{"as_of":"2026-08-14T13:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:efb003cec23e54e6dc9aee71a9cf0d4966b7f22839c12ab447c18ff38ea931af","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T21:21:53.232067Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2501.19187/citation-record","integrity":"/paper/2501.19187/integrity","json":"/paper/2501.19187/citation-record.json","paper":"/paper/2501.19187"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T21:21:53.747697Z","title":"A General Nullstellensatz for Generalised Spaces","venue":null,"work_id":"63669744-06ab-4411-a9cd-6bcacca9c680","year":2024},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.187914Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:fc22effab0e3a8158141e904bb0cdb6d287db4f1212c96e517989cae7a19517a","observation_id":"7b52817b-0258-4328-9b71-026e4ad7e28c","resolution":{"observed_at":"2026-08-09T21:21:53.750899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.736917Z","title":"Čech Cohomology in Homotopy Type Theory","venue":null,"work_id":"c0d8f313-8ec3-4441-a44f-15bb8dd70fc8","year":2024},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.192079Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:8b41a14bc407f2d2fc8f4610b519f656f563036a46ae529e17c44058a5098f10","observation_id":"dfb7459c-9267-4f52-bd92-38f4c4270944","resolution":{"observed_at":"2026-08-09T21:21:53.740527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.00073","last_updated":"2023-09-12T08:57:44Z","snapshot_observed_at":"2026-08-13T11:04:55.254191Z","submitted_at":"2023-06-30T18:23:04Z","title":"A Foundation for Synthetic Algebraic Geometry","version":2},"cited_work":{"arxiv_id":"2307.00073","doi":null,"metadata_source":"pith","pith_arxiv_id":"2307.00073","snapshot_observed_at":"2026-08-09T21:21:53.678764Z","title":"A Foundation for Synthetic Algebraic Geometry","venue":"math.AG","work_id":"6ff63a9c-289d-444c-b912-681f594dbb94","year":2023},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.195627Z"},"links":{"cited_paper":"/paper/2307.00073","citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:ee827c47aec50d4be921231131f798e6ec18ce283dcbfc3d66951a09c9baf2f9","observation_id":"d6697358-6183-4a5a-abc1-50162c0f1a78","resolution":{"observed_at":"2026-08-09T21:21:53.683374Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.199409Z","title":"Directed univalence in simpli- cial homotopy type theory","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.199409Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:175d6788857a5f1557fadee8e6f032db3a78bb0a62f7041aed82158e09d29327","observation_id":"24efa128-bcf3-4147-b932-76e6dee851f8","resolution":{"observed_at":"2026-08-09T21:21:53.199409Z","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":"10.46298/lmcs-17(3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T21:21:53.263162Z","title":"Multimodal Dependent Type Theory","venue":null,"work_id":"43ded53f-901d-49e8-b5ff-31bf7cb406a4","year":2021},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.203198Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:915fda3cef977e6fe9d6b6d3ab6f80664833564005fcc0bbb4456866874aac46","observation_id":"2ef12e48-3255-4ac2-82ff-e0e8a910b050","resolution":{"observed_at":"2026-08-09T21:21:53.268333Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.725928Z","title":null,"venue":null,"work_id":"a7f2f36b-1572-4430-a972-72d3535dc852","year":2009},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.206830Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:bd793093bc0b8a291791693a4e2eb1012b8468458ad8ccea9978102f9828b9c9","observation_id":"c1f4ee4f-ba4b-4579-8ce3-01f4fbba434e","resolution":{"observed_at":"2026-08-09T21:21:53.729595Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T21:21:53.468221Z","title":"Eilenberg-MacLane s paces in homotopy type theory","venue":null,"work_id":"27cd2e1e-643b-406f-845e-0d51b601162a","year":2014},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.210388Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:bd0208fca8af258d7d2fde9e14d85e18bffa1293e9d38800fb81502968c3a5f0","observation_id":"0da430f1-a03c-45ea-9d78-7fbe6396da65","resolution":{"observed_at":"2026-08-09T21:21:53.471969Z","resolver_source":"arxiv_id_nonexistent","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.213619Z","title":"Commutative Algebra: Constructive Methods: Finite Projective Modules","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.213619Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:4215d5be60c4b5e5ed38477fbfbdef21533fe38895f8005580004ae72ea0d27c","observation_id":"29ecc6d5-a9f8-4239-ac29-d04e914387f7","resolution":{"observed_at":"2026-08-09T21:21:53.213619Z","resolver_source":null,"status":"malformed_identifier"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T21:21:53.714322Z","title":"Sheaves