{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VRAPFM4NIUJ4NICVNLVZRLNBHQ","short_pith_number":"pith:VRAPFM4N","canonical_record":{"source":{"id":"2505.22936","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T23:34:14Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"4bc59973d70919495db556f43e9c5f0c6435d12f23682e762a9be4432e7fd3c7","abstract_canon_sha256":"6a8285414d712cd05319df7bc43ed5a0e9ff63e9f9ec7e50177fbb75616ff3bf"},"schema_version":"1.0"},"canonical_sha256":"ac40f2b38d4513c6a0556aeb98ada13c11587bc356bf060fd9cc7dfb2f3809b3","source":{"kind":"arxiv","id":"2505.22936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22936","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22936v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22936","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"VRAPFM4NIUJ4","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"VRAPFM4NIUJ4NICV","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"VRAPFM4N","created_at":"2026-07-05T11:11:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VRAPFM4NIUJ4NICVNLVZRLNBHQ","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22936","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T23:34:14Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"4bc59973d70919495db556f43e9c5f0c6435d12f23682e762a9be4432e7fd3c7","abstract_canon_sha256":"6a8285414d712cd05319df7bc43ed5a0e9ff63e9f9ec7e50177fbb75616ff3bf"},"schema_version":"1.0"},"canonical_sha256":"ac40f2b38d4513c6a0556aeb98ada13c11587bc356bf060fd9cc7dfb2f3809b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:51.992658Z","signature_b64":"olQzJNzQO+dq7eCi5FSjkXwvNKzuAST+9HX+XL2V7/wOvlt/zoOVvHfwN/BjZUXhC6lwCGyRbKXq3CSO7TnHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac40f2b38d4513c6a0556aeb98ada13c11587bc356bf060fd9cc7dfb2f3809b3","last_reissued_at":"2026-07-05T11:11:51.992179Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:51.992179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22936","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":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6iHIXewZDc8refIdVvYo/D+p8nsY9WeewKEpjjikRBTom5U0Ru3t1JZb4zQk+71VOVA3GyAN353yncFuD+pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T04:25:12.123597Z"},"content_sha256":"5cfe8b0a14d5a46ba39c9df5e399c2ef832d30443bf81fb49bc59b1537c7bf36","schema_version":"1.0","event_id":"sha256:5cfe8b0a14d5a46ba39c9df5e399c2ef832d30443bf81fb49bc59b1537c7bf36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VRAPFM4NIUJ4NICVNLVZRLNBHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-Field Games with two-sided singular controls for L\\'evy processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Facundo Oli\\'u","submitted_at":"2025-05-28T23:34:14Z","abstract_excerpt":"In a probabilistic mean field game driven by a L\\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\\`adl\\`ag processes, while he is interacting with an aggregate of players through the expectation of a controlled process by another pair of c\\`adl\\`ag processes. With the Brouwer fixed point theorem, we provide easy to check conditions for the existence of mean field game equilibrium controls for both the discounted and ergodic control problem, characterize them as the solution of an integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22936","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/2505.22936/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":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkVQ79OvNQoi3gLk7kK6uDVqtMvTqvZuU/3ocsmkdFncDtvZf3mU/EYDDWDq6XlF6Qop0voCSXaKJsr1CATmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T04:25:12.124107Z"},"content_sha256":"0908e1be841b208c2f4c23675c7b64dcd22d864b0a45ec28887ccafdb3b24576","schema_version":"1.0","event_id":"sha256:0908e1be841b208c2f4c23675c7b64dcd22d864b0a45ec28887ccafdb3b24576"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/bundle.json","state_url":"https://pith.science/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/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":"2026-08-23T04:25:12Z","links":{"resolver":"https://pith.science/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ","bundle":"https://pith.science/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/bundle.json","state":"https://pith.science/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRAPFM4NIUJ4NICVNLVZRLNBHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VRAPFM4NIUJ4NICVNLVZRLNBHQ","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":"6a8285414d712cd05319df7bc43ed5a0e9ff63e9f9ec7e50177fbb75616ff3bf","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T23:34:14Z","title_canon_sha256":"4bc59973d70919495db556f43e9c5f0c6435d12f23682e762a9be4432e7fd3c7"},"schema_version":"1.0","source":{"id":"2505.22936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22936","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22936v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22936","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"VRAPFM4NIUJ4","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"VRAPFM4NIUJ4NICV","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"VRAPFM4N","created_at":"2026-07-05T11:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:0908e1be841b208c2f4c23675c7b64dcd22d864b0a45ec28887ccafdb3b24576","target":"graph","created_at":"2026-07-05T11:11:51Z","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/2505.22936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a probabilistic mean field game driven by a L\\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\\`adl\\`ag processes, while he is interacting with an aggregate of players through the expectation of a controlled process by another pair of c\\`adl\\`ag processes. With the Brouwer fixed point theorem, we provide easy to check conditions for the existence of mean field game equilibrium controls for both the discounted and ergodic control problem, characterize them as the solution of an integ","authors_text":"Facundo Oli\\'u","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T23:34:14Z","title":"Mean-Field Games with two-sided singular controls for L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22936","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":"sha256:5cfe8b0a14d5a46ba39c9df5e399c2ef832d30443bf81fb49bc59b1537c7bf36","target":"record","created_at":"2026-07-05T11:11:51Z","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":"6a8285414d712cd05319df7bc43ed5a0e9ff63e9f9ec7e50177fbb75616ff3bf","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T23:34:14Z","title_canon_sha256":"4bc59973d70919495db556f43e9c5f0c6435d12f23682e762a9be4432e7fd3c7"},"schema_version":"1.0","source":{"id":"2505.22936","kind":"arxiv","version":1}},"canonical_sha256":"ac40f2b38d4513c6a0556aeb98ada13c11587bc356bf060fd9cc7dfb2f3809b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac40f2b38d4513c6a0556aeb98ada13c11587bc356bf060fd9cc7dfb2f3809b3","first_computed_at":"2026-07-05T11:11:51.992179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:51.992179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"olQzJNzQO+dq7eCi5FSjkXwvNKzuAST+9HX+XL2V7/wOvlt/zoOVvHfwN/BjZUXhC6lwCGyRbKXq3CSO7TnHAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:51.992658Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cfe8b0a14d5a46ba39c9df5e399c2ef832d30443bf81fb49bc59b1537c7bf36","sha256:0908e1be841b208c2f4c23675c7b64dcd22d864b0a45ec28887ccafdb3b24576"],"state_sha256":"920869fd2a1ba9b24868347d1b6fe81954fe6b66e96ffb315b6abe6b6ce2a15b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TH8BBViEYFsX1wTBJ1PHxzX+MRMXyaaWdizvI1J/bv5jyESaM/Xj0om8M0/09hrokuOxPcBrPtuem7+dOaAXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T04:25:12.128581Z","bundle_sha256":"ee3971f80b50c0d681b1d9fbba187065669e2d411c47e8b63f2822ef38135b6f"}}