{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LHGNVJGL7ELQR56CBZ6HAXLTHG","short_pith_number":"pith:LHGNVJGL","canonical_record":{"source":{"id":"2404.02871","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-03T17:08:23Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"ef6ffb9d8297b005e632b26b4dadfe1a2b867c6fdf398fed472da8038368a76b","abstract_canon_sha256":"02efe533b2efa09e9b09b68ca071a53721ecabd2c3a68478c8ed722da95415e0"},"schema_version":"1.0"},"canonical_sha256":"59ccdaa4cbf91708f7c20e7c705d733997bd8b5752938db6a8f64e4ca9e52c71","source":{"kind":"arxiv","id":"2404.02871","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.02871","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.02871v4","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02871","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"LHGNVJGL7ELQ","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_16","alias_value":"LHGNVJGL7ELQR56C","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_8","alias_value":"LHGNVJGL","created_at":"2026-05-20T00:00:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LHGNVJGL7ELQR56CBZ6HAXLTHG","target":"record","payload":{"canonical_record":{"source":{"id":"2404.02871","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-03T17:08:23Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"ef6ffb9d8297b005e632b26b4dadfe1a2b867c6fdf398fed472da8038368a76b","abstract_canon_sha256":"02efe533b2efa09e9b09b68ca071a53721ecabd2c3a68478c8ed722da95415e0"},"schema_version":"1.0"},"canonical_sha256":"59ccdaa4cbf91708f7c20e7c705d733997bd8b5752938db6a8f64e4ca9e52c71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:15.066707Z","signature_b64":"GEu8Cp4mrmHHTICvFlaJ42+OiqKbTenHIdxkyEl8EPXHVPaQinSSTfZlfz9ZJ5BWviZo5mJPnGyvL6b5pZcICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59ccdaa4cbf91708f7c20e7c705d733997bd8b5752938db6a8f64e4ca9e52c71","last_reissued_at":"2026-05-20T00:00:15.065746Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:15.065746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.02871","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tC3tDgbkiijO0/IKFjNJHcrVkJyCtRpNbLipGDLqHscHh6OmhIztUmYIUwY9F5zJ58kDLTaYvD6v4qyfjosuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:35:17.284632Z"},"content_sha256":"034ca6f2b0acd7c8032be4bc4997e7e55c45c5c9d4e0c5f75a6e6acb25c543a7","schema_version":"1.0","event_id":"sha256:034ca6f2b0acd7c8032be4bc4997e7e55c45c5c9d4e0c5f75a6e6acb25c543a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LHGNVJGL7ELQR56CBZ6HAXLTHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and uniqueness results for a mean-field game of optimal investment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH"],"primary_cat":"math.OC","authors_text":"Alessandro Calvia, Fausto Gozzi, Giorgio Ferrari, Salvatore Federico","submitted_at":"2024-04-03T17:08:23Z","abstract_excerpt":"We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02871","kind":"arxiv","version":4},"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/2404.02871/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":"2026-05-20T00:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OGh4frlLADyDfxOYSNVPe6t5Ed41CFHc50ziQGtTpNnzRFtGMMclgOQDEKH1CzHouXyICRbcgNAB2hK9AixEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:35:17.285083Z"},"content_sha256":"294ba7c684959eace40f1f8f3fcd6280447088db4c3ae0d8211d3afb3b730f89","schema_version":"1.0","event_id":"sha256:294ba7c684959eace40f1f8f3fcd6280447088db4c3ae0d8211d3afb3b730f89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/bundle.json","state_url":"https://pith.science/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/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":"2026-05-26T11:35:17Z","links":{"resolver":"https://pith.science/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG","bundle":"https://pith.science/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/bundle.json","state":"https://pith.science/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHGNVJGL7ELQR56CBZ6HAXLTHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LHGNVJGL7ELQR56CBZ6HAXLTHG","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":"02efe533b2efa09e9b09b68ca071a53721ecabd2c3a68478c8ed722da95415e0","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-03T17:08:23Z","title_canon_sha256":"ef6ffb9d8297b005e632b26b4dadfe1a2b867c6fdf398fed472da8038368a76b"},"schema_version":"1.0","source":{"id":"2404.02871","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.02871","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.02871v4","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02871","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"LHGNVJGL7ELQ","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_16","alias_value":"LHGNVJGL7ELQR56C","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_8","alias_value":"LHGNVJGL","created_at":"2026-05-20T00:00:15Z"}],"graph_snapshots":[{"event_id":"sha256:294ba7c684959eace40f1f8f3fcd6280447088db4c3ae0d8211d3afb3b730f89","target":"graph","created_at":"2026-05-20T00:00:15Z","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/2404.02871/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-fie","authors_text":"Alessandro Calvia, Fausto Gozzi, Giorgio Ferrari, Salvatore Federico","cross_cats":["econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-03T17:08:23Z","title":"Existence and uniqueness results for a mean-field game of optimal investment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02871","kind":"arxiv","version":4},"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":"sha256:034ca6f2b0acd7c8032be4bc4997e7e55c45c5c9d4e0c5f75a6e6acb25c543a7","target":"record","created_at":"2026-05-20T00:00:15Z","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":"02efe533b2efa09e9b09b68ca071a53721ecabd2c3a68478c8ed722da95415e0","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-03T17:08:23Z","title_canon_sha256":"ef6ffb9d8297b005e632b26b4dadfe1a2b867c6fdf398fed472da8038368a76b"},"schema_version":"1.0","source":{"id":"2404.02871","kind":"arxiv","version":4}},"canonical_sha256":"59ccdaa4cbf91708f7c20e7c705d733997bd8b5752938db6a8f64e4ca9e52c71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59ccdaa4cbf91708f7c20e7c705d733997bd8b5752938db6a8f64e4ca9e52c71","first_computed_at":"2026-05-20T00:00:15.065746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:15.065746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GEu8Cp4mrmHHTICvFlaJ42+OiqKbTenHIdxkyEl8EPXHVPaQinSSTfZlfz9ZJ5BWviZo5mJPnGyvL6b5pZcICQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:15.066707Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.02871","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:034ca6f2b0acd7c8032be4bc4997e7e55c45c5c9d4e0c5f75a6e6acb25c543a7","sha256:294ba7c684959eace40f1f8f3fcd6280447088db4c3ae0d8211d3afb3b730f89"],"state_sha256":"853cd1f0a300016db6263508c042511d18ab929e10ae0ab9c72e5552db73f819"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEH3d1XTbnhK+N51mvQgq7EfvYqCt97czdVW+E/gKMR0CKBozeCrsVFGdwHw/gJUTlG3dUf5+omHHZVYcIFCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:35:17.288572Z","bundle_sha256":"6ef2cf020fff1dc02b7b467d4365006fa963a965ba4123fc2ea146f9d6e6b1a5"}}