{"as_of":"2026-08-14T22:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ba1c19b4b101a4a687fca5a5b38e9c917554fb45a3930d9b1dcea0be27344bac","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:56:42.674622Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2411.19883/citation-record","integrity":"/paper/2411.19883/integrity","json":"/paper/2411.19883/citation-record.json","paper":"/paper/2411.19883"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.18645","last_updated":"2025-06-30T03:18:35Z","snapshot_observed_at":"2026-08-12T23:55:40.256869Z","submitted_at":"2024-05-28T23:07:16Z","title":"Facets of module theory over semirings","version":3},"cited_work":{"arxiv_id":"2405.18645","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.18645","snapshot_observed_at":"2026-08-12T05:56:42.774792Z","title":"Facets of module theory over semirings","venue":"math.AG","work_id":"233a6c40-5ea8-4b8f-bab3-eac0150c23a1","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":1,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.620166Z"},"links":{"cited_paper":"/paper/2405.18645","citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:e008bcc20c9b81e84ebc56a55c599f458a642ece8afea3c7ed4ff79a1b111fbf","observation_id":"c19333ae-c98c-4a68-9505-a325a3d11197","resolution":{"observed_at":"2026-08-12T05:56:42.779742Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T05:56:42.885148Z","title":"A module-theoretic approach to matroids","venue":null,"work_id":"7aeefe6d-c8d9-460e-91b0-9b6d9ffb4cac","year":2020},"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":2,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.625642Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:d37389cff7402fbe6bef3f63520f8a8691acc9f36250ef4bf4bcf601ee139eaf","observation_id":"24407dfd-19ce-4cd0-a8d3-29c286e4ac70","resolution":{"observed_at":"2026-08-12T05:56:42.890748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T05:56:42.869722Z","title":"Equations of tropical varieties","venue":null,"work_id":"5312c5e9-1754-46b5-b09d-466a89e2f9e1","year":2016},"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":3,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.629896Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:0bfa128c7b59d3138b692a176300985047b6037b0d0e5104da726e2a2aa5cfdd","observation_id":"71833e36-c4f6-4eb3-99cf-2c824e641df8","resolution":{"observed_at":"2026-08-12T05:56:42.875483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T05:56:42.634666Z","title":"A G rassmann algebra for matroids","venue":null,"work_id":null,"year":2018},"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":4,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.634666Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:c6d38f3b5bf279063917342ce81404d0d2c130d0c38c1889f39a08611342c5e5","observation_id":"8bfd8be0-eb1b-4343-8dfd-2bd24c5c896e","resolution":{"observed_at":"2026-08-12T05:56:42.634666Z","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":"2026-08-12T05:56:42.846785Z","title":"Prime congruences of additively idempotent semirings and a nullstellensatz for tropical polynomials","venue":null,"work_id":"cae24ad1-0b7e-4976-8b9d-994011524338","year":2018},"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":5,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.640122Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:d52654f6ad0632544556e025d0667e3c3414f65e4bc1599c7aa953f3bbbb90ab","observation_id":"d5f8d7d3-0428-4942-baf9-32dde4c1b8ff","resolution":{"observed_at":"2026-08-12T05:56:42.851648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T05:56:42.832218Z","title":"Vector bundles on tropical schemes","venue":null,"work_id":"f58fae77-f888-4e37-842a-eae71b16721d","year":2023},"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":6,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.644353Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:73e659d49ce6afcdb8df93a07961c133b6fa8ce01b0cd4df185c65c0e86b47c8","observation_id":"8a903fb7-25fc-4f53-a060-a7200a0c17a7","resolution":{"observed_at":"2026-08-12T05:56:42.837323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.06933","last_updated":"2024-06-11T04:15:13Z","snapshot_observed_at":"2026-08-14T11:50:25.657090Z","submitted_at":"2024-06-11T04:15:13Z","title":"Equivariant vector bundles on toric schemes over semirings","version":1},"cited_work":{"arxiv_id":"2406.06933","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.06933","snapshot_observed_at":"2026-08-12T05:56:42.757686Z","title":"Equivariant