{"as_of":"2026-08-16T21:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9aef9fec5a60cc894366dae692f8b61dc156c759cabb14de6b6aeab8997ccd9f","coverage":[{"denominator":19,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":19,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:14:09.542969Z","state":"measured"},{"denominator":19,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":19,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.09750/citation-record","integrity":"/paper/1908.09750/integrity","json":"/paper/1908.09750/citation-record.json","paper":"/paper/1908.09750"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:14:09.851077Z","title":"Abeasis and A","venue":null,"work_id":"04bf847b-71eb-437a-b80b-b5452f735e6a","year":1980},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.456423Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:a1deb297f522eef55d424f927074df6cbd968dbe5b41ceae8f24db39d45e25ab","observation_id":"d1067a47-38b9-482c-b75d-4e0e188cae0e","resolution":{"observed_at":"2026-08-14T11:14:09.855982Z","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":"1811.08946","last_updated":"2019-10-04T16:06:12Z","snapshot_observed_at":"2026-08-16T17:48:05.092169Z","submitted_at":"2018-11-21T20:54:39Z","title":"Decomposition of persistence modules","version":3},"cited_work":{"arxiv_id":"1811.08946","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.08946","snapshot_observed_at":"2026-08-14T11:14:09.779170Z","title":"Decomposition of persistence modules","venue":"math.RT","work_id":"9ec64cc1-7bfc-4508-b3a3-dfec01b8184f","year":2018},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.471207Z"},"links":{"cited_paper":"/paper/1811.08946","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:4459c51bd824a79dd12cf8913949c5ada6c8b4a7951dec08b3a53ae63eac13bf","observation_id":"408126fc-9678-4064-8ae9-d9d24c3a2bc5","resolution":{"observed_at":"2026-08-14T11:14:09.783854Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"1907.09416","last_updated":"2019-07-22T16:44:01Z","snapshot_observed_at":"2026-08-03T13:47:07.947825Z","submitted_at":"2019-07-22T16:44:01Z","title":"Functors on Posets Left Kan Extend to Cosheaves: an Erratum","version":1},"cited_work":{"arxiv_id":"1907.09416","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.09416","snapshot_observed_at":"2026-08-14T11:14:09.715028Z","title":"Functors on Posets Left Kan Extend to Cosheaves: an Erratum","venue":"math.CT","work_id":"3ae26e77-a407-4ed2-b0bb-f57d712ac373","year":2019},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.491360Z"},"links":{"cited_paper":"/paper/1907.09416","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:653160527d308c14f8b01e413d0a9f74cd68b69b901fc01046aabb2455aca0e3","observation_id":"68dacba9-6639-4b0f-9349-3413c3d908c1","resolution":{"observed_at":"2026-08-14T11:14:09.719629Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"1805.00349","last_updated":"2019-06-02T01:56:25Z","snapshot_observed_at":"2026-08-14T19:20:34.870632Z","submitted_at":"2018-04-30T12:02:48Z","title":"Piecewise linear sheaves","version":3},"cited_work":{"arxiv_id":"1805.00349","doi":null,"metadata_source":"pith","pith_arxiv_id":"1805.00349","snapshot_observed_at":"2026-08-14T11:14:09.663942Z","title":"Piecewise linear sheaves","venue":"math.AG","work_id":"a615888e-4834-487a-9ae2-b1ecc8e04fd7","year":2018},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.512421Z"},"links":{"cited_paper":"/paper/1805.00349","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:60d3bb29746dcfb16cc399beaf6a7bc72d181f902d8559447b63459afb72e460","observation_id":"fdeb6450-0519-41da-960f-93994b63edce","resolution":{"observed_at":"2026-08-14T11:14:09.668181Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"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":"2026-08-14T11:14:09.807169Z","title":"Madden and Trevor McGuire, Neighbors, generic sets and Scarf-Buchberger hy- persurfaces, preprint,","venue":null,"work_id":"7efc8407-2252-4661-8af9-fae6402ad8a7","year":2017},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.521245Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:06e7592e31f4912818de42a71ff8e912d6ed713673f83074fc733eeeb49a1fdb","observation_id":"022f234f-4f21-40e1-815f-f1d7ef38dea1","resolution":{"observed_at":"2026-08-14T11:14:09.811968Z","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":"1511.08224","last_updated":"2015-11-25T21:03:40Z","snapshot_observed_at":"2026-08-14T22:21:17.211123Z","submitted_at":"2015-11-25T21:03:40Z","title":"Neighbors, Generic Sets and Scarf-Buchberger Hypersurfaces","version":1},"cited_work":{"arxiv_id":"1511.08224","doi":null,"metadata_source":"pith","pith_arxiv_id":"1511.08224","snapshot_observed_at":"2026-08-14T11:14:09.631383Z","title":"Neighbors, Generic Sets and Scarf-Buchberger Hypersurfaces","venue":"math.CO","work_id":"950bff3c-473f-4d7e-b60f-123e56b6e460","year":2015},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.525159Z"},"links":{"cited_paper":"/paper/1511.08224","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:e2d7effd7220d1e6833b634f434c1676b1d6196b73faaecb12df132735961d85","observation_id":"51ba5924-081e-4fa2-9f29-ffa97b6863f6","resolution":{"observed_at":"2026-08-14T11:14:09.636018Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"1709.08155","last_updated":"2020-08-12T02:56:11Z","snapshot_observed_at":"2026-08-14T20:30:18.979485Z","submitted_at":"2017-09-24T06:50:44Z","title":"Data