{"as_of":"2026-08-10T08:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:eb088926b310afc523d583a58a4affd331a4664e6ab705cc0580387857ec5824","coverage":[{"denominator":17,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":17,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T23:05:18.452849Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2607.26718/citation-record","integrity":"/paper/2607.26718/integrity","json":"/paper/2607.26718/citation-record.json","paper":"/paper/2607.26718"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:05:18.390648Z","title":"54 SMF, Paris, 1978","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.390648Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:056cb199cccf8893020c847243b8f77d1608ccfd799af626d59654e0a76dff3a","observation_id":"1a2be250-34dc-4144-853e-d03ff9cc6135","resolution":{"observed_at":"2026-07-30T23:05:18.390648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.30450","last_updated":"2026-05-28T18:20:20Z","snapshot_observed_at":"2026-08-08T10:13:09.627841Z","submitted_at":"2026-05-28T18:20:20Z","title":"Quantum cohomology and birational geometry of Verra fourfolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.30450","snapshot_observed_at":"2026-07-30T23:05:18.395069Z","title":"Gu´ er´ e, Manivel L., Perrin N.,Quantum cohomology and birational geometry of Verra fourfolds, arXiv:2605.30450","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.395069Z"},"links":{"cited_paper":"/paper/2605.30450","citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:8e38fb22609cb3ba1db59bd35abbfb60cc16594281b0c360a52a4ff5a33492b1","observation_id":"24df78fd-6f56-4510-8ada-9713dac9d56f","resolution":{"observed_at":"2026-07-30T23:05:18.395069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2603.17487","last_updated":"2026-05-27T09:04:45Z","snapshot_observed_at":"2026-08-08T10:13:34.304352Z","submitted_at":"2026-03-18T08:51:53Z","title":"Quantum cohomology and irrationality of Gushel-Mukai fourfolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2603.17487","snapshot_observed_at":"2026-07-30T23:05:18.399287Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.399287Z"},"links":{"cited_paper":"/paper/2603.17487","citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:d18045d2895e32658be04e78bc7b21c95f5941bc17c15bcef3705fd96decaedf","observation_id":"1b6630a3-f0c8-4f70-af8b-3b2cad32850a","resolution":{"observed_at":"2026-07-30T23:05:18.399287Z","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":"2026-07-30T23:05:18.403324Z","title":"Universitext Springer-Verlag, New York, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.403324Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:786916b2b7fb96400932bac59bbf51cc94cbf6c1c89083e2e8bf2044769aa466","observation_id":"50fdce43-668f-45a6-9be0-ed32179340e9","resolution":{"observed_at":"2026-07-30T23:05:18.403324Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.13030","last_updated":"2025-05-22T13:26:27Z","snapshot_observed_at":"2026-08-05T11:44:45.281267Z","submitted_at":"2021-11-25T11:22:25Z","title":"Fano fourfolds of K3 type","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.13030","snapshot_observed_at":"2026-07-30T23:05:18.407475Z","title":"Institut Fourier","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.407475Z"},"links":{"cited_paper":"/paper/2111.13030","citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:7376273a6ed9365330c3a940c77a11fda420eddd2a8d024e41456398a5bd0edd","observation_id":"74e1a7f0-aa5e-4007-a2c9-245c6a361bf4","resolution":{"observed_at":"2026-07-30T23:05:18.407475Z","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":"2026-07-30T23:05:18.411343Z","title":"Math.59 (2019), no","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.411343Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:6317a18e6723806148eab1cc498a4f32018737ce4bf882b738bc977e21de10ac","observation_id":"2f4887ca-a37b-4c21-b46f-d411a0b8e40e","resolution":{"observed_at":"2026-07-30T23:05:18.411343Z","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":"2026-07-30T23:05:18.415128Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.415128Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:6d0af5cdc1a623342a78c1455d9b0fa9dff4823b91ac2ed4a7ee0db2457467b2","observation_id":"29a397f4-52d2-4e41-b6bc-e2d21eaf3dcb","resolution":{"observed_at":"2026-07-30T23:05:18.415128Z","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":"2026-07-30T23:05:18.418520Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.418520Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:bdec752c7ea83d18529c632a848789ca5c579d568517ac4a969075f42b0595e2","observation_id":"063ff0a8-96bb-4386-93d4-1150e426253c","resolution":{"observed_at":"2026-07-30T23:05:18.418520Z","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":"2026-07-30T23:05:18.421960Z","title":"Springer-Verlag, Berlin, 