vector bundles on toric schemes over semirings","venue":"math.AG","work_id":"07e926f9-880d-4c8b-b660-48204bdda62a","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":7,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.649043Z"},"links":{"cited_paper":"/paper/2406.06933","citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:4488279d5afa8e0fbb7f7bf80142c467f9404c5ec937876b82a9eb00c12bd441","observation_id":"656031b5-7f76-410f-be26-474d27c2e676","resolution":{"observed_at":"2026-08-12T05:56:42.762863Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:56:42.818282Z","title":"Matroidal representations","venue":null,"work_id":"3f781647-fa9b-418c-b755-a71932069583","year":2025},"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":9,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.657709Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:dd144edf22b4fde2e4958be06e0dace1c96025ef66bac958a6d5560c5ee7068f","observation_id":"21ff7714-be7a-4400-9fcf-f20e3692f530","resolution":{"observed_at":"2026-08-12T05:56:42.822811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1508.07949","last_updated":"2022-06-02T14:15:01Z","snapshot_observed_at":"2026-08-14T20:44:03.503497Z","submitted_at":"2015-08-31T18:32:03Z","title":"A unifying approach to tropicalization","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.07949","snapshot_observed_at":"2026-08-12T05:56:42.661564Z","title":"Scheme theoretic tropicalization","venue":null,"work_id":null,"year":2015},"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":10,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.661564Z"},"links":{"cited_paper":"/paper/1508.07949","citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:4370d394633e5fc72950c9a34caddcfe5680b9544fa03c61ed219d7135cb0c91","observation_id":"61febc5d-7407-4318-9ebd-ac22ebbff239","resolution":{"observed_at":"2026-08-12T05:56:42.661564Z","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":"2026-08-12T05:56:42.803604Z","title":"Tropical ideals","venue":null,"work_id":"98788102-7b94-422c-976d-01651123a852","year":2018},"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":11,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.666391Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:c8cdb180993c3ca45393c5738514417472acaa13c3ce3479fe987781dd88b097","observation_id":"de8fa743-f354-4fb4-8f9b-f830db7068cd","resolution":{"observed_at":"2026-08-12T05:56:42.808987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T05:56:42.790468Z","title":"Tropical schemes, tropical cycles, and valuated matroids","venue":null,"work_id":"331a34d5-d8fa-4f3b-b85e-cac2f7eae01b","year":2020},"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":12,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.670130Z"},"links":{"citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:eeb767787fe38123bdd79e3081c927ce80be3bfa0c6277e982d161bc5043a907","observation_id":"3d77d441-8b39-4cab-80a2-8735ae4f4354","resolution":{"observed_at":"2026-08-12T05:56:42.795094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1709.03174","last_updated":"2018-05-18T14:37:37Z","snapshot_observed_at":"2026-08-14T20:34:33.803729Z","submitted_at":"2017-09-10T20:37:57Z","title":"An informal overview of triples and systems","version":5},"cited_work":{"arxiv_id":"1709.03174","doi":null,"metadata_source":"pith","pith_arxiv_id":"1709.03174","snapshot_observed_at":"2026-08-12T05:56:42.709163Z","title":"An informal overview of triples and systems","venue":"math.AC","work_id":"1b8724b4-7daa-419e-8e91-db620a990a41","year":2017},"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":13,"source":"arxiv_source","source_observed_at":"2026-08-12T05:56:42.674622Z"},"links":{"cited_paper":"/paper/1709.03174","citing_paper":"/paper/2411.19883"},"observation_digest":"sha256:d08721da745e8f5d210fc87779d83ca498346935722cac026b8a1e3e3b5ba5b1","observation_id":"889c9e8f-204c-42f5-a1fc-c358b0a1355b","resolution":{"observed_at":"2026-08-12T05:56:42.716644Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.19883","last_updated":"2025-02-14T18:24:17Z","latest_version":3,"primary_category":"math.RT","snapshot_observed_at":"2026-08-12T05:40:42.463146Z","submitted_at":"2024-11-29T17:48:59Z","title":"Representation theory over semifields"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":3,"verified_fuzzy":7},"total_outbound_references":13},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2411.19883."}