{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:INRS74SCK3UEALRUZ6G5CZ6PZA","short_pith_number":"pith:INRS74SC","schema_version":"1.0","canonical_sha256":"43632ff24256e8402e34cf8dd167cfc82f936afe15c474f6e2617c6715e9f3bd","source":{"kind":"arxiv","id":"2608.04386","version":1},"attestation_state":"computed","paper":{"title":"An $\\alpha$-Potential Game Approach to $N$-Player Stochastic Linear-Quadratic Differential Games","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chenhui Hao, Jingtao Shi","submitted_at":"2026-08-05T02:43:24Z","abstract_excerpt":"This paper studies $N$-player stochastic linear-quadratic (LQ) differential games from the perspective of $\\alpha$-potential games. We first consider a closed-loop LQ game with multiplicative noise, where both the drift and the diffusion coefficients depend linearly on the state and the full control vector. For this model, we derive probabilistic and partial differential equation (PDE) representations for the first- and second-order linear derivatives of the players' cost function and prove the equivalence between them. We then develop an open-loop stochastic LQ \\(\\alpha\\)-potential game frame"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.04386","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2026-08-05T02:43:24Z","cross_cats_sorted":[],"title_canon_sha256":"edb8623886f65c621b9074c1a80b7f9bc305772243953cacb3d0c23870ce259f","abstract_canon_sha256":"21db4f7984bad9c8815e8cfdf8d6b0f4c7f0ffdce8e4524fe15104435c56981c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:34:37.855150Z","signature_b64":"NzXexqoh3gx+s5zQZKXIFTvpiglb3jwcMA1J9RKL17zPpgJv5rspKyLkkzMiua2K0kwfk2Z8hmzwdsXcixn9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43632ff24256e8402e34cf8dd167cfc82f936afe15c474f6e2617c6715e9f3bd","last_reissued_at":"2026-08-06T01:34:37.853652Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:34:37.853652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An $\\alpha$-Potential Game Approach to $N$-Player Stochastic Linear-Quadratic Differential Games","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chenhui Hao, Jingtao Shi","submitted_at":"2026-08-05T02:43:24Z","abstract_excerpt":"This paper studies $N$-player stochastic linear-quadratic (LQ) differential games from the perspective of $\\alpha$-potential games. We first consider a closed-loop LQ game with multiplicative noise, where both the drift and the diffusion coefficients depend linearly on the state and the full control vector. For this model, we derive probabilistic and partial differential equation (PDE) representations for the first- and second-order linear derivatives of the players' cost function and prove the equivalence between them. We then develop an open-loop stochastic LQ \\(\\alpha\\)-potential game frame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04386","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04386/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.04386","created_at":"2026-08-06T01:34:37.855476+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04386v1","created_at":"2026-08-06T01:34:37.855476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04386","created_at":"2026-08-06T01:34:37.855476+00:00"},{"alias_kind":"pith_short_12","alias_value":"INRS74SCK3UE","created_at":"2026-08-06T01:34:37.855476+00:00"},{"alias_kind":"pith_short_16","alias_value":"INRS74SCK3UEALRU","created_at":"2026-08-06T01:34:37.855476+00:00"},{"alias_kind":"pith_short_8","alias_value":"INRS74SC","created_at":"2026-08-06T01:34:37.855476+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA","json":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA.json","graph_json":"https://pith.science/api/pith-number/INRS74SCK3UEALRUZ6G5CZ6PZA/graph.json","events_json":"https://pith.science/api/pith-number/INRS74SCK3UEALRUZ6G5CZ6PZA/events.json","paper":"https://pith.science/paper/INRS74SC"},"agent_actions":{"view_html":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA","download_json":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA.json","view_paper":"https://pith.science/paper/INRS74SC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04386&json=true","fetch_graph":"https://pith.science/api/pith-number/INRS74SCK3UEALRUZ6G5CZ6PZA/graph.json","fetch_events":"https://pith.science/api/pith-number/INRS74SCK3UEALRUZ6G5CZ6PZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA/action/storage_attestation","attest_author":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA/action/author_attestation","sign_citation":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA/action/citation_signature","submit_replication":"https://pith.science/pith/INRS74SCK3UEALRUZ6G5CZ6PZA/action/replication_record"}},"created_at":"2026-08-06T01:34:37.855476+00:00","updated_at":"2026-08-06T01:34:37.855476+00:00"}