{"as_of":"2026-08-10T16:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2aa474aa2b3bc129cb839b848adf93e7a81fde25609244ed06198da4cde98b63","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T12:24:49.642615Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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":"2026-08-04T16:34:15.095325Z","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":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.10351","snapshot_observed_at":"2026-08-04T16:34:15.095325Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.02025","last_updated":"2026-08-03T10:23:43Z","snapshot_observed_at":"2026-08-08T10:39:43.281016Z","submitted_at":"2026-08-03T10:23:43Z","title":"A torsion-free non-sofic group","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T16:34:15.095325Z"},"links":{"cited_paper":"/paper/2607.10351","citing_paper":"/paper/2608.02025"},"observation_digest":"sha256:aaa9fba5f86134ddb32d4cafab499dfe2a2e9c82f43366610ff5f3163ca8a645","observation_id":"0258d5e7-94ce-4a09-bcbc-1314b91e9f08","resolution":{"observed_at":"2026-08-04T16:34:15.095325Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2607.10351/citation-record","integrity":"/paper/2607.10351/integrity","json":"/paper/2607.10351/citation-record.json","paper":"/paper/2607.10351"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T12:24:49.642615Z","title":"Abrams, P","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:b1b9cd61051ce8b8d3da9f9521c328eb5763d3ae43d870fd8f7b1a86a927795b","observation_id":"1e49a7fb-7038-4541-ac0f-0b83642fd153","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":"Abrams and G","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:8f9b4ffe55f00c940f550da99c8b13fc406e33c4b79cea565863f34c3b88b72e","observation_id":"13bf497a-2605-4558-a1e0-14c668faafb0","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":"Ara and E","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:f5ae37382e4bcb8144c6bd98cf26ecc13b173f73b297c3e1fda9b98e2ab4d0ac","observation_id":"0cba8bd2-f8f7-4200-88c7-5caf578af446","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:7464bc28bb0db673aa29b64be2a5a430521a186b7ac88601cd0bd27695d9ec29","observation_id":"764c9807-65af-442f-8279-a827fdfa48ae","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:d1cb047099180c7a80b5d8cee32273405f4c3336771009cecb35ffe390d86728","observation_id":"2b14547c-227b-445a-b09b-a71acf28f1b7","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":"Brownlowe and A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:cc599f118d7cc542a1359d6125e23de47a3991795c3f3440a0614804431cfa8d","observation_id":"0f85bdeb-ef44-40e3-a647-0bf10bba6c1b","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"10.17863/cam.52134","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Apollo (University of Cambridge)","work_id":"b59d133a-bd96-4a0e-abc0-caa528f4f124","year":2019},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:cf362d4b367c4b0c00fb19c77701e5fe875764ac2f6f20ff638469c17df815f9","observation_id":"4368177c-9f2c-4d7e-8194-262359dd4501","resolution":{"observed_at":"2026-07-14T12:30:28.654509Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-07-15T21:50:20.24579+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-15T21:50:20.24579+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-07-14T12:24:49.642615Z","title":"Krsti´ c and J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:3a1049a8d19cabe2599143687d109b950e04fc574be02d133cd3bc0251ce1cce","observation_id":"7f3d7456-588b-4d1f-95ce-e9aaae8df3c3","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":"Lopatkin and T","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:7ed432bf7f24594b186b79204590dfac3c87df5570ebbb3e8722a23a648ef50b","observation_id":"82d260a6-68c8-4e34-8576-370054823dcd","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":"Pardo, The isomorphism problem for Higman–Thompson groups,J","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:1659bfb6cffc994ba87922feb482b222a6a6448825ff093fae1e72331ad6a8c4","observation_id":"54a8deeb-7455-4733-ad2b-e68d2bda3645","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","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":"2026-07-14T12:24:49.642615Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T12:24:49.642615Z"},"links":{"citing_paper":"/paper/2607.10351"},"observation_digest":"sha256:f9e12c03c20b1542d648154fb354428c034d617fdd92624a74c684b841fc8e91","observation_id":"999385cd-ef43-4de5-93fc-acc924687274","resolution":{"observed_at":"2026-07-14T12:24:49.642615Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.10351","last_updated":"2026-07-11T15:24:49Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-08T06:27:12.439063Z","submitted_at":"2026-07-11T15:24:49Z","title":"Matrix generators for the unit groups of $L_K(1,d)$"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":11},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 1 inbound Pith citation observation for arXiv:2607.10351."}