structures for real multiparameter persistence modules","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1709.08155","snapshot_observed_at":"2026-08-14T11:14:09.529365Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.529365Z"},"links":{"cited_paper":"/paper/1709.08155","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:db99c29d80bb06c0cf8911342013560461d68a41bff032a0a1f0f0af2b019c95","observation_id":"8a82835d-afbf-4e34-826f-0d68c3a983db","resolution":{"observed_at":"2026-08-14T11:14:09.529365Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1210.1932","last_updated":"2015-12-21T11:53:28Z","snapshot_observed_at":"2026-07-06T02:57:05.724875Z","submitted_at":"2012-10-06T08:40:00Z","title":"A presentation of general multipersistence modules computable in polynomial time?","version":2},"cited_work":{"arxiv_id":"1210.1932","doi":null,"metadata_source":"pith","pith_arxiv_id":"1210.1932","snapshot_observed_at":"2026-08-14T11:14:09.595152Z","title":"A presentation of general multipersistence modules computable in polynomial time?","venue":"math.AT","work_id":"a04ffcc9-cb7b-4e74-8558-ccc9e25e583e","year":2012},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.538238Z"},"links":{"cited_paper":"/paper/1210.1932","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:2db7bc5436d0ac307db0122749ea2da2d43450f2b371aec30494d7fde2601fb5","observation_id":"7c1d68bd-33c8-4c9d-a473-5e6d8f591d83","resolution":{"observed_at":"2026-08-14T11:14:09.601595Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"1705.00955","last_updated":"2018-09-07T09:02:39Z","snapshot_observed_at":"2026-08-14T21:03:21.940565Z","submitted_at":"2017-05-02T13:23:03Z","title":"Persistent homology and microlocal sheaf theory","version":6},"cited_work":{"arxiv_id":"1705.00955","doi":null,"metadata_source":"pith","pith_arxiv_id":"1705.00955","snapshot_observed_at":"2026-08-14T11:14:09.682521Z","title":"Persistent homology and microlocal sheaf theory","venue":"math.AT","work_id":"6f798dd1-29e0-466d-bc74-4e4cf64f2d62","year":2017},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":990,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.507823Z"},"links":{"cited_paper":"/paper/1705.00955","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:1fe63b337da8484b84054fb876718f64378e3b961f75cfbaefc3c791d59a7435","observation_id":"634d1608-c40d-43da-8b1e-26a0d7463e5f","resolution":{"observed_at":"2026-08-14T11:14:09.687252Z","resolver_source":"local_arxiv","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"}},{"citation":{"cited_paper":{"arxiv_id":"1708.07390","last_updated":"2019-06-18T14:10:14Z","snapshot_observed_at":"2026-08-14T20:39:19.987221Z","submitted_at":"2017-08-24T13:22:59Z","title":"Stratifying multiparameter persistent homology","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.07390","snapshot_observed_at":"2026-08-14T11:14:09.503692Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":1986,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.503692Z"},"links":{"cited_paper":"/paper/1708.07390","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:78f1a1f24c0b05e0b1b55fb0ccda06af79060308e35b3d57a3d699fe2abe8839","observation_id":"1e8af044-cdef-4289-8b09-dbf585df9cdd","resolution":{"observed_at":"2026-08-14T11:14:09.503692Z","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":"2026-08-14T11:14:09.542969Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":1997,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.542969Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:ae17dce42bea202e2c4968e8b89564ba40c998c70431ef76124ac9a93f7c38ca","observation_id":"4f4fb1c6-6130-436b-86dd-a5095717c7e6","resolution":{"observed_at":"2026-08-14T11:14:09.542969Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-14T11:14:09.533819Z","title":"[NR72] L","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2005,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.533819Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:b915604cea9e56ef6aca71cf3e725c67146e29200bc618358392c0696de42be5","observation_id":"13c9243f-0254-4a14-93ad-d6226e7c192a","resolution":{"observed_at":"2026-08-14T11:14:09.533819Z","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":"2026-08-14T11:14:09.821296Z","title":null,"venue":null,"work_id":"a41534f9-aee0-4ff7-9cac-e52551e642f8","year":2002},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.496252Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:4cc9ae9d5b7884ec8e8f5ff471e1f484112f5e3534a40886dcf7c903ff22b535","observation_id":"748f0ba6-1b93-430c-9fbf-1fd0f9bcee88","resolution":{"observed_at":"2026-08-14T11:14:09.825849Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"1303.3255","last_updated":"2014-12-17T19:59:07Z","snapshot_observed_at":"2026-08-15T00:25:17.823138Z","submitted_at":"2013-03-13T19:40:51Z","title":"Sheaves, Cosheaves