{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AINEQ6TWVS4DVOEXKIAFMQRL4Q","short_pith_number":"pith:AINEQ6TW","canonical_record":{"source":{"id":"2405.03102","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-06T01:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"eaf5bed462ea30af220075b1de6386e136b4608d0f71d2e8eb346d3ed27d7a41","abstract_canon_sha256":"9352a7b49ce94dc516106bf02999f2ea6cf33fb64281f7ae163d0c317ff8e8bf"},"schema_version":"1.0"},"canonical_sha256":"021a487a76acb83ab897520056422be4192d9911373af45e686113ae8f1ead2d","source":{"kind":"arxiv","id":"2405.03102","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03102","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03102v2","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03102","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_12","alias_value":"AINEQ6TWVS4D","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_16","alias_value":"AINEQ6TWVS4DVOEX","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_8","alias_value":"AINEQ6TW","created_at":"2026-07-05T10:37:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AINEQ6TWVS4DVOEXKIAFMQRL4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2405.03102","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-06T01:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"eaf5bed462ea30af220075b1de6386e136b4608d0f71d2e8eb346d3ed27d7a41","abstract_canon_sha256":"9352a7b49ce94dc516106bf02999f2ea6cf33fb64281f7ae163d0c317ff8e8bf"},"schema_version":"1.0"},"canonical_sha256":"021a487a76acb83ab897520056422be4192d9911373af45e686113ae8f1ead2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:37:26.127965Z","signature_b64":"YBvfcmlVZBWIv2eTehC2RLJqh1AhBRIs6XSN5xu67R/mJpwmTxl1WCDIweMiTmTGFiQidkGrHPTF1w4ANcFyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021a487a76acb83ab897520056422be4192d9911373af45e686113ae8f1ead2d","last_reissued_at":"2026-07-05T10:37:26.127501Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:37:26.127501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.03102","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:37:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHeS+8BACnOQ4eoyXF4cGNjmSM08L7BWY1Gp7IaQNMxAM9qauldrtf9EL63gEfNKQAXTkTRJytX7mW9omF9+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:42:42.534228Z"},"content_sha256":"51abfed8a2081231771b7b6b274c45727813c2c1d95229ec2d6569cf2d301fb4","schema_version":"1.0","event_id":"sha256:51abfed8a2081231771b7b6b274c45727813c2c1d95229ec2d6569cf2d301fb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AINEQ6TWVS4DVOEXKIAFMQRL4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear-Quadratic Mean Field Stackelberg Stochastic Differential Game with Partial Information and Common Noise","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jingtao Shi, Yu Si","submitted_at":"2024-05-06T01:38:11Z","abstract_excerpt":"This paper is concerned with a linear-quadratic mean field Stackelberg stochastic differential game with partial information and common noise, which contains a leader and a large number of followers. To be specific, the followers face a large population Nash game after the leader first announces his strategy, while the leader will then optimize his own cost functional on consideration of the followers' reactions. The state equation of the leader and followers are both general stochastic differential equations, where the diffusion terms contain both the control and state variables. However, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03102","kind":"arxiv","version":2},"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/2405.03102/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":"2026-07-05T10:37:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwNRSAHl+vjofPu8eWWtRDIAuuuv1CLetXey5jUAo5ARI5OLd+p9eBbu0V96VC7WmoDzoFEyInAQ0zjV9snZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:42:42.535587Z"},"content_sha256":"b685f9a70d06a80665112066b92fdf2b2fc5e3f1619b2cb017152c04bb50aab2","schema_version":"1.0","event_id":"sha256:b685f9a70d06a80665112066b92fdf2b2fc5e3f1619b2cb017152c04bb50aab2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/bundle.json","state_url":"https://pith.science/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/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":"2026-08-18T16:42:42Z","links":{"resolver":"https://pith.science/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q","bundle":"https://pith.science/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/bundle.json","state":"https://pith.science/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AINEQ6TWVS4DVOEXKIAFMQRL4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AINEQ6TWVS4DVOEXKIAFMQRL4Q","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":"9352a7b49ce94dc516106bf02999f2ea6cf33fb64281f7ae163d0c317ff8e8bf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-06T01:38:11Z","title_canon_sha256":"eaf5bed462ea30af220075b1de6386e136b4608d0f71d2e8eb346d3ed27d7a41"},"schema_version":"1.0","source":{"id":"2405.03102","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03102","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03102v2","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03102","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_12","alias_value":"AINEQ6TWVS4D","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_16","alias_value":"AINEQ6TWVS4DVOEX","created_at":"2026-07-05T10:37:26Z"},{"alias_kind":"pith_short_8","alias_value":"AINEQ6TW","created_at":"2026-07-05T10:37:26Z"}],"graph_snapshots":[{"event_id":"sha256:b685f9a70d06a80665112066b92fdf2b2fc5e3f1619b2cb017152c04bb50aab2","target":"graph","created_at":"2026-07-05T10:37:26Z","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/2405.03102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with a linear-quadratic mean field Stackelberg stochastic differential game with partial information and common noise, which contains a leader and a large number of followers. To be specific, the followers face a large population Nash game after the leader first announces his strategy, while the leader will then optimize his own cost functional on consideration of the followers' reactions. The state equation of the leader and followers are both general stochastic differential equations, where the diffusion terms contain both the control and state variables. However, the","authors_text":"Jingtao Shi, Yu Si","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-06T01:38:11Z","title":"Linear-Quadratic Mean Field Stackelberg Stochastic Differential Game with Partial Information and Common Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03102","kind":"arxiv","version":2},"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":"sha256:51abfed8a2081231771b7b6b274c45727813c2c1d95229ec2d6569cf2d301fb4","target":"record","created_at":"2026-07-05T10:37:26Z","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":"9352a7b49ce94dc516106bf02999f2ea6cf33fb64281f7ae163d0c317ff8e8bf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-06T01:38:11Z","title_canon_sha256":"eaf5bed462ea30af220075b1de6386e136b4608d0f71d2e8eb346d3ed27d7a41"},"schema_version":"1.0","source":{"id":"2405.03102","kind":"arxiv","version":2}},"canonical_sha256":"021a487a76acb83ab897520056422be4192d9911373af45e686113ae8f1ead2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021a487a76acb83ab897520056422be4192d9911373af45e686113ae8f1ead2d","first_computed_at":"2026-07-05T10:37:26.127501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:37:26.127501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBvfcmlVZBWIv2eTehC2RLJqh1AhBRIs6XSN5xu67R/mJpwmTxl1WCDIweMiTmTGFiQidkGrHPTF1w4ANcFyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:37:26.127965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03102","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51abfed8a2081231771b7b6b274c45727813c2c1d95229ec2d6569cf2d301fb4","sha256:b685f9a70d06a80665112066b92fdf2b2fc5e3f1619b2cb017152c04bb50aab2"],"state_sha256":"af3d41fe23085e850c6ff2e19be686186258fa6e3be22bb720f8b5ad5b715873"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdKhd1gZoSR89GaPC+6LsjHIsWnGhtFSZFp92zHx7y41dOaFcbGL5p3tkeRmR208AkNojrf0xFDN1nvWzn0oAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T16:42:42.541116Z","bundle_sha256":"a231bfc05104eb5997df6475e4b31760e9614f5eb6f7493dafdcc60055b2456b"}}