{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:C6ANX5HXVTQBBMBW3BOIMELJS6","short_pith_number":"pith:C6ANX5HX","canonical_record":{"source":{"id":"2405.10083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-16T13:26:16Z","cross_cats_sorted":[],"title_canon_sha256":"c5a520b56ea186231e7fa96cb73a116b6364950c0dc5cee14aaeb5e4c8af9cb2","abstract_canon_sha256":"b52f929fdbecfda6151e2d1fd38a994eada86af4cf923228fefac4cabeef124b"},"schema_version":"1.0"},"canonical_sha256":"1780dbf4f7ace010b036d85c8611699799aea154520f42ef9a573805d98b9d90","source":{"kind":"arxiv","id":"2405.10083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.10083","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2405.10083v1","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.10083","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"C6ANX5HXVTQB","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"C6ANX5HXVTQBBMBW","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"C6ANX5HX","created_at":"2026-07-05T08:19:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:C6ANX5HXVTQBBMBW3BOIMELJS6","target":"record","payload":{"canonical_record":{"source":{"id":"2405.10083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-16T13:26:16Z","cross_cats_sorted":[],"title_canon_sha256":"c5a520b56ea186231e7fa96cb73a116b6364950c0dc5cee14aaeb5e4c8af9cb2","abstract_canon_sha256":"b52f929fdbecfda6151e2d1fd38a994eada86af4cf923228fefac4cabeef124b"},"schema_version":"1.0"},"canonical_sha256":"1780dbf4f7ace010b036d85c8611699799aea154520f42ef9a573805d98b9d90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:19:52.468666Z","signature_b64":"TGIBhMHe4Ooz9kHHMc14XfhavT8O13L1OFlAgK2oKtCjBJlaWxFQSB3mziHefWQE2EfLSmAoLZRnA8rmLRi5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1780dbf4f7ace010b036d85c8611699799aea154520f42ef9a573805d98b9d90","last_reissued_at":"2026-07-05T08:19:52.468109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:19:52.468109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.10083","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNmahmMeW4phfRJRSWXuyAKrRww/7aObXMeBE+Ipjw/e7AN2euyRXGcNjJKQOLo87L1//cqupvAOm1RpjyQKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:25:55.753116Z"},"content_sha256":"f4363d70002ef960c207984d6c9ab466605eedfb9ee0ca6f266bf77fb92e0bdd","schema_version":"1.0","event_id":"sha256:f4363d70002ef960c207984d6c9ab466605eedfb9ee0ca6f266bf77fb92e0bdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:C6ANX5HXVTQBBMBW3BOIMELJS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two person non-zero-sum linear-quadratic differential game with Markovian jumps in infinite horizon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fan Wu, Xin Zhang, Xun Li","submitted_at":"2024-05-16T13:26:16Z","abstract_excerpt":"This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first provide a sufficient condition to ensure the $L^2$-integrability of the state process and study a class of linear backward stochastic differential equation (BSDE, for short) in infinite horizon. Then, we seriously discuss the LQ problem and show that the closed-loop optimal control is characterized by the solutions to coupled algebra Riccati equations (CAREs, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.10083","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/2405.10083/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHxsKohv8KRQIzbrCfcEFU13IBvb6lP0NqpZWrRT0/KHIy8f+qu99LPS5ovll4WVAE8MOcKj6uTFk1V0NIyQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:25:55.753619Z"},"content_sha256":"d0e9ef2706f6b490d20e0847144ff6d17b9ac31b1659baf0a561b2be8fa0c5b5","schema_version":"1.0","event_id":"sha256:d0e9ef2706f6b490d20e0847144ff6d17b9ac31b1659baf0a561b2be8fa0c5b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/bundle.json","state_url":"https://pith.science/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T20:25:55Z","links":{"resolver":"https://pith.science/pith/C6ANX5HXVTQBBMBW3BOIMELJS6","bundle":"https://pith.science/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/bundle.json","state":"https://pith.science/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6ANX5HXVTQBBMBW3BOIMELJS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:C6ANX5HXVTQBBMBW3BOIMELJS6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b52f929fdbecfda6151e2d1fd38a994eada86af4cf923228fefac4cabeef124b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-16T13:26:16Z","title_canon_sha256":"c5a520b56ea186231e7fa96cb73a116b6364950c0dc5cee14aaeb5e4c8af9cb2"},"schema_version":"1.0","source":{"id":"2405.10083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.10083","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2405.10083v1","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.10083","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"C6ANX5HXVTQB","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"C6ANX5HXVTQBBMBW","created_at":"2026-07-05T08:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"C6ANX5HX","created_at":"2026-07-05T08:19:52Z"}],"graph_snapshots":[{"event_id":"sha256:d0e9ef2706f6b490d20e0847144ff6d17b9ac31b1659baf0a561b2be8fa0c5b5","target":"graph","created_at":"2026-07-05T08:19:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.10083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first provide a sufficient condition to ensure the $L^2$-integrability of the state process and study a class of linear backward stochastic differential equation (BSDE, for short) in infinite horizon. Then, we seriously discuss the LQ problem and show that the closed-loop optimal control is characterized by the solutions to coupled algebra Riccati equations (CAREs, ","authors_text":"Fan Wu, Xin Zhang, Xun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-16T13:26:16Z","title":"Two person non-zero-sum linear-quadratic differential game with Markovian jumps in infinite horizon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.10083","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f4363d70002ef960c207984d6c9ab466605eedfb9ee0ca6f266bf77fb92e0bdd","target":"record","created_at":"2026-07-05T08:19:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b52f929fdbecfda6151e2d1fd38a994eada86af4cf923228fefac4cabeef124b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-16T13:26:16Z","title_canon_sha256":"c5a520b56ea186231e7fa96cb73a116b6364950c0dc5cee14aaeb5e4c8af9cb2"},"schema_version":"1.0","source":{"id":"2405.10083","kind":"arxiv","version":1}},"canonical_sha256":"1780dbf4f7ace010b036d85c8611699799aea154520f42ef9a573805d98b9d90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1780dbf4f7ace010b036d85c8611699799aea154520f42ef9a573805d98b9d90","first_computed_at":"2026-07-05T08:19:52.468109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:19:52.468109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TGIBhMHe4Ooz9kHHMc14XfhavT8O13L1OFlAgK2oKtCjBJlaWxFQSB3mziHefWQE2EfLSmAoLZRnA8rmLRi5DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:19:52.468666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.10083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4363d70002ef960c207984d6c9ab466605eedfb9ee0ca6f266bf77fb92e0bdd","sha256:d0e9ef2706f6b490d20e0847144ff6d17b9ac31b1659baf0a561b2be8fa0c5b5"],"state_sha256":"6c0b6a53d42a69460d1c6f463e6ff9dce3c5c923e2c678af6e589988ea47ec27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWzpomSyvU4bML4rZ+PAI0QvC6xQAp3Z68ZFTAEjnwmZ5GWNoVAPFz7RIM9SLCCVUlrwF8idHEhyUpunDx+mBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T20:25:55.757642Z","bundle_sha256":"16a0431c1677c7802911ca2bc9094b3fbbe5cb363a29121cd7100ae3ea86cf55"}}