{"as_of":"2026-08-12T11:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d2a81114d41c07dbd0ded589a2784d02c6e16737bbace7a857060ac6e8292f8d","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T22:44:43.877002Z","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":"2026-08-12T06:34:41.77262+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/2506.21079/citation-record","integrity":"/paper/2506.21079/integrity","json":"/paper/2506.21079/citation-record.json","paper":"/paper/2506.21079"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T22:44:44.060591Z","title":"Markov games as a framework for multi- agent reinforcement learning","venue":null,"work_id":"41f885c6-4031-481d-b48b-6d44b4a1e62e","year":1994},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.829640Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:9762835d80b703ce666044d167efe40238a977178ccbf7bf30954f9678d9bee9","observation_id":"e2193548-ba8c-4151-b783-bc6f920fc665","resolution":{"observed_at":"2026-08-06T22:44:44.064820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:44.047852Z","title":"Algorithms, machine learning, and col lusion","venue":null,"work_id":"e114af5a-51a2-4036-811b-bf4bed1a93b5","year":2018},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.834075Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:41ffac6230394a845a8e498320027dbe9607dc3489d21b704862c4d7ca8d91f8","observation_id":"4c118239-f9a6-4790-b67d-c1b7b8c7b5f2","resolution":{"observed_at":"2026-08-06T22:44:44.051804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:44.035403Z","title":"Artificial intelligence, algorith- mic pricing, and collusion","venue":null,"work_id":"afa36739-db05-4af9-ab16-15b6ec769112","year":2020},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.838373Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:40e552561e76cf54be894c9cad28e9139c8c3b2627b4c44455b046ec05474682","observation_id":"97b4f1d0-7833-458c-b48f-02a600b69210","resolution":{"observed_at":"2026-08-06T22:44:44.039428Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.05946","last_updated":"2023-09-19T17:51:34Z","snapshot_observed_at":"2026-07-06T12:36:59.131772Z","submitted_at":"2022-02-12T00:50:15Z","title":"Artificial Intelligence and Spontaneous Collusion","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.05946","snapshot_observed_at":"2026-08-06T22:44:43.842096Z","title":"Artificial inte lligence and spontaneous collusion","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.842096Z"},"links":{"cited_paper":"/paper/2202.05946","citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:3817e8ea9c677c1725923b8ffae3f3ae93871dc2b51591f9db38823d49ae4b62","observation_id":"9aeca44c-b4c2-4b9f-ba07-fe05c75082ad","resolution":{"observed_at":"2026-08-06T22:44:43.842096Z","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":"2026-08-06T22:44:44.021830Z","title":"Solutions of ordinary differential equat ions as limits of pure jump markov processes","venue":null,"work_id":"6068c93a-52ec-4c42-a634-dad7c29494cc","year":1970},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.846653Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:7586d358a66e803e1f222c10a781169cd98667422b5d591c42de837487c10455","observation_id":"37c7f90b-1b73-4116-9ad9-fd758a0ae867","resolution":{"observed_at":"2026-08-06T22:44:44.026570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0210109","last_updated":"2002-12-23T21:57:34Z","snapshot_observed_at":"2026-07-07T05:31:46.068383Z","submitted_at":"2002-10-08T15:31:50Z","title":"Fluid Limits of Pure Jump Markov Processes: a Practical Guide","version":3},"cited_work":{"arxiv_id":"math/0210109","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0210109","snapshot_observed_at":"2026-08-06T22:44:43.931682Z","title":"Fluid Limits of Pure Jump Markov Processes: a Practical Guide","venue":"math.PR","work_id":"ae486519-a6b0-456f-a623-752fcc7c7c6f","year":2002},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.850700Z"},"links":{"cited_paper":"/paper/math/0210109","citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:8a63908ace655f72b1982c001edd09f0bc91404f48850a8eac29ef701f780049","observation_id":"dd0c8f5f-4e11-47b1-8eda-e9ffe9a19481","resolution":{"observed_at":"2026-08-06T22:44:43.936279Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:44.009264Z","title":"Geometric fluid approximation for general continuous-time markov chains","venue":null,"work_id":"f7445e91-2eec-485e-bf2c-c98097b47d7b","year":2019},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.855623Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:fe6bae69a41be278f37859b15ed44423992f23db79ccc65da23ff88ebbe4c918","observation_id":"7e5a10c4-3253-4c5a-8848-7de98dbbf248","resolution":{"observed_at":"2026-08-06T22:44:44.013098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:43.996015Z","title":"Differential equation approximati ons for markov chains","venue":null,"work_id":"1e6bc249-7d72-4171-a920-1ffd8fb1d6f4","year":2008},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.859606Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:1c1e59208db61241fee9a2640959b98e46ffcb8682090ae83ddad56baeae776b","observation_id":"ea3df568-8ef7-46ce-b6a3-8a97c4d675c3","resolution":{"observed_at":"2026-08-06T22:44:44.000624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:43.984389Z","title":"Stochastic approximation with two time s cales","venue":null,"work_id":"55e026fa-32fc-47be-9296-f3d9af0bd4f4","year":1997},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.863846Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:429b3cbace0ad05a2061b209009b62dc9b3dce8dce9308dd3f18317bb22430ca","observation_id":"e8bd5a7e-ca84-4376-b9ea-6c13d40e91f8","resolution":{"observed_at":"2026-08-06T22:44:43.988204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.14285","last_updated":"2024-10-25T08:25:02Z","snapshot_observed_at":"2026-07-06T18:18:25.746022Z","submitted_at":"2024-05-23T08:00:45Z","title":"Computing the Bias of Constant-step Stochastic Approximation with Markovian Noise","version":2},"cited_work":{"arxiv_id":"2405.14285","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.14285","snapshot_observed_at":"2026-08-06T22:44:43.910792Z","title":"Computing the Bias of Constant-step Stochastic Approximation with Markovian Noise","venue":"stat.ML","work_id":"3dbb0845-2f74-4fe0-b4ca-5cb6bf1c8e4f","year":2024},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.868732Z"},"links":{"cited_paper":"/paper/2405.14285","citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:2df101f21f98a1f85227e6ec9670631ef76d207a85e324d5b9a8cb799a7033f9","observation_id":"438fce0e-a78a-4666-8213-2ad45889bdc3","resolution":{"observed_at":"2026-08-06T22:44:43.917905Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:43.972625Z","title":"Multiscale methods: averaging and homogenization , volume 53","venue":null,"work_id":"93b19c86-9628-46fc-8b7f-8c381c4c0edc","year":2008},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.873034Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:b6d00c77abda5b563263e4ef4f9495ac6c5e48f77ffcde6fdcd589f6ef07c6b3","observation_id":"06a45649-9c2d-4fda-b6b6-c34af1a14b04","resolution":{"observed_at":"2026-08-06T22:44:43.977036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T22:44:43.959132Z","title":"Lectures on finite markov chains","venue":null,"work_id":"a8509f90-03db-47ae-88b2-09dea84734c8","year":1996},"citing_paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T22:44:43.877002Z"},"links":{"citing_paper":"/paper/2506.21079"},"observation_digest":"sha256:aabeea6e2e1c8ac09257f71e52b63fdfdca7d0bef3e7a6d2a966038eaede287a","observation_id":"103fd063-f745-433e-9afb-fbdcc78250c9","resolution":{"observed_at":"2026-08-06T22:44:43.964256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.21079","last_updated":"2025-06-26T08:08:49Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-12T06:50:10.070472Z","submitted_at":"2025-06-26T08:08:49Z","title":"Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":2,"verified_fuzzy":9},"total_outbound_references":12},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2506.21079."}