{"as_of":"2026-08-15T18:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2376a39fdc85d6bcd3a7ee60a085a26e4f1e89d05b06a15e0a6dd0535478e768","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T05:25:05.866733Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/2607.22308/citation-record","integrity":"/paper/2607.22308/integrity","json":"/paper/2607.22308/citation-record.json","paper":"/paper/2607.22308"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2202.07613","last_updated":"2022-02-15T17:59:25Z","snapshot_observed_at":"2026-08-14T19:13:58.608713Z","submitted_at":"2022-02-15T17:59:25Z","title":"$q$-deformed rational numbers and the 2-Calabi--Yau category of type $A_2$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.07613","snapshot_observed_at":"2026-08-01T05:25:04.147321Z","title":"Bapat, L","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.147321Z"},"links":{"cited_paper":"/paper/2202.07613","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:77a8de82388798292bfadd90e99465a520c0c61d63429b82a9f08f8a02c7a37c","observation_id":"a1174f84-aad1-464b-bd0b-80ae59c0701e","resolution":{"observed_at":"2026-08-01T05:25:04.147321Z","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":"2026-08-01T05:25:04.250355Z","title":"Culler and P","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.250355Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:26fc8eab437094a0804d8dbc81f7685cf3ffbf7ef71ad5b8fa1a14bae58378b8","observation_id":"d46cbda4-8301-4751-8f56-f02cca5da252","resolution":{"observed_at":"2026-08-01T05:25:04.250355Z","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":"2026-08-01T05:25:04.359509Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.359509Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:2eb81673cf38fdd94ea5031fdc80067ec8a89e3b2fb75f9f8c36fd204dfa0232","observation_id":"51966de1-8c32-44e1-a120-8314d70245c8","resolution":{"observed_at":"2026-08-01T05:25:04.359509Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.1404","last_updated":"2009-01-11T00:17:45Z","snapshot_observed_at":"2026-08-15T08:33:59.362757Z","submitted_at":"2009-01-11T00:17:45Z","title":"Trace Coordinates on Fricke spaces of some simple hyperbolic surfaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.1404","snapshot_observed_at":"2026-08-01T05:25:04.489577Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.489577Z"},"links":{"cited_paper":"/paper/0901.1404","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:0dbfc57059d8d2c115e73f24aaa8df324c0ebf8dfaf43b348e36e1bf69e4d42f","observation_id":"0aefb4ef-b6e8-41f5-b564-5e7bcf4bd95b","resolution":{"observed_at":"2026-08-01T05:25:04.489577Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.02122","last_updated":"2025-03-03T23:10:10Z","snapshot_observed_at":"2026-08-15T03:17:17.685791Z","submitted_at":"2025-03-03T23:10:10Z","title":"Symmetries of the q-deformed real projective line","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.02122","snapshot_observed_at":"2026-08-01T05:25:04.640150Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.640150Z"},"links":{"cited_paper":"/paper/2503.02122","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:a7c8ec9c71783d1af868093a2138c76b5f70fa19654950da86396b8aae2b1f16","observation_id":"03a14290-c0fb-4886-a1f5-d3f8c73b3bf6","resolution":{"observed_at":"2026-08-01T05:25:04.640150Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2603.04295","last_updated":"2026-05-13T10:14:56Z","snapshot_observed_at":"2026-08-07T11:32:16.334881Z","submitted_at":"2026-03-04T17:12:06Z","title":"Plane geometry of $q$-rationals and Springborn Operations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2603.04295","snapshot_observed_at":"2026-08-01T05:25:04.750824Z","title":"Jouteur, O","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.750824Z"},"links":{"cited_paper":"/paper/2603.04295","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:1c4d40d1b8ed4767bbdea853e69f0f513225c51fcd02f63a1f4d1857dcf0f4e7","observation_id":"48ab3e5e-9979-4145-9e81-800df97dcc27","resolution":{"observed_at":"2026-08-01T05:25:04.750824Z","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":"2026-08-01T05:25:04.844459Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.844459Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:44279be801333d5c9a524071cc749018ae604719318f404ebc9906f2eec2dd63","observation_id":"fda3bd81-bcfd-407d-90ac-3329679b6418","resolution":{"observed_at":"2026-08-01T05:25:04.844459Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.02953","last_updated":"2021-01-08T10:50:35Z","snapshot_observed_at":"2026-08-14T19:14:05.424109Z","submitted_at":"2021-01-08T10:50:35Z","title":"$q$-deformations