{"as_of":"2026-08-18T14:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5a4573e1bed5cfba59b1b91d95845976c4f08aa14742717fa75ada9bbcb57830","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:27:06.691529Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2608.12073/citation-record","integrity":"/paper/2608.12073/integrity","json":"/paper/2608.12073/citation-record.json","paper":"/paper/2608.12073"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.01066","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:27:06.946557Z","title":"Agrawal, Y","venue":null,"work_id":"749f0e94-b772-43d1-8bb6-32d8642c1c7e","year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.633227Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:842bd16029289aafa72bfacf13f90e2f4f633945cf729d84434f527b18fea42e","observation_id":"d12b5b86-2bc7-40e1-8119-5be70e835d45","resolution":{"observed_at":"2026-08-16T00:27:06.953773Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1287/mnsc.46.3.375.12063","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:27:06.728652Z","title":"31 Appendix A: Missing Proofs of Section 3 A.1","venue":null,"work_id":"6c1eaa58-ad32-4e2f-960c-5eb09c713e45","year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.670554Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:7cb14847f3141b96db1ff33364d07ed99dbe4383bd30b6f554b2bbef4cfc9c49","observation_id":"d7b753d7-3768-4608-9bcc-bbcf56904b4a","resolution":{"observed_at":"2026-08-16T00:27:06.735317Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:07.018888Z","title":"We introduce the regularization below is to remove flat switching ties and all perturbation terms will be sent to zero at the end","venue":null,"work_id":"61a93532-b209-458f-9c8e-f26e555c8652","year":2012},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.675428Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:3ccb85ac80bc79d613671110dfb4afa634361403dc27b1ba4529690969f62498","observation_id":"d3be5338-8c6f-4a8e-b193-0be09a35b31b","resolution":{"observed_at":"2026-08-16T00:27:07.023611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:06.998962Z","title":"We introduce the auxiliary states ˙a(t) =c(t),˙g 3(t) =D(t)· sX k=1 xk t +c(t)·H(t),˙g 4(t) =D(t)· sX k=1 xk t +H(t), with zero initial values","venue":null,"work_id":"73e7e2d0-0f0b-4f7a-966f-77b00a193bd4","year":2000},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.680406Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:d5e70b1d755de718d409a50d2361341251265f508609e1908101b24f7b4b8d07","observation_id":"a6478654-65e0-47ff-9081-4c7dfcd7e3a2","resolution":{"observed_at":"2026-08-16T00:27:07.006179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:06.979112Z","title":"Define U(t) := Z t 0 ¯x(s)ds, U max :=U(M).(82) For everyt>0, ¯x(t)>0, soUis strictly increasing","venue":null,"work_id":"7c67ffc7-8f3c-4792-9f16-ac2a38001efc","year":2000},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.685349Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:78a94863433fc7e0c63b15da8e18fcb6cdeb727818830ccdb59556207d6a3333","observation_id":"9ace1544-01db-4056-a2e0-b780f8ff0d84","resolution":{"observed_at":"2026-08-16T00:27:06.987102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:06.964492Z","title":"ThereforeW−ahas at most 2rstrict sign changes on (0,L)","venue":null,"work_id":"d39a1653-3025-42c6-8db0-87f50fab1848","year":1948},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.691529Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:dad188a232ec6fe55b099f0db52cb00d386b86a491958eb712a5da7332a27369","observation_id":"0fd0f59c-0607-4452-9982-6a143feed3d9","resolution":{"observed_at":"2026-08-16T00:27:06.968815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:06.666141Z","title":"34.4.164","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":1948,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.666141Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:4aecd735ec3bf45ad8515e7ada4f8e079e7f51ab8f095da20fd3047321815e68","observation_id":"cf037b90-88bb-4796-a1ba-8c1a5c74e786","resolution":{"observed_at":"2026-08-16T00:27:06.666141Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:27:06.657559Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.657559Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:8670c07498a27a605bb5be2946866ef8959b70cac0d608abfa097561d584f8b5","observation_id":"e0fd7b76-b2fa-4309-9744-2911be5bec04","resolution":{"observed_at":"2026-08-16T00:27:06.657559Z","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":"10.1287/mnsc.46.7.941.12035","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:27:06.768011Z","title":null,"venue":null,"work_id":"2c61bca9-9368-4643-8888-049521cba176","year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":2000,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.652284Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:50616bdf99f019e9b8ee1c42f58a63393a79f35df0ac9f734d6c740a245a0402","observation_id":"721c07da-e89d-4bc6-b599-27d904e398be","resolution":{"observed_at":"2026-08-16T00:27:06.771829Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T00:27:07.034829Z","title":"Patel and D","venue":null,"work_id":"bd215bb7-414b-44ea-b72e-9e2abe5ca309","year":2024},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.662158Z"},"links":{"citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:5f22d4f151491d137c63af60654d2a0e13cb1c594e7c963cec6048c2f2f593f9","observation_id":"f9897701-e1d3-466c-9bed-5867126276a5","resolution":{"observed_at":"2026-08-16T00:27:07.040355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.08218","last_updated":"2024-11-12T22:21:09Z","snapshot_observed_at":"2026-08-12T21:48:25.215478Z","submitted_at":"2024-11-12T22:21:09Z","title":"Improved Approximations for Stationary Bipartite Matching: Beyond Probabilistic Independence","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.08218","snapshot_observed_at":"2026-08-16T00:27:06.637991Z","title":"AmaniHamedani, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.637991Z"},"links":{"cited_paper":"/paper/2411.08218","citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:0cb9206d7ad7dd80af55ed1d964b40d2f544d53e0bb246f66289900322cdb5ca","observation_id":"17f5131c-198b-4d9a-b9a5-31fe11e9adb8","resolution":{"observed_at":"2026-08-16T00:27:06.637991Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16054","last_updated":"2025-05-21T22:07:52Z","snapshot_observed_at":"2026-08-07T15:05:36.788507Z","submitted_at":"2025-05-21T22:07:52Z","title":"Multi-Unit Combinatorial Prophet Inequalities","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16054","snapshot_observed_at":"2026-08-16T00:27:06.647669Z","title":"Chawla, T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.647669Z"},"links":{"cited_paper":"/paper/2505.16054","citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:7b1fe79a2441916f1ba29097259a7bf8601f9edfd8a747eaf254bbb19fc21928","observation_id":"c1450814-9476-400f-a91b-2aef39637e67","resolution":{"observed_at":"2026-08-16T00:27:06.647669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2603.21532","last_updated":"2026-07-15T18:46:05Z","snapshot_observed_at":"2026-08-18T00:32:04.450555Z","submitted_at":"2026-03-23T03:43:31Z","title":"Stationary Online Contention Resolution Schemes","version":2},"cited_work":{"arxiv_id":"2603.21532","doi":null,"metadata_source":"pith","pith_arxiv_id":"2603.21532","snapshot_observed_at":"2026-08-16T00:27:06.798817Z","title":"Stationary Online Contention Resolution Schemes","venue":"cs.GT","work_id":"547b8e45-6b4c-45d9-aa61-5870a9096551","year":2026},"citing_paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-16T00:27:06.643266Z"},"links":{"cited_paper":"/paper/2603.21532","citing_paper":"/paper/2608.12073"},"observation_digest":"sha256:1ca42c58690285cec58b5afef12774ace1b474b91329d63044a536423d98ae70","observation_id":"0950763a-f638-48b1-ae7e-ce486728ee4d","resolution":{"observed_at":"2026-08-16T00:27:06.802822Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.12073","last_updated":"2026-08-12T13:56:24Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-18T06:51:58.540477Z","submitted_at":"2026-08-12T13:56:24Z","title":"Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":4,"verified_fuzzy":5},"total_outbound_references":13},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2608.12073."}