{"as_of":"2026-08-12T10:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9e3c08e62bd2954c2bc0dedd6720dadd00dd3b9ea65e4047bbf3d6e4a8155ad2","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T02:35:18.003611Z","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":"2026-08-12T06:34:41.77262+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":"2026-08-10T21:21:12.188443Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-10T21:21:12.305664Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"cited_work":{"arxiv_id":"2607.14332","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.14332","snapshot_observed_at":"2026-08-10T21:21:12.305664Z","title":"Dimers, filters, and $q$-deformed real numbers","venue":"math.PR","work_id":"8103eebf-86b4-42bf-bef9-f60caa6ea83b","year":2026},"citing_paper":{"arxiv_id":"2608.06761","last_updated":"2026-08-07T03:28:01Z","snapshot_observed_at":"2026-08-12T10:10:24.263853Z","submitted_at":"2026-08-07T03:28:01Z","title":"Coefficients of $q$-real numbers: their combinatorial meaning and growth","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T21:21:12.188443Z"},"links":{"cited_paper":"/paper/2607.14332","citing_paper":"/paper/2608.06761"},"observation_digest":"sha256:338557e3520b56ef94b39d9cfef29b02f7b455eb289a1eaf5a01b88da0496e42","observation_id":"51297070-7da8-4262-9fa0-8ed58a63d837","resolution":{"observed_at":"2026-08-10T21:21:12.310137Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.14332/citation-record","integrity":"/paper/2607.14332/integrity","json":"/paper/2607.14332/citation-record.json","paper":"/paper/2607.14332"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:35:16.722242Z","title":"Aval and S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:16.722242Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:37db816684c40fd2902389cc74bd011396a625f8a430ab89b170412c9fd94d30","observation_id":"5fed470b-d20d-40c4-9f31-384f01795d4f","resolution":{"observed_at":"2026-08-02T02:35:16.722242Z","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":"2026-08-02T02:35:16.795352Z","title":"Bapat, L","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:16.795352Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:19046d8e6029801a356698c4cc1e09ed0b4017ba9df51493b086ef4fd35a9453","observation_id":"940ad061-1437-444f-bc42-256cbda0264c","resolution":{"observed_at":"2026-08-02T02:35:16.795352Z","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":"2026-08-02T02:35:16.880972Z","title":"Burcroff, N","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:16.880972Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:06e2d3d8c1e1386d02e38293545afc0c7f3212f1c17f2e3d241384fe8a9f1ad2","observation_id":"b56bbdec-346c-44a0-8a1c-f34d65a4f1f1","resolution":{"observed_at":"2026-08-02T02:35:16.880972Z","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":"2026-08-02T02:35:16.951630Z","title":"Calkin and H","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:16.951630Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:2ecd9d6edae5417af3a686eedef2f3f0fc7ef8c272e0832337b435c2c8e089b1","observation_id":"e8ce2f8f-2e26-4b5c-a2fb-7662f19822b6","resolution":{"observed_at":"2026-08-02T02:35:16.951630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.08440","last_updated":"2026-08-06T06:14:09Z","snapshot_observed_at":"2026-08-09T23:09:15.191871Z","submitted_at":"2025-08-11T19:56:33Z","title":"On $q$-real and $q$-complex numbers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.08440","snapshot_observed_at":"2026-08-02T02:35:17.030385Z","title":"Etingof, Onq-real andq-complex numbers (arXiv:2508.08440), preprint (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.030385Z"},"links":{"cited_paper":"/paper/2508.08440","citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:68ded10db293ec25505c85404af632e3239c4218d0f60137a93a7ffb86ed69b1","observation_id":"600ede8d-3565-475c-aac7-fd6864549b26","resolution":{"observed_at":"2026-08-02T02:35:17.030385Z","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":"2026-08-02T02:35:17.096490Z","title":"Georgii, Gibbs Measures and Phase Transitions, De Gruyter Studies in Mathe- matics9, De Gruyter (2011)","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.096490Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:994169923df8033ced266ecb1db64edb4ea54f8dc832222e613b6398ef5bb346","observation_id":"462fdfc5-88b3-4e29-b477-11b133585958","resolution":{"observed_at":"2026-08-02T02:35:17.096490Z","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":"2026-08-02T02:35:17.216974Z","title":"McConville, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.216974Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:a39ecef2f8f4488c27e012cfc9f4e8ab0b25b6f00af67bc54e2f8f67e1d805e1","observation_id":"0dec7307-8c49-4620-9b82-aac150839084","resolution":{"observed_at":"2026-08-02T02:35:17.216974Z","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":"2026-08-02T02:35:17.325733Z","title":"Morier-Genoud