{"as_of":"2026-08-16T21:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cc2677be24d9dee7854912c99951aa27dcbcb1c9de3816baa80e5288abb0c26c","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:14:45.073436Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"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/1908.05921/citation-record","integrity":"/paper/1908.05921/integrity","json":"/paper/1908.05921/citation-record.json","paper":"/paper/1908.05921"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.019591Z","title":"Akbari, M","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.019591Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:fb14a9cd7729159bd8ae7c99308fafe737092e626ae79e9b4a8bf0063ed8898f","observation_id":"17e08917-99a0-4579-a940-8072c3a1ba28","resolution":{"observed_at":"2026-08-14T13:14:45.019591Z","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":"10.1142/s0219498812","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.212823Z","title":"Akbari, R","venue":null,"work_id":"0aa17717-e157-4ace-94eb-32bbe7a12972","year":2013},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.025538Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:2b7b722127aa99d727c7fd265a7812691713b3d0f9ba6e44094a8276fdb31994","observation_id":"d12674a8-91fa-4b6e-9ea2-a55e49429af6","resolution":{"observed_at":"2026-08-14T13:14:45.218310Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s02194988","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.196327Z","title":"Akbari, H","venue":null,"work_id":"e970b27e-54cb-41ba-8c5e-4be2439eb565","year":2012},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.031008Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:8df9e705c54de18ea831a8c6168a6b2e192905b3fb0d99e4a52c663f8983bc4a","observation_id":"95a6ddf6-0f18-4100-a16d-0ff4fe6e5808","resolution":{"observed_at":"2026-08-14T13:14:45.201631Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10474-011-0121-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.178502Z","title":"Amini, B","venue":null,"work_id":"af3c1103-f68f-4aa0-bdf7-57a8d83c4a16","year":2012},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.036087Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:eedd0b44f6733517c177e5eca75997b5c53c5ec7f6354759b9ae81da5eaded51","observation_id":"12ad03d3-3ab2-4339-b7aa-b62d2a767203","resolution":{"observed_at":"2026-08-14T13:14:45.184325Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s1793557118500584","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.161975Z","title":"Amjadi, The essential ideal graph of a commutative rin g, Asian-Eur","venue":null,"work_id":"f745c9f3-2d0a-464d-8b85-ae7dab79a5b4","year":2018},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.043085Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:b986d3fd8d71aec6471b50fdf5656e30b8f65e489d481fa67b6d25fe500afe33","observation_id":"6099a159-217e-4503-895a-3ef4e8ae2d6f","resolution":{"observed_at":"2026-08-14T13:14:45.167309Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.397674Z","title":"Lam, A First Course in Noncommutative Rings, Spring er-Verlag, New York, 2001","venue":null,"work_id":"4bf2b284-b348-42f4-afe0-e8c9fba9bce5","year":2001},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.049637Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:fb81e2df14fa1d7b5cc41af975e5f3fe09725325765e04332ff8e7dcde733073","observation_id":"3be8a0d5-24c8-4fcf-9b2f-756ce2c62401","resolution":{"observed_at":"2026-08-14T13:14:45.402508Z","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":"2026-08-14T13:14:45.381882Z","title":"Lam, Lectures on Modules and Rings, Springer-Verla g, New York 1999","venue":null,"work_id":"c18cbf15-7e63-4de9-926e-3f2785dec717","year":1999},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.058037Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:0a07ca0f1e9d7e4b9bc9b8ee17041c8c7b7f8f7ba09fd858aea762651da9ba18","observation_id":"69870891-0e6c-4d44-853e-cf96f9b4b67f","resolution":{"observed_at":"2026-08-14T13:14:45.387374Z","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":"10.1142/s02194988185013","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.145344Z","title":"Matczuk, M","venue":null,"work_id":"7f030d5c-a190-4494-8cdf-e638ab1c8d9f","year":2018},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.063281Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:2989ef6ad6f9f687bae5b4170da4a0ef531180e05da3052429067c019156a676","observation_id":"67df2537-04d5-4d77-be45-614071e864de","resolution":{"observed_at":"2026-08-14T13:14:45.150230Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jalgebra.2008.06.020","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.128880Z","title":null,"venue":null,"work_id":"ec3a78fd-c0e6-4406-8cd0-2eaf4edcb512","year":2008},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.068388Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:1ba1bccc8908bec8de744c47ce4c25e420e1d5547d90c6739c05dec3247bb25b","observation_id":"9f7607b0-49ac-4f2a-8554-0704c3d8d668","resolution":{"observed_at":"2026-08-14T13:14:45.134160Z","resolver_source":"doi","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":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.laa.2008.08.026","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:14:45.106035Z","title":null,"venue":null,"work_id":"41f26fcb-bc35-454b-9ef8-f051fc162f8d","year":2009},"citing_paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:14:45.073436Z"},"links":{"citing_paper":"/paper/1908.05921"},"observation_digest":"sha256:b9d97a21d4b14df20ec041977a38eeb9de9c33738ef7c30a664f5a4d98661079","observation_id":"fbce9641-b65b-40e6-b64d-41da530999a4","resolution":{"observed_at":"2026-08-14T13:14:45.112205Z","resolver_source":"doi","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"}}],"paper":{"arxiv_id":"1908.05921","last_updated":"2019-08-16T10:22:17Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-16T05:23:09.614866Z","submitted_at":"2019-08-16T10:22:17Z","title":"Sum-Essential Graphs of Modules"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":7,"verified_fuzzy":2},"total_outbound_references":10},"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 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:1908.05921."}