{"as_of":"2026-08-18T09:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aed665b36ba256c0df61586ff49ddab547a8d7d6ec8951010d8eca2fa979f71c","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T15:46:57.836912Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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":"2026-06-26T13:33:52.887784Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T07:19:38.100458Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"cited_work":{"arxiv_id":"2512.16141","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2512.16141","snapshot_observed_at":"2026-07-14T02:20:21.031592Z","title":"Existence of solutions for non-monotone vis and implications for games","venue":null,"work_id":"9c2438e6-d61f-442b-90ea-e82c79975631","year":2025},"citing_paper":{"arxiv_id":"2606.21573","last_updated":"2026-06-19T16:14:55Z","snapshot_observed_at":"2026-08-06T08:41:11.795069Z","submitted_at":"2026-06-19T16:14:55Z","title":"On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-26T13:33:52.887784Z"},"links":{"cited_paper":"/paper/2512.16141","citing_paper":"/paper/2606.21573"},"observation_digest":"sha256:8ab1666365961ecb2732cdb276686c25b750c466578fd23bde0a0ab3c4f07cc9","observation_id":"6234fff7-9137-465b-b9f7-a06d5ec087aa","resolution":{"observed_at":"2026-07-14T02:20:21.031592Z","resolver_source":"arxiv_id","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"}}],"links":{"evidence":"/evidence","html":"/paper/2512.16141/citation-record","integrity":"/paper/2512.16141/integrity","json":"/paper/2512.16141/citation-record.json","paper":"/paper/2512.16141"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.156708Z","title":"Springer, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.156708Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:639bfb58c46c0178213593217a8319292b54909d113930ced13cc2644ebfa226","observation_id":"434e2845-408f-4814-ac59-d1d1076339d9","resolution":{"observed_at":"2026-08-03T15:46:54.156708Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.210801Z","title":"A distributed algorithm for aggregative games on directed communication graphs","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.210801Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:0418c8c82b06e908c22b2fb3a730b956ef768ab4b3c2d7b3c9bae60bbd30fbdc","observation_id":"c5373024-3682-4ab3-8778-21428a27e996","resolution":{"observed_at":"2026-08-03T15:46:54.210801Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.290303Z","title":"Non-monotone variational inequalities","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.290303Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:ec34312ca628134bb90e073013b070f7ee7f6fd1ccdaabe0a116286bb35afb3a","observation_id":"c0c9c23d-33f0-400e-a5bb-b4278e1bd4f1","resolution":{"observed_at":"2026-08-03T15:46:54.290303Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.401337Z","title":"On non-monotone variational inequalities","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.401337Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:98893f44b906b28ef5db5ebf83e92876eb451500751cea2b46292477896e5cc8","observation_id":"d566c275-57be-4693-8f33-fdda1241b0ba","resolution":{"observed_at":"2026-08-03T15:46:54.401337Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.507085Z","title":"Quasi nash equilibrium in low interaction network games","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.507085Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:06113451a8d9d7e7a10846921e6592fe73ee861ef2715072aa46d004429a918b","observation_id":"f5388f02-daeb-4d93-830d-d1251a641274","resolution":{"observed_at":"2026-08-03T15:46:54.507085Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.588216Z","title":"Tracking-based distributed equilibrium seeking for aggregative games.IEEE Transactions on Automatic Control, 69(9):6026–6041, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.588216Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:833ec207e7f20f33431089d9320f94c5f0fd75552dfc075a3bd74a8a3d291538","observation_id":"18649b69-cc3c-43a9-bf03-66547529be38","resolution":{"observed_at":"2026-08-03T15:46:54.588216Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.648990Z","title":"On the inverse function theorem.Pacific Journal of Mathematics, 64(1):97–102, 1976","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.648990Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:5e231c15779a3fc3a28fcada6d26ed61a84112b25cfe6c7ae03b927b5a0bb1f2","observation_id":"87d32551-203e-46b4-89b0-2ab78d310f61","resolution":{"observed_at":"2026-08-03T15:46:54.648990Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.709683Z","title":"SIAM, 1990","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.709683Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:dd11bd4aa4b7aee1ffcb555f15b96ff5f0e267d5b3362e14fe9aa8287bf4c11c","observation_id":"058df637-5b80-43b5-b1ea-265913bbb74e","resolution":{"observed_at":"2026-08-03T15:46:54.709683Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.783993Z","title":"United we fall: On the nash equilibria of multiplex and multilayer network games.IEEE Transactions on Control of Network Systems, pages 1238–1250, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.783993Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:b11b4dfb0813d5467e74d7fe5c140a63dbf4b52bd4191866342f5658566ad7f2","observation_id":"0e5336a3-a121-4cfd-a3c0-3e12899953d4","resolution":{"observed_at":"2026-08-03T15:46:54.783993Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:54.897907Z","title":"Springer, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:54.897907Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:565c7d4e7436cecee7c316ade1c18468cddca99597a9cc4e0d98df04a0b1d637","observation_id":"999e4b5c-1665-48f8-96af-0477c4b2025e","resolution":{"observed_at":"2026-08-03T15:46:54.897907Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.016328Z","title":"On