{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HH5G2WNZJSY2UYSPFRSGBCBERZ","short_pith_number":"pith:HH5G2WNZ","canonical_record":{"source":{"id":"1503.05238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2015-03-17T22:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"f081de02d71f7c2c62053da36d51a8f53f5db7b9b5cf7ff39698d59a55c67b3f","abstract_canon_sha256":"c1c0fe40a6234833f5f4dd16bd8cce5e3b80c95531c7aa39d7c6310e7dd33f37"},"schema_version":"1.0"},"canonical_sha256":"39fa6d59b94cb1aa624f2c646088248e69ca20f58d576d7f7ad050d117823991","source":{"kind":"arxiv","id":"1503.05238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05238","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05238v1","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05238","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"HH5G2WNZJSY2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HH5G2WNZJSY2UYSP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HH5G2WNZ","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HH5G2WNZJSY2UYSPFRSGBCBERZ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2015-03-17T22:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"f081de02d71f7c2c62053da36d51a8f53f5db7b9b5cf7ff39698d59a55c67b3f","abstract_canon_sha256":"c1c0fe40a6234833f5f4dd16bd8cce5e3b80c95531c7aa39d7c6310e7dd33f37"},"schema_version":"1.0"},"canonical_sha256":"39fa6d59b94cb1aa624f2c646088248e69ca20f58d576d7f7ad050d117823991","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.169240Z","signature_b64":"z3b53n+Ad2GjfnUgVZm0Od8lUn3/zUny0I+aaLlJpdZcQY8SyexeZSLJRAfmG0liT/yTTWkE6Rq4mmKAQM1bAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39fa6d59b94cb1aa624f2c646088248e69ca20f58d576d7f7ad050d117823991","last_reissued_at":"2026-05-18T01:19:16.168720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.168720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05238","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":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NKnlahiUUKKsmgN2sxwzaQe+KTQaj3Z7/34E1rNMr1LO5dBMbJ/3qebkRI5fpo+F7hPHgArzPNPDcOr/BugKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:41:17.833135Z"},"content_sha256":"2294538c7cc6e0b903b734fdf767e56560621727be09e01fa61768339e90380a","schema_version":"1.0","event_id":"sha256:2294538c7cc6e0b903b734fdf767e56560621727be09e01fa61768339e90380a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HH5G2WNZJSY2UYSPFRSGBCBERZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit value for optimal control with general means","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"J\\'er\\^ome Renault (GREMAQ), Marc Quincampoix (LM-Brest), Xiaoxi Li (IMJ-PRG)","submitted_at":"2015-03-17T22:42:15Z","abstract_excerpt":"We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\\`aro average. The limit of the value with Ces\\`aro mean when the horizon tends to infinity is widely studied in the literature. We address the more general question of the existence of a limit when the averaging parameter converges, for values defined with means of general types.\n  We consider a given function and a family of costs defined as the mean of the function with respect to a family of probability measures -- the evaluations -- on R_+. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05238","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":""},"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":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWLMZwRAQejr/ynjz2I465XIn8ygL0uDwJO8S7+jVe9Ubhay7pH8xGdOl64H259+ScPNNxLbAt6spBYkQx15AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:41:17.833521Z"},"content_sha256":"fe2561351b3658afd46622d03273bfa7a5e66712de5814afb46d357116d9fe95","schema_version":"1.0","event_id":"sha256:fe2561351b3658afd46622d03273bfa7a5e66712de5814afb46d357116d9fe95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/bundle.json","state_url":"https://pith.science/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/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":"2026-06-26T14:41:17Z","links":{"resolver":"https://pith.science/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ","bundle":"https://pith.science/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/bundle.json","state":"https://pith.science/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HH5G2WNZJSY2UYSPFRSGBCBERZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HH5G2WNZJSY2UYSPFRSGBCBERZ","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":"c1c0fe40a6234833f5f4dd16bd8cce5e3b80c95531c7aa39d7c6310e7dd33f37","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2015-03-17T22:42:15Z","title_canon_sha256":"f081de02d71f7c2c62053da36d51a8f53f5db7b9b5cf7ff39698d59a55c67b3f"},"schema_version":"1.0","source":{"id":"1503.05238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05238","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05238v1","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05238","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"HH5G2WNZJSY2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HH5G2WNZJSY2UYSP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HH5G2WNZ","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fe2561351b3658afd46622d03273bfa7a5e66712de5814afb46d357116d9fe95","target":"graph","created_at":"2026-05-18T01:19:16Z","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"},"paper":{"abstract_excerpt":"We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\\`aro average. The limit of the value with Ces\\`aro mean when the horizon tends to infinity is widely studied in the literature. We address the more general question of the existence of a limit when the averaging parameter converges, for values defined with means of general types.\n  We consider a given function and a family of costs defined as the mean of the function with respect to a family of probability measures -- the evaluations -- on R_+. We p","authors_text":"J\\'er\\^ome Renault (GREMAQ), Marc Quincampoix (LM-Brest), Xiaoxi Li (IMJ-PRG)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2015-03-17T22:42:15Z","title":"Limit value for optimal control with general means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05238","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":"sha256:2294538c7cc6e0b903b734fdf767e56560621727be09e01fa61768339e90380a","target":"record","created_at":"2026-05-18T01:19:16Z","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":"c1c0fe40a6234833f5f4dd16bd8cce5e3b80c95531c7aa39d7c6310e7dd33f37","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2015-03-17T22:42:15Z","title_canon_sha256":"f081de02d71f7c2c62053da36d51a8f53f5db7b9b5cf7ff39698d59a55c67b3f"},"schema_version":"1.0","source":{"id":"1503.05238","kind":"arxiv","version":1}},"canonical_sha256":"39fa6d59b94cb1aa624f2c646088248e69ca20f58d576d7f7ad050d117823991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39fa6d59b94cb1aa624f2c646088248e69ca20f58d576d7f7ad050d117823991","first_computed_at":"2026-05-18T01:19:16.168720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:16.168720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z3b53n+Ad2GjfnUgVZm0Od8lUn3/zUny0I+aaLlJpdZcQY8SyexeZSLJRAfmG0liT/yTTWkE6Rq4mmKAQM1bAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:16.169240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2294538c7cc6e0b903b734fdf767e56560621727be09e01fa61768339e90380a","sha256:fe2561351b3658afd46622d03273bfa7a5e66712de5814afb46d357116d9fe95"],"state_sha256":"00d48c9297a0d787269b2efb1dbf99b182bb3f7bc779fe817284e92af1d035e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWjbBHNktgYPF5xYU1OgD4gBMF/xyLNVe4E3XkohzYdMFWW7D+TokZsYCfEx9hPPRJZHSBoMNf+Itq8flpDvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:41:17.835514Z","bundle_sha256":"07cace7031ba64dda2414dc348ee4050e709253ede0063a8546bea5bcf457aec"}}