{"as_of":"2026-08-14T21:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cc1c628d31692b56aa045916b225cd24a9247a5cb1f4c1b430355acf87f44f9d","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":"2026-08-11T13:59:38.926037Z","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":"2026-08-14T06:32:32.682623+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":"2026-08-11T12:31:44.034342Z","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":"2026-08-11T12:31:44.551198Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"cited_work":{"arxiv_id":"2412.12670","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.12670","snapshot_observed_at":"2026-08-11T12:31:44.551198Z","title":"Local expansion properties of paracontrolled systems","venue":"math.PR","work_id":"e3b84889-2a8c-4105-a3a7-7783b412c48a","year":2024},"citing_paper":{"arxiv_id":"2608.09700","last_updated":"2026-08-10T15:06:06Z","snapshot_observed_at":"2026-08-13T23:46:17.442002Z","submitted_at":"2026-08-10T15:06:06Z","title":"A general paracontrolled ansatz for singular SPDEs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:44.034342Z"},"links":{"cited_paper":"/paper/2412.12670","citing_paper":"/paper/2608.09700"},"observation_digest":"sha256:5d009ea7bf2ae46c162206dc6813d2c420b9bb57c1f24845131abd5643f6ef26","observation_id":"368da30e-98f6-4cbf-9cbb-89ee01452300","resolution":{"observed_at":"2026-08-11T12:31:44.555204Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2412.12670/citation-record","integrity":"/paper/2412.12670/integrity","json":"/paper/2412.12670/citation-record.json","paper":"/paper/2412.12670"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:59:39.069992Z","title":"and Bernicot F","venue":null,"work_id":"b283f623-458c-40ad-b2c4-eaeb05b7993a","year":2019},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.887817Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:5b727b87c5799359da37b6e28aecc26a0f7dee9b071e201079012d59d380af29","observation_id":"36308aed-f496-4c63-961e-6d89827575c8","resolution":{"observed_at":"2026-08-11T13:59:39.074647Z","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":"2006.03525","last_updated":"2020-06-10T22:58:07Z","snapshot_observed_at":"2026-08-13T07:45:11.651285Z","submitted_at":"2020-06-05T15:58:01Z","title":"Formalizing line editors in Coq","version":2},"cited_work":{"arxiv_id":"2006.03525","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.03525","snapshot_observed_at":"2026-08-11T13:59:38.964931Z","title":"Formalizing line editors in Coq","venue":"cs.LO","work_id":"6a8dc36e-8aa0-45cd-b744-a47a246403ed","year":2020},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.891955Z"},"links":{"cited_paper":"/paper/2006.03525","citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:bfb09514d196c96a59ca921880afeffc26f533b7d9a991fbfc0015ff2cca2cc1","observation_id":"ec55193c-918b-4f53-b7db-061982c697a8","resolution":{"observed_at":"2026-08-11T13:59:38.969820Z","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":"2026-08-11T13:59:39.058724Z","title":"and Hoshino M","venue":null,"work_id":"79e38113-c495-4de1-bafd-3de16e98fe86","year":2021},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.895858Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:2ebc6651285a0648b6af27c7f6e7a534754682bb079ecafec31cc7805e91b90c","observation_id":"5103a097-620b-4c74-adf4-ccd36c3e23f0","resolution":{"observed_at":"2026-08-11T13:59:39.062340Z","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":"2026-08-11T13:59:39.047903Z","title":"and Hoshino M., Paracontrolled calculus and regularity structures II","venue":null,"work_id":"709e6743-1a6c-4e2c-891a-31c4fae27dcf","year":2021},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.899537Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:21ef0a8495d8afb7e871e1d44f7403524968fcb9ad166ded4a3c1b0f1f6c74ef","observation_id":"64e31d67-5fa7-4c04-87b5-3c07bbe7e946","resolution":{"observed_at":"2026-08-11T13:59:39.051392Z","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":"2026-08-11T13:59:39.036927Z","title":"and Mouzard