{"as_of":"2026-08-21T15:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:99219b07cf946006aeec6d7974088eb1a7fc33707e428cb1d6a8e0cc23e09858","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T20:06:01.776561Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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":"2026-08-08T15:33:30.893190Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"pith","source_observed_at":"2026-08-10T05:30:23.456663Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-10T05:30:23.456663Z","source":"pith"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"cited_work":{"arxiv_id":"2411.10107","doi":"10.48550/arxiv.2411.10107","metadata_source":"pith","pith_arxiv_id":"2411.10107","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Monotone Contractions","venue":"cs.CC","work_id":"bf8dda9a-a6d5-4004-9a28-cb12e0be85cc","year":2024},"citing_paper":{"arxiv_id":"2502.06477","last_updated":"2025-07-03T11:46:26Z","snapshot_observed_at":"2026-08-16T22:28:44.195466Z","submitted_at":"2025-02-10T13:55:59Z","title":"ARRIVAL: Recursive Framework & $\\ell_1$-Contraction","version":2},"reference_index":1922,"source":"pdf_text","source_observed_at":"2026-08-08T15:33:30.893190Z"},"links":{"cited_paper":"/paper/2411.10107","citing_paper":"/paper/2502.06477"},"observation_digest":"sha256:ed5fa0c192eb21a3a0978190f911383eed35c739154fe23ad8cff4cff48624cb","observation_id":"1536dc57-9e67-4e6f-8ebb-aed9737d1f76","resolution":{"observed_at":"2026-08-08T15:33:31.495476Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2411.10107/citation-record","integrity":"/paper/2411.10107/integrity","json":"/paper/2411.10107/citation-record.json","paper":"/paper/2411.10107"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.268884Z","title":"Sur les opérations dans les ensembles abs traits et leur application aux équations intégrales","venue":null,"work_id":"b2459aef-2788-499b-9a61-cf8da29b7761","year":1922},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.642063Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:2569a744f855e0b404a75387b3c2499422bb63d2262b5a1e84d1157d764ecf55","observation_id":"9c9b8fc2-4d4f-451d-aa8c-a4d3600c0407","resolution":{"observed_at":"2026-08-12T20:06:02.274374Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.246835Z","title":"Boonyasiriwat, Kris Sikorski, and Ch","venue":null,"work_id":"2be2a0ce-3f2b-4969-9fe4-b50c49b05425","year":2007},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.647074Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:be20ffa409dd75f1a69637fc94cc0be886fe19c08f35f8a278cc4894dd4e1d6b","observation_id":"9f22c68f-08f5-4609-8fca-5161571ee2a7","resolution":{"observed_at":"2026-08-12T20:06:02.256050Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.229131Z","title":"Improved upper bounds for finding Tar ski fixed points","venue":null,"work_id":"ac32ee29-6a1b-4109-aee0-37ccf522adf8","year":2022},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.651610Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:7ddcfee1be3389c8b3488f0ace45810d31e4615956474e749efd5b44aac4e722","observation_id":"3e0a4853-2138-4ad0-901a-ff21795efd13","resolution":{"observed_at":"2026-08-12T20:06:02.234058Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.213767Z","title":"Reducing Tars ki to unique Tarski (in the black-box model)","venue":null,"work_id":"d3209719-f59d-4ecd-9444-8ea2111b3035","year":2023},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.656461Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:c553f54379b33243ee24ed636f0cd6d5fef34415128f48a0c628dab5a8272e8f","observation_id":"65a6495a-3ad4-4174-a32f-aed83fe184cc","resolution":{"observed_at":"2026-08-12T20:06:02.219565Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.198018Z","title":"Computing a fix ed point of contraction maps in polynomial queries","venue":null,"work_id":"96d19964-2579-49e4-882a-d4c24e4f6253","year":2024},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.661177Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:10d84ef823821bdbffe7018d74f4fe5fa965a33add906fd0495b27e3d782b028","observation_id":"a4caa194-056b-45ac-82b3-fa6879de9840","resolution":{"observed_at":"2026-08-12T20:06:02.204382Z","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":"2005.09836","last_updated":"2020-05-20T03:32:37Z","snapshot_observed_at":"2026-08-16T19:01:03.926538Z","submitted_at":"2020-05-20T03:32:37Z","title":"Computations