matrices with non-positive off-diagonal elements and positive principal minors.Czechoslovak Mathematical Journal, 12:382–400, 1962","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.016328Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:1beea12f8172985068096e1bb12ea2a0ad06de857309e9865feecba7029b08f0","observation_id":"da72bd46-1c41-4f91-a905-f934eb209df1","resolution":{"observed_at":"2026-08-03T15:46:55.016328Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.115828Z","title":"A generalized iterative water-filling algorithm for distributed power control in the presence of a jammer.IEEE Transactions on Signal Processing, 57(7):2660–2674, 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.115828Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:e2d5798fbc15c9399e26eea873de9e12c97ac9dc26104237c8ce2892fb603990","observation_id":"49543800-bd7c-4534-8b25-31bf323c2034","resolution":{"observed_at":"2026-08-03T15:46:55.115828Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.260802Z","title":"Nash-cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints.Operations Research, 55(1):113–127, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.260802Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:ce7613d2fc592b977e902d298cf28b9a084b7f297a4558fe66766ddde9ff89ff","observation_id":"4f2ca518-b2a0-48cd-b323-9258a3835511","resolution":{"observed_at":"2026-08-03T15:46:55.260802Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.368132Z","title":"Beyond monotone variational inequalities: solution methods and iteration complexities.Pacific Journal of Optimization, 20(3):403–428, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.368132Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:86b9fd1b9ae07f08dae96574bed7a7d3bf9cbd7877327f2a52de2f704fed6461","observation_id":"d512b231-cc78-45d2-bd6d-7bb2d10f41ed","resolution":{"observed_at":"2026-08-03T15:46:55.368132Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.480505Z","title":"Support functions of the clarke generalized jacobian and of its plenary hull.Nonlinear Analysis: Theory, Methods & Applications, 49(8):1111–1125, 2002","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.480505Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:01b25911f46580e0a45c1538fd9f16d18ff788b76c1ddd8b315c4188e017ee05","observation_id":"1cc58e2f-2f37-46ac-be49-f58c442da0a1","resolution":{"observed_at":"2026-08-03T15:46:55.480505Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.612892Z","title":"SIAM, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.612892Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:94ffbc22724253e40a8c88722deafa243da6831ae16a6a8755cb17c36381807b","observation_id":"5e67f206-92f2-4c9c-8a26-0278aac863b8","resolution":{"observed_at":"2026-08-03T15:46:55.612892Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.696042Z","title":"Mathematics in Science and Engineering, C","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.696042Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:ff51a142eafdcaaa750dfeede6d3aa278525836c24fad3f0c2a6de9275468453","observation_id":"ec9e3a73-89ae-45b7-b262-1c8ca2565f33","resolution":{"observed_at":"2026-08-03T15:46:55.696042Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.841166Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.841166Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:6a559941a42069b6df1f5403c0b91343db95097339b53e456789f6f429ccf701","observation_id":"c9f9dcac-b6e3-49c0-beca-1ddc442f3d8d","resolution":{"observed_at":"2026-08-03T15:46:55.841166Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:55.993652Z","title":"Cambridge University Press, 1996","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:55.993652Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:21d6bc7008f13040919f5e519a69595c08d7ea371f92e6d840a741cfc659327c","observation_id":"c1ea11f8-055f-4bd9-b112-3e23863914eb","resolution":{"observed_at":"2026-08-03T15:46:55.993652Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.119610Z","title":"A variational approach to network games","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.119610Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:c572c3e4f3205377211e135ae2151ef9b7cf0f5ce357133afefbbcd01868a067","observation_id":"ad228e7b-a74d-4b85-897c-f019d6b13816","resolution":{"observed_at":"2026-08-03T15:46:56.119610Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.240829Z","title":"SIAM, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.240829Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:9c2fcd0846122eb17a5ea921d740ca2b2b0f81ade8c735b75fc1ba5864a464e6","observation_id":"1ca43f33-20b5-41bd-91e0-e82239a28b32","resolution":{"observed_at":"2026-08-03T15:46:56.240829Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.373105Z","title":"On the uniqueness and stability of equilibria of network games","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.373105Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:daf42e2a9f93423703b9f97a1d24f60b4346b0d4ca08e619ce53eef3c88f4dc9","observation_id":"c9341bb5-a896-45c5-a3a9-d3d36fd32e0a","resolution":{"observed_at":"2026-08-03T15:46:56.373105Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.503036Z","title":"Infinite dimensional clarke generalized jacobian.Journal of Convex Analysis, 14(2):433–454, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.503036Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:c79794ee4de6c3e2b249c90c15e21382563534e1f4e96a451b57db9a0d54472d","observation_id":"e99b8662-6a1e-4354-8be9-6d192fe7db72","resolution":{"observed_at":"2026-08-03T15:46:56.503036Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.615413Z","title":"Infinite dimensional generalized jacobian: properties and calculus rules.Journal of mathematical analysis and applications, 