in Synthetic Algebraic Geometry","venue":null,"work_id":"163e853c-267c-4bba-949c-aef78eb014fa","year":2024},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.216862Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:531b802737834d50318bcbd72154bc8b4594c5657490c2a23e8d448f05a5c771","observation_id":"786ab79f-93a2-47da-a465-0e14e6a9256f","resolution":{"observed_at":"2026-08-09T21:21:53.718223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2205.15887","last_updated":"2022-05-31T15:39:14Z","snapshot_observed_at":"2026-08-13T15:33:04.131549Z","submitted_at":"2022-05-31T15:39:14Z","title":"Orbifolds as microlinear types in synthetic differential cohesive homotopy type theory","version":1},"cited_work":{"arxiv_id":"2205.15887","doi":null,"metadata_source":"pith","pith_arxiv_id":"2205.15887","snapshot_observed_at":"2026-08-09T21:21:53.303450Z","title":"Orbifolds as microlinear types in synthetic differential cohesive homotopy type theory","venue":"math.AT","work_id":"2896aa7e-ff7b-4a09-9e63-ade84d5bd6c1","year":2022},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.220014Z"},"links":{"cited_paper":"/paper/2205.15887","citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:8cf3994be8d49e9a7682600c0806a17fa0aff703631cf0e5b6ac0f9ded8303fc","observation_id":"e949df05-9fcf-4bc7-8950-db3ba10b2ea2","resolution":{"observed_at":"2026-08-09T21:21:53.307408Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1701.07538","last_updated":"2017-01-26T01:31:53Z","snapshot_observed_at":"2026-08-06T17:32:56.768945Z","submitted_at":"2017-01-26T01:31:53Z","title":"The join construction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.07538","snapshot_observed_at":"2026-08-09T21:21:53.223069Z","title":"The join construction","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.223069Z"},"links":{"cited_paper":"/paper/1701.07538","citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:03c11936ee4f7b4a0f59a4a7e053ffb5335d215013173df16e3582bcd28b75e2","observation_id":"5a4d650c-e9ea-454c-9a40-cb14ec4057ec","resolution":{"observed_at":"2026-08-09T21:21:53.223069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.01939","last_updated":"2024-03-04T11:15:10Z","snapshot_observed_at":"2026-08-13T04:04:11.049644Z","submitted_at":"2024-03-04T11:15:10Z","title":"A Type Theory with a Tiny Object","version":1},"cited_work":{"arxiv_id":"2403.01939","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.01939","snapshot_observed_at":"2026-08-09T21:21:53.278045Z","title":"A Type Theory with a Tiny Object","venue":"math.CT","work_id":"e8f51bd6-ca77-43c6-8595-3e8be083ddbc","year":2024},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.226150Z"},"links":{"cited_paper":"/paper/2403.01939","citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:c19743727c0f41a9c94d8f8d59c3d7c84f50d16bce16f9980bd561545ebec56a","observation_id":"4bafd51e-bc0b-46f0-a58a-8aebb888a8fb","resolution":{"observed_at":"2026-08-09T21:21:53.281690Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.702074Z","title":"Moda lities in homotopy type theory","venue":null,"work_id":"ab43fe81-aaa3-4499-b6fb-217b99e93537","year":2020},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.229203Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:3e69ee0aef4abbd083b556ee8e1490aec5382a1ee4c7f1dfe4ef2bc2f58ce063","observation_id":"849c52e9-ae7d-4313-bd24-9a9dda856c33","resolution":{"observed_at":"2026-08-09T21:21:53.705987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-09T21:21:53.690908Z","title":"Homotopy Type Theory: Univalent Foundations of Mathematics","venue":null,"work_id":"34bfe519-b81d-4a50-b006-86f476368262","year":2013},"citing_paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-09T21:21:53.232067Z"},"links":{"citing_paper":"/paper/2501.19187"},"observation_digest":"sha256:cb20eec6699a90c761df4d762d167dea70a9d954f8bcb4d1b3b9a0f2b85cf948","observation_id":"57fb7d2e-825d-47fd-983b-6f33cbad83e1","resolution":{"observed_at":"2026-08-09T21:21:53.694775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.19187","last_updated":"2025-01-31T14:51:24Z","latest_version":1,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-13T22:27:36.554764Z","submitted_at":"2025-01-31T14:51:24Z","title":"Projective Presentations of Lex Modalities"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":5,"verified_fuzzy":5},"total_outbound_references":14},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2501.19187."}