and Complexities of Tarski's Fixed Points and Supermodular Games","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.09836","snapshot_observed_at":"2026-08-12T20:06:01.665996Z","title":"Computations and com plexities of Tarski’s fixed points and supermodular games","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.665996Z"},"links":{"cited_paper":"/paper/2005.09836","citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:f7dda3a7590b7e040b0386cbc85a4d175b17c09d909d5cd691ad24610d62f01b","observation_id":"bc866386-1128-42c4-aed1-6442afbf3bf5","resolution":{"observed_at":"2026-08-12T20:06:01.665996Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.181111Z","title":"Papadimitriou","venue":null,"work_id":"4394c37e-a3f7-4ae2-ad2d-588cb4b34fea","year":2011},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.677835Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:e9d2abaa5b5c7fca3aa2f43188feb74709538187277b34b89626eda79590801c","observation_id":"ebef1b5e-38ad-45f9-aa8d-3eeb89369c7b","resolution":{"observed_at":"2026-08-12T20:06:02.186165Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.163781Z","title":"A Converse to Banach’s Fixed Point Theorem and its CLS Completeness","venue":null,"work_id":"dffbd1ef-be11-42e5-8363-647ca27540f8","year":2018},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.683839Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:9e4387e5cf3f6be7cf7332b708a3cc0162856f528868b02df385d88fd7432a3e","observation_id":"b591491a-3571-44b5-9aae-4eb58461c014","resolution":{"observed_at":"2026-08-12T20:06:02.169298Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.149379Z","title":"Papadimitriou, A viad Rubi nstein, and Mihalis Yannakakis","venue":null,"work_id":"cb670415-f2cd-4ac0-95f8-d9c7f0e12e35","year":2020},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.688491Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:15c28441eb632aab461a4ed38a2161968b991418b1733a7e728dda1ccdde76aa","observation_id":"6e9a13cd-1d63-4a70-a7a7-d059eb0cccd2","resolution":{"observed_at":"2026-08-12T20:06:02.153861Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.136182Z","title":"On the complex ity of nash equilibria and other fixed points","venue":null,"work_id":"a7115fa3-4b66-45a6-afc1-6128b0d7e351","year":2010},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.693515Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:fd711ca349dd4a8e12aaf21bb8b273bf57b083d73434ec48463c63b46e6ec18e","observation_id":"29e2bf21-a681-42ec-a264-fe643f7f0656","resolution":{"observed_at":"2026-08-12T20:06:02.140968Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.120792Z","title":"The complexity of gradient descent: CLS = PPAD ∩ PLS","venue":null,"work_id":"02b9c78f-2c7e-4f6d-a289-8d07c60a4bdc","year":2023},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.697875Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:55f9634695d8af743ffce65faa5c7d54ba4180f96c0ed8f45b9c9bdcc5ee0915","observation_id":"3f72d717-1676-4cfb-b389-2aa67d18316a","resolution":{"observed_at":"2026-08-12T20:06:02.125685Z","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":"1702.06017","last_updated":"2017-04-07T15:55:54Z","snapshot_observed_at":"2026-08-14T21:15:41.525460Z","submitted_at":"2017-02-20T15:39:13Z","title":"CLS: New Problems and Completeness","version":2},"cited_work":{"arxiv_id":"1702.06017","doi":null,"metadata_source":"pith","pith_arxiv_id":"1702.06017","snapshot_observed_at":"2026-08-12T20:06:01.850938Z","title":"CLS: New Problems and Completeness","venue":"cs.CC","work_id":"1edb0f3c-02aa-40de-85c4-9b0b8f428e66","year":2017},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.702676Z"},"links":{"cited_paper":"/paper/1702.06017","citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:a0958195979619014eaf48f4ccfb219330d0af94e80c3a82eb6bbfce7891c1fd","observation_id":"ad044b58-da4c-4e97-926d-a283c03bbac2","resolution":{"observed_at":"2026-08-12T20:06:01.856499Z","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":{"arxiv_id":"1811.03841","last_updated":"2018-11-09T10:06:17Z","snapshot_observed_at":"2026-08-14T18:01:44.232345Z","submitted_at":"2018-11-09T10:06:17Z","title":"Unique