"observed_at":"2026-08-12T05:56:44.102315Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.09255","last_updated":"2026-04-13T11:41:19Z","snapshot_observed_at":"2026-07-06T17:59:55.100798Z","submitted_at":"2024-04-14T13:42:57Z","title":"Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\\mathbb{F}_1$-points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.09255","snapshot_observed_at":"2026-08-12T05:56:44.106342Z","title":"Quiver matroids-- M atroid morphisms, quiver G rassmannians, their E uler characteristics and F _1 -points","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.106342Z"},"links":{"cited_paper":"/paper/2404.09255","citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:6658d8812b7ca4b2d70f43814b274b460e746002a8c6c82829c674ffd5aab71e","observation_id":"a94de358-ab77-413f-ba36-462e3820486f","resolution":{"observed_at":"2026-08-12T05:56:44.106342Z","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":"2026-08-12T05:56:44.111218Z","title":"Vector bundles on tropical schemes","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.111218Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:f802ce40a8b02dc6a1aba0467643d8148f2aa4ff435d4eb55a91c7dd057e1114","observation_id":"3ba5d048-7f8b-47dd-9720-5854145fcfcd","resolution":{"observed_at":"2026-08-12T05:56:44.111218Z","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":"2026-08-12T05:56:44.273396Z","title":"Representation theory over semifields and matroidal representations","venue":null,"work_id":"921204f1-d68e-4389-aa5d-5e11989a5ca9","year":2024},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.114509Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:abfa51b361720fcc2808a23c9d595315a975b2e31c7de831dde624c4dd76abfc","observation_id":"3041ab5b-43cf-4cb7-bc35-1efe63f769c9","resolution":{"observed_at":"2026-08-12T05:56:44.278390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.260820Z","title":"Th \\'e orie alg \\'e brique des syst \\`e mes \\`a \\'e v \\'e nements discrets","venue":null,"work_id":"056a31ed-7411-4c9c-8ac9-0dfaa98cd1b2","year":1988},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.118219Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:2999963c4c9fd95a91eaf5368829a466d3e8a2122c358dce07e884a50b6701d6","observation_id":"95b4de88-df97-478a-a396-5a828af93b85","resolution":{"observed_at":"2026-08-12T05:56:44.264908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.08349","last_updated":"2024-10-10T20:13:22Z","snapshot_observed_at":"2026-08-16T13:10:32.604447Z","submitted_at":"2024-10-10T20:13:22Z","title":"Tropical subrepresentations of the boolean regular representation in low dimension","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.08349","snapshot_observed_at":"2026-08-12T05:56:44.121875Z","title":"Tropical subrepresentations of the B oolean regular representation in low dimension","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.121875Z"},"links":{"cited_paper":"/paper/2410.08349","citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:9c3acfddc0ec81bab765bc585871326b2177c7ccf6c859a18b6e42ecd1e66f26","observation_id":"aaae21b1-79b6-488f-ac1f-f6016211aedb","resolution":{"observed_at":"2026-08-12T05:56:44.121875Z","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":"2026-08-12T05:56:44.249069Z","title":"Introduction to tropical geometry , volume 161","venue":null,"work_id":"6838a389-6491-4730-84bb-da531599cfc8","year":2021},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.126410Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:863749df70ec234a3644cc76c6bd76a560174e81347c46edfbc10abbd4077368","observation_id":"02ee54c2-88dd-4bc4-a5b6-49f732272965","resolution":{"observed_at":"2026-08-12T05:56:44.253055Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.236906Z","title":"Zeta functions of graphs: a stroll through the garden , volume 128","venue":null,"work_id":"99848b85-0dd9-403d-9f7f-789fa56f0293","year":2010},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.130791Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:66771b37c34775801f7e710ab241e99a215fa281c9966ef5af9530f5ffa189ec","observation_id":"5f843b03-0f66-4eff-b17c-0d411d20031c","resolution":{"observed_at":"2026-08-12T05:56:44.241744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.224119Z","title":"Modul\\\"oids and pseudomodules 1","venue":null,"work_id":"47f0783f-f717-45de-bf08-7e4d667bcdd4","year":1991},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.134376Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:70ce7933f21c6d6576e92b06400d76c01aba1611ac9c484a2fcd0a646707ff2f","observation_id":"ead839fe-b467-42a0-809d-e310903498cf","resolution":{"observed_at":"2026-08-12T05:56:44.228726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-12T05:56:44.209353Z","title":"An introduction to homological algebra","venue":null,"work_id":"9cd87d26-4302-4a7e-923d-fecb833f1395","year":1994},"citing_paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:44.138182Z"},"links":{"citing_paper":"/paper/2411.19889"},"observation_digest":"sha256:d31e64392a815eda103ef38dc4bd9c5db59c8ee817580e208f5727e2cbf9f160","observation_id":"7780eaa8-d58c-4f59-88eb-d0806d149f6d","resolution":{"observed_at":"2026-08-12T05:56:44.215021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.19889","last_updated":"2024-11-29T17:54:59Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-12T05:40:16.924946Z","submitted_at":"2024-11-29T17:54:59Z","title":"Tropical representations and valuated matroids"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":10},"total_outbound_references":20},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 2 inbound Pith citation observations for arXiv:2411.19889."}