and V","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.325733Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:8e25fe6f6e3503201a94b7e6e57d51bdccfd7585c39a74e1cfa5da76335e0e9b","observation_id":"92d7a7b4-8065-4464-a348-1b2993bd3878","resolution":{"observed_at":"2026-08-02T02:35:17.325733Z","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":"2026-08-02T02:35:17.396843Z","title":"Morier-Genoud and V","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.396843Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:317b8fb07b08fa95150783ff7d299a3795f5ad20b77dd742614cc0585a84a862","observation_id":"e646c290-3601-4047-a65e-740d841e9410","resolution":{"observed_at":"2026-08-02T02:35:17.396843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.23834","last_updated":"2025-03-31T08:28:41Z","snapshot_observed_at":"2026-08-07T16:25:50.904928Z","submitted_at":"2025-03-31T08:28:41Z","title":"$q$-deformed rationals and irrationals","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.23834","snapshot_observed_at":"2026-08-02T02:35:17.485472Z","title":"Morier-Genoud and V","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.485472Z"},"links":{"cited_paper":"/paper/2503.23834","citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:59a1062f11656d5c681c8bb4656d3e2d08b52bdce4df2fbd75224ff12a9f9931","observation_id":"520d5f77-8b87-4333-a1d4-86ee86d32021","resolution":{"observed_at":"2026-08-02T02:35:17.485472Z","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":"2026-08-02T02:35:17.606455Z","title":"Ovsienko,q-rationals and dimers (arXiv:2510.16270), preprint (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.606455Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:8b7c26db6840977dadbf76b187833fcd4a4d91012e6d958b9770456c98d2b68c","observation_id":"8b98d9b7-e59c-40c8-ad45-f7ecdc01b9a4","resolution":{"observed_at":"2026-08-02T02:35:17.606455Z","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":"2026-08-02T02:35:17.687170Z","title":"Propp, A reciprocity theorem for domino tilings,Electron","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.687170Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:f7f7c11beb9fc0cc44949994fe4ac9fe2f0c05e1a66c7033dbcad1a56a7d82bc","observation_id":"184cfe53-48ef-4a6e-97ef-b947595c47c4","resolution":{"observed_at":"2026-08-02T02:35:17.687170Z","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":"2026-08-02T02:35:17.775148Z","title":"Propp, The combinatorics of frieze patterns and Markoff numbers,Integers20(2020), #A12","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.775148Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:32a44ea86a97fcaab6df227a531ce5edd1da73660c8ddc2e48d1771fc71e9323","observation_id":"01ee1d3a-bd4f-4a6d-b520-f6c00e04cf44","resolution":{"observed_at":"2026-08-02T02:35:17.775148Z","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":"2026-08-02T02:35:17.851196Z","title":"Propp, Lattice structure for orientations of graphs,Electron","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.851196Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:08389c26a446e6c1550bf835c36352089268612be8a7374c4cddab514da8a056","observation_id":"07f1f33e-83ce-4803-bc68-568f75c4f4cf","resolution":{"observed_at":"2026-08-02T02:35:17.851196Z","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":"2026-08-02T02:35:17.947334Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:17.947334Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:9314b51a228c4437656978fbcad51c9c0ca4c389e964fe6ac6443d2402fdca73","observation_id":"4637c68e-511e-48d8-8ab1-65ee7f96f83f","resolution":{"observed_at":"2026-08-02T02:35:17.947334Z","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":"2026-08-02T02:35:18.003611Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T02:35:18.003611Z"},"links":{"citing_paper":"/paper/2607.14332"},"observation_digest":"sha256:04310157c7d3c4369e02bfedc58ff1341580f98b57b4b2f60c35a16251d949a2","observation_id":"41671518-1b70-4026-b8ae-e1ff899d9744","resolution":{"observed_at":"2026-08-02T02:35:18.003611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.14332","last_updated":"2026-07-22T23:29:28Z","latest_version":3,"primary_category":"math.PR","snapshot_observed_at":"2026-08-07T11:33:32.104440Z","submitted_at":"2026-07-15T19:53:30Z","title":"Dimers, filters, and $q$-deformed real numbers"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":16},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2607.14332."}