End of Potential Line","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03841","snapshot_observed_at":"2026-08-12T20:06:01.708958Z","title":"Unique end of potential line","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.708958Z"},"links":{"cited_paper":"/paper/1811.03841","citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:ce9e44615b17651b33ca2981fae791e88c8d9a5389063ce8d7ac73bf4298a45f","observation_id":"8b104992-c48a-4606-ae08-3a5138597df1","resolution":{"observed_at":"2026-08-12T20:06:01.708958Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.106239Z","title":"Unique end of potential line","venue":null,"work_id":"4d961cb6-e632-4029-9a01-440092337b1f","year":2020},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.713306Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:4d8695bbbe62f2882315b7b6c3b21d08ad985e0e6d3ae0e497429d9727a29e5f","observation_id":"6658dff6-0811-4563-a0d6-79b613343db2","resolution":{"observed_at":"2026-08-12T20:06:02.111272Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.091901Z","title":"A f aster algorithm for finding Tarski fixed points","venue":null,"work_id":"c762a2d8-dc00-4f69-988e-5bc13a73dc05","year":2022},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.717575Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:ea5e6037073bfef536395f6317e5edf21ae6e9c50efbd56fa07fd412e1b24de0","observation_id":"d4019eef-0436-4189-8c69-af2aef6f0366","resolution":{"observed_at":"2026-08-12T20:06:02.096946Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.074143Z","title":"Tsi- garidas","venue":null,"work_id":"1d7b5514-88a2-414f-b612-57999b2d56d3","year":2011},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.722195Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:d096ba2961e105698aa114773a1c1252941824e05ce012928b6b27e240baf162","observation_id":"10a875a5-357d-468e-8c27-5dd3179bda8a","resolution":{"observed_at":"2026-08-12T20:06:02.080418Z","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":"1202.3898","last_updated":"2012-02-17T12:37:42Z","snapshot_observed_at":"2026-08-15T04:19:00.804748Z","submitted_at":"2012-02-17T12:37:42Z","title":"Exact Algorithms for Solving Stochastic Games","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1202.3898","snapshot_observed_at":"2026-08-12T20:06:01.726432Z","title":"Tsi- garidas","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.726432Z"},"links":{"cited_paper":"/paper/1202.3898","citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:116968a72ba38ad24d6d72b5ec653ddbe8c1fa4337613179a9abc26f2e38b2e5","observation_id":"d7708438-6fa0-41cb-8540-d3cd0ab7d434","resolution":{"observed_at":"2026-08-12T20:06:01.726432Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.057817Z","title":"Huang, Leonid G","venue":null,"work_id":"7613fcd5-5086-4b01-8091-43bb96f9d849","year":1999},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.731446Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:92c2a22a1260144209a0af6323add15de45cf0044692a1868e742caab140e3c9","observation_id":"f4914019-5a95-4105-a3f5-fd7d25735052","resolution":{"observed_at":"2026-08-12T20:06:02.062270Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.041462Z","title":"Prism-games 3.0: Stochas- tic game verification with concurrency, equilibria and time","venue":null,"work_id":"a6b7e71e-999b-495a-9acb-f7ad9bfbeb53","year":2020},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.735934Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:a1aa7fcd5ba2c31fe5d299de6da746c33c08dc23b219ec38ab03f70af33da5ba","observation_id":"d5f15ee0-35d8-46ea-a871-e8b492b81e02","resolution":{"observed_at":"2026-08-12T20:06:02.046226Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.025140Z","title":"New algorithms for solving zero-s um stochastic