344(1):55–75, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.615413Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:0cf7e013f1fafe5af9da6b39dc746c36f81935313ea310531980cd1f6f63e223","observation_id":"f50ddbd6-6f57-4aee-bef1-d493d157ade8","resolution":{"observed_at":"2026-08-03T15:46:56.615413Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.767437Z","title":"Nonconvex games with side constraints.SIAM Journal on Optimization, 21(4):1491–1522, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.767437Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:9ecea975b3bd8542656fcd59c66ece049dde563d309298ff2c8bf3eec95e21c5","observation_id":"1e30cd4c-dce0-47ce-a286-a230a64cb02d","resolution":{"observed_at":"2026-08-03T15:46:56.767437Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:56.961001Z","title":"Joint sensing and power allocation in nonconvex cognitive radio games: Quasi-nash equilibria.IEEE Transactions on Signal Processing, 61(9):2366–2382, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:56.961001Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:7043fdc9947d465c79e5e76ab72a6c71d69654556210244806a450672bc2833f","observation_id":"254fd604-dd59-46db-926b-a45152f52006","resolution":{"observed_at":"2026-08-03T15:46:56.961001Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.115729Z","title":"A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis.Games and Economic Behavior, 114:47–82, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.115729Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:5ba3abca21111cb74883dd05f4d6d3e7ef7987f846ae43bbdcf8106fd9dee94a","observation_id":"8d697e4e-6ebd-4323-a79d-800055954621","resolution":{"observed_at":"2026-08-03T15:46:57.115729Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.275332Z","title":"Gradient methods for the minimisation of functionals.USSR Computational Mathematics and Mathematical Physics, 3(4):864–878, 1963","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.275332Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:a110e678dc80a583667b32da39fcef57aa5379a9d963e197e8584f487e71b7ab","observation_id":"3ffef690-c43b-4565-9390-ae5e9f134e83","resolution":{"observed_at":"2026-08-03T15:46:57.275332Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.375678Z","title":"Generalized nash equilibrium seeking for aggregative games over weight-unbalanced digraphs","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.375678Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:0cbac019478fcf2706eb1661fd9375285a2b918288a75bfda9fb450a9b50853c","observation_id":"4fa4d847-c8cf-4203-a659-d7f73f7610c7","resolution":{"observed_at":"2026-08-03T15:46:57.375678Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.427721Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.427721Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:7452dbc801eebab63a86a1ae7621f1dbf7a1a069ce0a0abf855746702c86b597","observation_id":"f76056c0-2899-4fc1-8b99-01efe2ec8078","resolution":{"observed_at":"2026-08-03T15:46:57.427721Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.533112Z","title":"Characterization and computation of local nash equilibria in continuous games","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.533112Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:49bc76368bf4d6d6415d0b18182de9c8e49af6e375d35b15206b246475671c1f","observation_id":"27c27d7a-83b9-4448-95e8-c24accbe03bf","resolution":{"observed_at":"2026-08-03T15:46:57.533112Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.594141Z","title":"On the characterization of solution sets of smooth and nonsmooth convex stochastic nash games.SIAM Journal on Optimization, 21(3):1168–1199, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.594141Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:5db56a82cef32afe60cf84f7b48564699f6e9f7b31615f718754709b59e9c3bd","observation_id":"5cb1a73f-7da9-49ba-bfa3-86f3e551a4de","resolution":{"observed_at":"2026-08-03T15:46:57.594141Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.655395Z","title":"Existence and uniqueness of equilibrium points for concave n-person games.Econometrica: Journal of the Econometric Society, pages 520–534, 1965","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.655395Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:959b24638cbaaa469051e96384959e3c18005caaac4dc622944616e039888925","observation_id":"430abb9f-0677-44ac-a2ef-7ac816b9a677","resolution":{"observed_at":"2026-08-03T15:46:57.655395Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.769356Z","title":"Convex optimization, game theory, and variational inequality theory.IEEE Signal Processing Magazine, 27(3):35–49, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.769356Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:e9ebe48530711c66eb3380cbf1851b8061fe00aa8b8059b535483003d301d3d5","observation_id":"554af6c8-cdb7-4089-a3a2-1238eaa0fe81","resolution":{"observed_at":"2026-08-03T15:46:57.769356Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:46:57.836912Z","title":"A behavioral model of rational choice.The quarterly journal of economics, pages 99–118, 1955","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T15:46:57.836912Z"},"links":{"citing_paper":"/paper/2512.16141"},"observation_digest":"sha256:456a21dc1fd4109a2582957c49bcea6b40da33cf7bc2f314f64b1338531d3531","observation_id":"e20a7acd-863a-489f-a42f-ca878b1fc82b","resolution":{"observed_at":"2026-08-03T15:46:57.836912Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.16141","last_updated":"2026-07-11T14:24:27Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-10T12:34:53.449361Z","submitted_at":"2025-12-18T03:54:31Z","title":"Existence of Solutions for Non-monotone Variational Inequalities and Implications for Games"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":35},"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 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2512.16141."}