{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:43CNF3J6NNL65SC3XCBYIXRK7E","short_pith_number":"pith:43CNF3J6","canonical_record":{"source":{"id":"1511.08922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-28T19:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"80594537e331644fbffc0de9e1e0b119e20ab7d53118d9f093337655c5deff61","abstract_canon_sha256":"2136f7a49e647cac9387160aa9771ffc29e3b110af5eb52cf0a36aca9073b8bb"},"schema_version":"1.0"},"canonical_sha256":"e6c4d2ed3e6b57eec85bb883845e2af91e34a69c9798c013c84565894ff4657e","source":{"kind":"arxiv","id":"1511.08922","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08922","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08922v1","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08922","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"43CNF3J6NNL6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"43CNF3J6NNL65SC3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"43CNF3J6","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:43CNF3J6NNL65SC3XCBYIXRK7E","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-28T19:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"80594537e331644fbffc0de9e1e0b119e20ab7d53118d9f093337655c5deff61","abstract_canon_sha256":"2136f7a49e647cac9387160aa9771ffc29e3b110af5eb52cf0a36aca9073b8bb"},"schema_version":"1.0"},"canonical_sha256":"e6c4d2ed3e6b57eec85bb883845e2af91e34a69c9798c013c84565894ff4657e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:46.104259Z","signature_b64":"H9+K/fZ443M1jYIl081ADoNId2y1JlegZab0wvm1ndu5W4MC973pAluj3Ykm+hA8y31TRktmmMBQZN3AFhNdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6c4d2ed3e6b57eec85bb883845e2af91e34a69c9798c013c84565894ff4657e","last_reissued_at":"2026-05-18T01:25:46.103799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:46.103799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08922","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":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yie+1MJs9cHJP5dpnDxzso5g5Bc04Vaq7Qe2TrcVB6HvfrY5O0Q/mMC48pLT6NirsIBbjrNGU4l3dpc3TFw3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:41:00.895470Z"},"content_sha256":"597b1dff35c059aba4cbec39126a476820185412e5ccefec02cab256a3cb5497","schema_version":"1.0","event_id":"sha256:597b1dff35c059aba4cbec39126a476820185412e5ccefec02cab256a3cb5497"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:43CNF3J6NNL65SC3XCBYIXRK7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control of a perturbed sweeping process via discrete discrete approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Tan H. Cao","submitted_at":"2015-11-28T19:33:51Z","abstract_excerpt":"The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled \"play and stop\" operator with separately controlled perturbations. This problem can be reduced to dynamic optimization of a state-constrained unbounded differential inclusion with highly irregular data that cannot be treated by means of known results in optimal control theory for differential inclusions. We develop the method of discrete approximations, which allows us to adequately replace the original optimal control problem by a sequence of well-p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08922","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":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFURYgkICo7/oKp5KIRI88qqErQ9Vk+I9KGHtGGEmUHmxmkdKEDZgDdrI90YspM4LDjF+ChUHLA/oCKLFpqdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:41:00.895876Z"},"content_sha256":"dcf9399e44a11ca080adfee0b663f87c320e643702f3bbbdfc103fa25bfa638d","schema_version":"1.0","event_id":"sha256:dcf9399e44a11ca080adfee0b663f87c320e643702f3bbbdfc103fa25bfa638d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/43CNF3J6NNL65SC3XCBYIXRK7E/bundle.json","state_url":"https://pith.science/pith/43CNF3J6NNL65SC3XCBYIXRK7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/43CNF3J6NNL65SC3XCBYIXRK7E/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":"2026-05-26T09:41:00Z","links":{"resolver":"https://pith.science/pith/43CNF3J6NNL65SC3XCBYIXRK7E","bundle":"https://pith.science/pith/43CNF3J6NNL65SC3XCBYIXRK7E/bundle.json","state":"https://pith.science/pith/43CNF3J6NNL65SC3XCBYIXRK7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/43CNF3J6NNL65SC3XCBYIXRK7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:43CNF3J6NNL65SC3XCBYIXRK7E","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":"2136f7a49e647cac9387160aa9771ffc29e3b110af5eb52cf0a36aca9073b8bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-28T19:33:51Z","title_canon_sha256":"80594537e331644fbffc0de9e1e0b119e20ab7d53118d9f093337655c5deff61"},"schema_version":"1.0","source":{"id":"1511.08922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08922","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08922v1","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08922","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"43CNF3J6NNL6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"43CNF3J6NNL65SC3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"43CNF3J6","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:dcf9399e44a11ca080adfee0b663f87c320e643702f3bbbdfc103fa25bfa638d","target":"graph","created_at":"2026-05-18T01:25:46Z","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":"The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled \"play and stop\" operator with separately controlled perturbations. This problem can be reduced to dynamic optimization of a state-constrained unbounded differential inclusion with highly irregular data that cannot be treated by means of known results in optimal control theory for differential inclusions. We develop the method of discrete approximations, which allows us to adequately replace the original optimal control problem by a sequence of well-p","authors_text":"Boris S. Mordukhovich, Tan H. Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-28T19:33:51Z","title":"Optimal control of a perturbed sweeping process via discrete discrete approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08922","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":"sha256:597b1dff35c059aba4cbec39126a476820185412e5ccefec02cab256a3cb5497","target":"record","created_at":"2026-05-18T01:25:46Z","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":"2136f7a49e647cac9387160aa9771ffc29e3b110af5eb52cf0a36aca9073b8bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-28T19:33:51Z","title_canon_sha256":"80594537e331644fbffc0de9e1e0b119e20ab7d53118d9f093337655c5deff61"},"schema_version":"1.0","source":{"id":"1511.08922","kind":"arxiv","version":1}},"canonical_sha256":"e6c4d2ed3e6b57eec85bb883845e2af91e34a69c9798c013c84565894ff4657e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6c4d2ed3e6b57eec85bb883845e2af91e34a69c9798c013c84565894ff4657e","first_computed_at":"2026-05-18T01:25:46.103799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:46.103799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9+K/fZ443M1jYIl081ADoNId2y1JlegZab0wvm1ndu5W4MC973pAluj3Ykm+hA8y31TRktmmMBQZN3AFhNdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:46.104259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:597b1dff35c059aba4cbec39126a476820185412e5ccefec02cab256a3cb5497","sha256:dcf9399e44a11ca080adfee0b663f87c320e643702f3bbbdfc103fa25bfa638d"],"state_sha256":"c2cb8a4182dbc4da010215fb6c921bbcdfe4b7230b13f9038e622eefd1547f00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQZlS0oZKcFZ/HzCRHItmgOjruciMmqs/Z4QQNn2Um1wL449Vpy+k46qe+EeBVDLTZCnS32VtfPC3Aso/hORAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:41:00.898789Z","bundle_sha256":"18a0e0c0ab3f399a82bf6b0c0b58b19774585b0dfd5d2dcf469dd4c5a15459a5"}}