and Applications","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1303.3255","snapshot_observed_at":"2026-08-14T11:14:09.485952Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.485952Z"},"links":{"cited_paper":"/paper/1303.3255","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:e9f5055aedaf6c73f4f299f091d68415e0032a3c248db5b9d69dced0c4889be0","observation_id":"ae75c9d4-5270-4165-8ad4-90180d20d541","resolution":{"observed_at":"2026-08-14T11:14:09.485952Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1512.00180","last_updated":"2015-12-01T09:12:26Z","snapshot_observed_at":"2026-08-16T19:02:51.131266Z","submitted_at":"2015-12-01T09:12:26Z","title":"Interactive Visualization of 2-D Persistence Modules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.00180","snapshot_observed_at":"2026-08-14T11:14:09.516587Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.516587Z"},"links":{"cited_paper":"/paper/1512.00180","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:40a76a22a345da498baa602a5b0de3acc2bf6a623177f7fb510a0d9b0b60e187","observation_id":"d26ab1dd-8ca4-464e-9814-99d3c313cfb6","resolution":{"observed_at":"2026-08-14T11:14:09.516587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1210.0819","last_updated":"2014-07-29T09:36:27Z","snapshot_observed_at":"2026-08-16T14:30:20.843216Z","submitted_at":"2012-10-02T16:04:11Z","title":"Decomposition of pointwise finite-dimensional persistence modules","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1210.0819","snapshot_observed_at":"2026-08-14T11:14:09.480650Z","title":"Clifford, Partially ordered abelian groups , Annals of Math","venue":null,"work_id":null,"year":1940},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.480650Z"},"links":{"cited_paper":"/paper/1210.0819","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:775c0e046088fd0cb8df5189dd5d8f8c03decc058cb9d425a697942de00b5375","observation_id":"41b761fe-6cca-46dd-ad8e-fc542ddb6589","resolution":{"observed_at":"2026-08-14T11:14:09.480650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1206.1819","last_updated":"2015-12-21T11:53:41Z","snapshot_observed_at":"2026-07-06T02:49:36.049110Z","submitted_at":"2012-06-08T16:54:47Z","title":"Combinatorial resolutions of multigraded modules and multipersistent homology","version":2},"cited_work":{"arxiv_id":"1206.1819","doi":null,"metadata_source":"pith","pith_arxiv_id":"1206.1819","snapshot_observed_at":"2026-08-14T11:14:09.760721Z","title":"Combinatorial resolutions of multigraded modules and multipersistent homology","venue":"math.AT","work_id":"c89821ca-e5ac-4896-91ed-e4cdcbd5a2ce","year":2012},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.500042Z"},"links":{"cited_paper":"/paper/1206.1819","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:dc92f3de090848b180d6560b1a564967c0e5985b4fbe3cf908458a7a36842a05","observation_id":"ad3374d5-8e8e-4747-8906-a71755333c08","resolution":{"observed_at":"2026-08-14T11:14:09.765043Z","resolver_source":"local_arxiv","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"}},{"citation":{"cited_paper":{"arxiv_id":"1902.09933","last_updated":"2020-06-30T14:09:59Z","snapshot_observed_at":"2026-08-15T00:53:39.944253Z","submitted_at":"2019-02-26T13:51:04Z","title":"Ephemeral persistence modules and distance comparison","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.09933","snapshot_observed_at":"2026-08-14T11:14:09.466119Z","title":"43 (1942), 298–331","venue":null,"work_id":null,"year":1942},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.466119Z"},"links":{"cited_paper":"/paper/1902.09933","citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:10e33f9495213b54bd434c1b0c415efd3617e66fc536ae4a63b857309e6aa010","observation_id":"d4aec7dc-c025-4a4b-9685-e9b8b2f6e52f","resolution":{"observed_at":"2026-08-14T11:14:09.466119Z","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":"2026-08-14T11:14:09.836160Z","title":null,"venue":null,"work_id":"070b735a-3196-45ad-94b7-34803490f4d7","year":2011},"citing_paper":{"arxiv_id":"1908.09750","last_updated":"2020-08-12T02:38:01Z","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra","version":2},"reference_index":3432,"source":"pdf_text","source_observed_at":"2026-08-14T11:14:09.461672Z"},"links":{"citing_paper":"/paper/1908.09750"},"observation_digest":"sha256:965d0c07b747cf90e300102803b896850594d766c2feaff433b28225251f7a53","observation_id":"a8d8e227-10d5-4cbe-a5ba-bae33ea8fb3a","resolution":{"observed_at":"2026-08-14T11:14:09.841027Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"1908.09750","last_updated":"2020-08-12T02:38:01Z","latest_version":2,"primary_category":"math.AC","snapshot_observed_at":"2026-08-16T19:58:15.535592Z","submitted_at":"2019-08-26T15:45:42Z","title":"Modules over posets: commutative and homological algebra"},"reference_resolution":{"displayed":19,"state_counts":{"malformed_identifier":2,"metadata_mismatch":4,"parse_uncertain":0,"unresolved":9,"verified_exact":2,"verified_fuzzy":2},"total_outbound_references":19},"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 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:1908.09750."}