of the modular group and of the real quadratic irrational numbers","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.02953","snapshot_observed_at":"2026-08-01T05:25:04.924454Z","title":"Leclere and S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:04.924454Z"},"links":{"cited_paper":"/paper/2101.02953","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:cdb971872aeb64cb1f6a0492a9f0da5cdc67d165df6509c19fab4e53b9007fbd","observation_id":"a2e81482-2611-4a9e-af24-c490931502ff","resolution":{"observed_at":"2026-08-01T05:25:04.924454Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.00170","last_updated":"2020-02-13T08:33:57Z","snapshot_observed_at":"2026-08-14T19:14:06.980205Z","submitted_at":"2018-12-01T07:43:35Z","title":"$q$-deformed rationals and $q$-continued fractions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.00170","snapshot_observed_at":"2026-08-01T05:25:05.038879Z","title":"Morier-Genoud and V","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.038879Z"},"links":{"cited_paper":"/paper/1812.00170","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:705c2a37623556c8023cf3a05b974aebaf28125ff7f3f8a080dc2a03af61761b","observation_id":"4037bcf8-70f2-4ea2-b21e-a829da8a5d2b","resolution":{"observed_at":"2026-08-01T05:25:05.038879Z","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":"2026-08-01T05:25:05.200732Z","title":"Morier-Genoud and V","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.200732Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:394209e616540452c11db5e8ffdd44e419a599da7f46854c4c20bfeacccb5c79","observation_id":"089cec2f-290b-4132-8e32-2c9b63305e31","resolution":{"observed_at":"2026-08-01T05:25:05.200732Z","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":"2026-08-01T05:25:05.354642Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.354642Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:b33bf308b55b935ad7ab78f508b5b9daf82fb62883ffca4bba2cb312492318a1","observation_id":"ef6376c4-8763-4655-a3e6-5bcbc458f4f5","resolution":{"observed_at":"2026-08-01T05:25:05.354642Z","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":"2026-08-01T05:25:05.466062Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.466062Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:5195f3caa5231ba8eebe6a11dc79ed09845d15e022a9cc0346dcb3bba599ab93","observation_id":"1f6c502f-13dd-4b06-8306-7815476954f2","resolution":{"observed_at":"2026-08-01T05:25:05.466062Z","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":"2026-08-01T05:25:05.574122Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.574122Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:a198b3bd0b412d4bf1db50f9404400a6d8505763d93428290548de3ec506385f","observation_id":"03142783-c962-4158-84d2-7d391142111d","resolution":{"observed_at":"2026-08-01T05:25:05.574122Z","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":"2026-08-01T05:25:05.727133Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.727133Z"},"links":{"citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:e0c0439941c282c6e31342496c1f3b57e867ee581c26c62523852c96e1d3b191","observation_id":"98850317-353e-4d02-b650-cd496cc09a41","resolution":{"observed_at":"2026-08-01T05:25:05.727133Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.06158","last_updated":"2024-06-20T07:20:34Z","snapshot_observed_at":"2026-08-14T19:14:03.293458Z","submitted_at":"2023-08-11T14:36:05Z","title":"Infinitesimal Modular Group: $q$-Deformed $\\mathfrak{sl}_2$ and Witt Algebra","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.06158","snapshot_observed_at":"2026-08-01T05:25:05.866733Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T05:25:05.866733Z"},"links":{"cited_paper":"/paper/2308.06158","citing_paper":"/paper/2607.22308"},"observation_digest":"sha256:a9a66073d11a9fb67aa60532e73b05e89a4de532e121c37aa8eac7de82364e0d","observation_id":"c79fb1e9-fdad-49f1-81b8-a21af5094a13","resolution":{"observed_at":"2026-08-01T05:25:05.866733Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.22308","last_updated":"2026-07-24T13:48:18Z","latest_version":1,"primary_category":"math.QA","snapshot_observed_at":"2026-08-12T13:30:51.666017Z","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":15},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2607.22308."}