games","venue":null,"work_id":"62c9310d-db3b-4e85-946f-887a4d57ac4c","year":2021},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.740963Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:722d9201a35439b2eff2ce890fd384c9da81293dea07ff70764902d3eeb1ea31","observation_id":"0ab5c906-1332-4a50-9d45-cf99d81ca613","resolution":{"observed_at":"2026-08-12T20:06:02.031006Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:02.006040Z","title":null,"venue":null,"work_id":"55e779c1-0fbb-47ec-b3a7-7d0965a58459","year":1953},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.745497Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:2f26b777c9d45f351a41bae73aa4a778f9894f82971c2e2f885bb5b2e28b13fc","observation_id":"97e390f1-07fb-40b2-a419-40ea85d4652c","resolution":{"observed_at":"2026-08-12T20:06:02.013495Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-12T20:06:01.991286Z","title":"Shellman and Christopher (Krzysztof) Sikor ski","venue":null,"work_id":"2a289111-9762-4818-b0af-171e7ff05665","year":2003},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.749428Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:30e50b603ad5ec7f21e434d8ffe8cdd0cf84e4ce17ffd03174dbaa12611e2bbd","observation_id":"82c666ea-3616-4f93-99ce-21cd999d21d8","resolution":{"observed_at":"2026-08-12T20:06:01.995777Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.974699Z","title":"Shellman and Kris Sikorski","venue":null,"work_id":"9b0c6b10-354e-4e75-a8bb-95175f8c5042","year":2002},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.753549Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:bf9ef0776d7f71697ef4a11c24e94851736fcc0e6c054262952fedab5c54e90d","observation_id":"a62c2321-d897-45ee-ad97-7b7dc15101d7","resolution":{"observed_at":"2026-08-12T20:06:01.979225Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.953725Z","title":"Shellman and Kris Sikorski","venue":null,"work_id":"f6953d41-9e07-4e83-92a0-8f4000a0d771","year":2003},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.759469Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:67846920267a237c096cd16cfc22f8ec6701e1ceb4aef8077f3fc692de7e48ba","observation_id":"e9b72ab0-a926-4727-806f-bd833fa3e7d3","resolution":{"observed_at":"2026-08-12T20:06:01.961215Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.933348Z","title":"Shellman and Kris Sikorski","venue":null,"work_id":"9dd0fa9e-0138-454f-a843-573f9c5a5f91","year":2005},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.763550Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:bb392cdbc1a40d6ae1437e75b770f0b523544b813f5e102a9aa08146635a55a6","observation_id":"adaa956c-cbab-4908-b2f9-00508b3f268d","resolution":{"observed_at":"2026-08-12T20:06:01.937889Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.917862Z","title":"Computational complexity of fixed points","venue":null,"work_id":"ad79efe5-99ba-4bb8-ae0c-ef7998c0ae32","year":2009},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.767692Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:28f5959ceec643f98cf2c4078420346c5f29f583968bccea593c17f778455118","observation_id":"2b488173-43dd-42f0-93ce-5559384768c3","resolution":{"observed_at":"2026-08-12T20:06:01.922140Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.896878Z","title":"Stochastic games","venue":null,"work_id":"4beef3d5-3b81-4d68-a3d1-3ad25dff0f7e","year":2015},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.772126Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:abd8bc404268d2bb03812f5281d5ba777e00153468cd2d45837109524f816443","observation_id":"00b21015-6e5d-4cb8-9201-0342f74fd0e3","resolution":{"observed_at":"2026-08-12T20:06:01.903608Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:06:01.879214Z","title":"A lattice-theoretical fixpoint theorem and its applications","venue":null,"work_id":"688bc2e2-7bc9-4c7f-b44c-24648abdde11","year":1955},"citing_paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T20:06:01.776561Z"},"links":{"citing_paper":"/paper/2411.10107"},"observation_digest":"sha256:6dce3f75bd8dd1ce79cd1c0f329dd3f7e4781e319bc79c23335eeca5bc0a4f28","observation_id":"03f99fda-1f8c-44c5-b58d-2038d86b9867","resolution":{"observed_at":"2026-08-12T20:06:01.885473Z","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"}}],"paper":{"arxiv_id":"2411.10107","last_updated":"2025-03-27T11:06:35Z","latest_version":2,"primary_category":"cs.CC","snapshot_observed_at":"2026-08-12T19:55:57.631184Z","submitted_at":"2024-11-15T11:07:05Z","title":"Monotone Contractions"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":1,"verified_fuzzy":23},"total_outbound_references":28},"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 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2411.10107."}