1995","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.421960Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:1a7f8d4829b962398da7b990a0d45eabab5aee7b9205cb9e0fab51c587d6e288","observation_id":"186cca45-946c-4bbd-8f65-109a715358dd","resolution":{"observed_at":"2026-07-30T23:05:18.421960Z","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":"2026-07-30T23:05:18.426177Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.426177Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:73e42ad298fb1ee9b67dd290d4e6fe1913cfc7580d85a8942b4b6ca404f1a4b0","observation_id":"4d2d7d38-f018-4a8b-bf1c-29e6b922cd1f","resolution":{"observed_at":"2026-07-30T23:05:18.426177Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.13555","last_updated":"2025-02-04T15:37:17Z","snapshot_observed_at":"2026-07-06T15:58:20.063904Z","submitted_at":"2023-07-25T14:59:41Z","title":"Quantum cohomology of blowups","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.13555","snapshot_observed_at":"2026-07-30T23:05:18.429646Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.429646Z"},"links":{"cited_paper":"/paper/2307.13555","citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:7379bc8821cce21be45eb6c95c5355ab3b36c959b50f66242d3defa0f9370104","observation_id":"9e345aab-a7f4-428e-81b5-3c8dd3341323","resolution":{"observed_at":"2026-07-30T23:05:18.429646Z","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":"2026-07-30T23:05:18.433566Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.433566Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:fd5f923e3f4a7a651ae6b92f3d2167b0c11fa06c0f6bcb5e501647b8db2e5b74","observation_id":"ade1be74-9977-40a1-910a-7ae074db21cc","resolution":{"observed_at":"2026-07-30T23:05:18.433566Z","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":"2026-07-30T23:05:18.437115Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.437115Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:550a91c76599bec83306bc9fd8cd7648822b4fedc4245d27b277c8bb681b6a22","observation_id":"4311bdff-9766-4747-9d50-97d61dd7e12c","resolution":{"observed_at":"2026-07-30T23:05:18.437115Z","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":"2026-07-30T23:05:18.440991Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.440991Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:34bf26c3d089a4b3f491cef103d0aa1ced3baafa6771eb283acb7294b6d4795c","observation_id":"35c73543-c0a5-4d15-834e-6bdc0fcea15b","resolution":{"observed_at":"2026-07-30T23:05:18.440991Z","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":"2026-07-30T23:05:18.444734Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.444734Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:d63d77265df16678b77e4a84d44f139131955508c40968b5735d3a90543817ae","observation_id":"d498bd00-8759-47ff-8a7f-0d89869eb98e","resolution":{"observed_at":"2026-07-30T23:05:18.444734Z","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":"2026-07-30T23:05:18.448869Z","title":"IICambridge Stud","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.448869Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:f3e7391acfa6df43ba7bc89cadafb21f74d44fd102b583208f34720c82caa860","observation_id":"79b94a0d-ba6f-43a1-83c6-628568d33b6a","resolution":{"observed_at":"2026-07-30T23:05:18.448869Z","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":"2026-07-30T23:05:18.452849Z","title":"Handbook of moduli","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-30T23:05:18.452849Z"},"links":{"citing_paper":"/paper/2607.26718"},"observation_digest":"sha256:96d44965038c0c463afe150b3a93d9e1a3aa9b5c430b33329aeeee510f376b06","observation_id":"2aee52e5-38a6-4958-9f33-a2506c5ddf87","resolution":{"observed_at":"2026-07-30T23:05:18.452849Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.26718","last_updated":"2026-07-29T10:07:13Z","latest_version":1,"primary_category":"math.AG","snapshot_observed_at":"2026-08-08T10:41:58.213105Z","submitted_at":"2026-07-29T10:07:13Z","title":"An atomic criterion for irrationality without quantum computations"},"reference_resolution":{"displayed":17,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":17},"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 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2607.26718."}