{"as_of":"2026-08-21T18:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e5797a8fb5b096ad566d9234d3b77db8fe056700c46182c8eaff3be0e31ec94f","coverage":[{"denominator":6,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:21:25.612425Z","state":"measured"},{"denominator":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2412.20728/citation-record","integrity":"/paper/2412.20728/integrity","json":"/paper/2412.20728/citation-record.json","paper":"/paper/2412.20728"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1403.4139","last_updated":"2014-06-27T10:39:41Z","snapshot_observed_at":"2026-08-14T23:41:59.728136Z","submitted_at":"2014-03-08T19:31:30Z","title":"Solving the Hard Problem of Bertrand's Paradox","version":2},"cited_work":{"arxiv_id":"1403.4139","doi":null,"metadata_source":"pith","pith_arxiv_id":"1403.4139","snapshot_observed_at":"2026-08-10T23:21:25.802086Z","title":"Solving the Hard Problem of Bertrand's Paradox","venue":"physics.hist-ph","work_id":"06e537cf-48b3-4f82-98d1-80978f02e5a9","year":2014},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.582352Z"},"links":{"cited_paper":"/paper/1403.4139","citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:7f5d6c3b99b8e8365bd4574050d4ec7bcd13b00cf1a1cddedd2e87eeccae0226","observation_id":"bf454595-86f1-49ac-a2ef-ed2a5cd42df3","resolution":{"observed_at":"2026-08-10T23:21:25.808442Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T23:21:25.819387Z","title":"(2011) Resolving Bertrand's Probability Paradox","venue":null,"work_id":"0ded1962-e134-41df-b71b-0647f9b92203","year":2011},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":1994,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.612425Z"},"links":{"citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:66cf9a3276f9c99c989e36d3d5d72f510efa889a503cec4db5c4653f0164c52d","observation_id":"dcf59b81-00f0-49cf-a231-d372a1edbca4","resolution":{"observed_at":"2026-08-10T23:21:25.825442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1008.1878","last_updated":"2010-08-11T10:23:48Z","snapshot_observed_at":"2026-08-15T05:11:42.742574Z","submitted_at":"2010-08-11T10:23:48Z","title":"Bertrand's paradox: a physical solution","version":1},"cited_work":{"arxiv_id":"1008.1878","doi":null,"metadata_source":"pith","pith_arxiv_id":"1008.1878","snapshot_observed_at":"2026-08-10T23:21:25.780229Z","title":"Bertrand's paradox: a physical solution","venue":"physics.data-an","work_id":"72e72e24-5c98-4322-9eee-57381d2dc6df","year":2010},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":2006,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.594073Z"},"links":{"cited_paper":"/paper/1008.1878","citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:637b43c8235fa7f78d784bc54bf8ef5a5166e1adb12bab5aca6ec39b8782c817","observation_id":"157a79f1-9fd6-4c51-9f63-1d05eb7027ac","resolution":{"observed_at":"2026-08-10T23:21:25.784992Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T23:21:25.837699Z","title":"(1889), Calcul des probabilités","venue":null,"work_id":"17cd105d-feb5-435c-9794-0b1c4399ba1b","year":2006},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.589287Z"},"links":{"citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:43cf7344c24d669e1e209de251a3d59d4f2da38571f990c6603b169c446e25b1","observation_id":"e7863122-fb97-442f-8a73-86ac6c7594d3","resolution":{"observed_at":"2026-08-10T23:21:25.842784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1501.03053","last_updated":"2015-01-09T16:21:27Z","snapshot_observed_at":"2026-08-14T23:04:38.653013Z","submitted_at":"2015-01-09T16:21:27Z","title":"Random Triangle Theory with Geometry and Applications","version":1},"cited_work":{"arxiv_id":"1501.03053","doi":null,"metadata_source":"pith","pith_arxiv_id":"1501.03053","snapshot_observed_at":"2026-08-10T23:21:25.757098Z","title":"Random Triangle Theory with Geometry and Applications","venue":"math.HO","work_id":"cea830fc-917c-4573-8c3e-3c14609e891d","year":2015},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.599427Z"},"links":{"cited_paper":"/paper/1501.03053","citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:e13d0364b334909027531a7cd2de24f2eec5183d32c847ec46f33a36cdc2c9e9","observation_id":"b278fa58-f7e8-44ff-b625-88835706d536","resolution":{"observed_at":"2026-08-10T23:21:25.763217Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"edu/1184515","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:21:25.732403Z","title":"at random","venue":null,"work_id":"63a02988-908f-4b00-961c-6be39ad37aff","year":2001},"citing_paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-10T23:21:25.606243Z"},"links":{"citing_paper":"/paper/2412.20728"},"observation_digest":"sha256:9e2f66117e33b19ad63f0ff0408f9b401d1b86e6b88f1c34ba78ba87f70b03fa","observation_id":"7a2a35dd-f6f7-403a-b3aa-ce778aaad56d","resolution":{"observed_at":"2026-08-10T23:21:25.741313Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.20728","last_updated":"2024-12-30T05:58:53Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-17T15:37:19.326087Z","submitted_at":"2024-12-30T05:58:53Z","title":"Probability and Ambiguity"},"reference_resolution":{"displayed":6,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":0,"verified_exact":2,"verified_fuzzy":2},"total_outbound_references":6},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 6 of 6 outbound references and 0 inbound Pith citation observations for arXiv:2412.20728."}