A","venue":null,"work_id":"70f6ce49-146c-4609-b9ef-9471a7afba07","year":2023},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.903148Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:01e89c272a7e85d9570166d697566cc153fdbd8adfd65bcd87b56a2d410155f4","observation_id":"9ae95724-797a-41f7-9646-ca3c3cda183d","resolution":{"observed_at":"2026-08-11T13:59:39.041470Z","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":"2026-08-11T13:59:39.024373Z","title":"and Perkowski N., Paracontrolled distributions and singular PDEs","venue":null,"work_id":"23266c84-4bc6-47aa-b365-b316d430d83d","year":2015},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.907282Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:3c3aa0e45b4da6b8d28f0de9675633dc79aaf94b6c833cadffaac36994b425d3","observation_id":"3aca7252-bd66-441e-ad7a-281676c6e4a5","resolution":{"observed_at":"2026-08-11T13:59:39.028927Z","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":"2026-08-11T13:59:39.014362Z","title":", A theory of regularity structures","venue":null,"work_id":"715cec8e-d468-4c73-b78b-e4bf5375ca0f","year":2014},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.911162Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:b2e88e66f8e39e797f9a6fdd876b448d8c594bfe26273d3a7960f513e6364218","observation_id":"5dd1a5fb-d142-4478-a820-24fcfbd2a967","resolution":{"observed_at":"2026-08-11T13:59:39.017736Z","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":"2026-08-11T13:59:39.001491Z","title":"and Kelly D., Geometric versus non-geometric rough paths","venue":null,"work_id":"fb3d96f5-c2ed-4b80-a8d9-c0db0009a7ad","year":2015},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.914596Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:89c2bed4e50b44eaa48083b4aeb6de91e2b8e32c351206e7d81a674f52b3f04b","observation_id":"a274f459-c72f-4dd9-b08a-61c243fd45af","resolution":{"observed_at":"2026-08-11T13:59:39.005441Z","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":"2026-08-11T13:59:38.989697Z","title":", Iterated paraproducts and iterated commutator estimates i n Besov spaces","venue":null,"work_id":"3c804988-c1bb-4867-bb29-e93ba71a21b0","year":2019},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.917897Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:3885193ca7a13bd456146737c367b463d620e0039938543c9787065906721fc7","observation_id":"67254b30-cb01-474a-b548-f3c710a947ea","resolution":{"observed_at":"2026-08-11T13:59:38.993441Z","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":"2026-08-11T13:59:38.977481Z","title":", Commutator estimates from a viewpoints of regularity struc tures","venue":null,"work_id":"b06c09e6-1ee0-45f8-aada-1b8e9efe67b7","year":2020},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.921836Z"},"links":{"citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:0264797b751b5f516de963653aef9ed7566085248a0450839a824009479919db","observation_id":"bdede839-958e-40a7-92b6-af35a037373e","resolution":{"observed_at":"2026-08-11T13:59:38.981791Z","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":"2409.10817","last_updated":"2024-09-17T01:23:05Z","snapshot_observed_at":"2026-08-12T22:43:35.759305Z","submitted_at":"2024-09-17T01:23:05Z","title":"A note on the Taylor estimates of iterated paraproducts","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.10817","snapshot_observed_at":"2026-08-11T13:59:38.926037Z","title":", A note on the Taylor estimates of iterated paraproducts","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T13:59:38.926037Z"},"links":{"cited_paper":"/paper/2409.10817","citing_paper":"/paper/2412.12670"},"observation_digest":"sha256:3cce2955083272d9d544dc20c941b109563aad7b9396581baf80b8bfd68deace","observation_id":"59917a2e-d410-421f-8e40-abc6b9b543cc","resolution":{"observed_at":"2026-08-11T13:59:38.926037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.12670","last_updated":"2024-12-17T08:40:56Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-13T22:08:01.821452Z","submitted_at":"2024-12-17T08:40:56Z","title":"Local expansion properties of paracontrolled systems"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":1,"verified_fuzzy":9},"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":"2026-08-14T06:32:32.682623+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 11 of 11 outbound references and 1 inbound Pith citation observation for arXiv:2412.12670."}