{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SGFU42UKQMF7MSJTQI4PBJ3BLN","short_pith_number":"pith:SGFU42UK","canonical_record":{"source":{"id":"1204.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-09T11:12:08Z","cross_cats_sorted":[],"title_canon_sha256":"cc462a8983f30499108efc194e737c328d3e012ad99b673b0fb8373375571529","abstract_canon_sha256":"93163b4d59eeccb689191d1e0ac97781acba0997827ba70f64c124e2d23dfabb"},"schema_version":"1.0"},"canonical_sha256":"918b4e6a8a830bf649338238f0a7615b4f45b92164fae024dbbdbcdfe0b1fd3d","source":{"kind":"arxiv","id":"1204.1856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1856","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1856v1","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1856","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"SGFU42UKQMF7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SGFU42UKQMF7MSJT","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SGFU42UK","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SGFU42UKQMF7MSJTQI4PBJ3BLN","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-09T11:12:08Z","cross_cats_sorted":[],"title_canon_sha256":"cc462a8983f30499108efc194e737c328d3e012ad99b673b0fb8373375571529","abstract_canon_sha256":"93163b4d59eeccb689191d1e0ac97781acba0997827ba70f64c124e2d23dfabb"},"schema_version":"1.0"},"canonical_sha256":"918b4e6a8a830bf649338238f0a7615b4f45b92164fae024dbbdbcdfe0b1fd3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:14.885572Z","signature_b64":"kNeCUdeNVwDLlqHGS5FzUAyq9tow4MRX4qbdZGaRhO76cQhEw31hgrTJnSeHA5Z4w1TdsD2cU92qrSnPxcBuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"918b4e6a8a830bf649338238f0a7615b4f45b92164fae024dbbdbcdfe0b1fd3d","last_reissued_at":"2026-05-18T03:58:14.885061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:14.885061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1856","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":"2026-05-18T03:58:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9lFMrEn6OmuYMIl+0Xfkj9iNNsY9z1C6yq+XiSgZptcmpqwK4/3SpldOzOZFkbgYXFO1bAW2rBjI90jFX1lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:55:43.934644Z"},"content_sha256":"2ccab1d37b563cf2fd01c14a998e3c4c547a57fe4bedc8b8c9c6d5be40e6d84b","schema_version":"1.0","event_id":"sha256:2ccab1d37b563cf2fd01c14a998e3c4c547a57fe4bedc8b8c9c6d5be40e6d84b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SGFU42UKQMF7MSJTQI4PBJ3BLN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiongmin Yong","submitted_at":"2012-04-09T11:12:08Z","abstract_excerpt":"A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent problem. Under certain conditions, we constructively prove the existence of such an equilibrium control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-perso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1856","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":"2026-05-18T03:58:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2K5MpB0Esmf23jitrM3VXDox2tpgPpjc+BTVZN5Lvr7A8r2Ck83cBuubfdFdd+QhbeN8H3f7knFf1EqbJmoHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:55:43.935070Z"},"content_sha256":"13598f838d94c8cf695c3590e68e4865a9f576b51808a8c33f2a00c8ecb8caf7","schema_version":"1.0","event_id":"sha256:13598f838d94c8cf695c3590e68e4865a9f576b51808a8c33f2a00c8ecb8caf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/bundle.json","state_url":"https://pith.science/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/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":"2026-05-31T03:55:43Z","links":{"resolver":"https://pith.science/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN","bundle":"https://pith.science/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/bundle.json","state":"https://pith.science/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGFU42UKQMF7MSJTQI4PBJ3BLN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SGFU42UKQMF7MSJTQI4PBJ3BLN","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":"93163b4d59eeccb689191d1e0ac97781acba0997827ba70f64c124e2d23dfabb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-09T11:12:08Z","title_canon_sha256":"cc462a8983f30499108efc194e737c328d3e012ad99b673b0fb8373375571529"},"schema_version":"1.0","source":{"id":"1204.1856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1856","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1856v1","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1856","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"SGFU42UKQMF7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SGFU42UKQMF7MSJT","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SGFU42UK","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:13598f838d94c8cf695c3590e68e4865a9f576b51808a8c33f2a00c8ecb8caf7","target":"graph","created_at":"2026-05-18T03:58:14Z","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":"A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent problem. Under certain conditions, we constructively prove the existence of such an equilibrium control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-perso","authors_text":"Jiongmin Yong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-09T11:12:08Z","title":"A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1856","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":"sha256:2ccab1d37b563cf2fd01c14a998e3c4c547a57fe4bedc8b8c9c6d5be40e6d84b","target":"record","created_at":"2026-05-18T03:58:14Z","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":"93163b4d59eeccb689191d1e0ac97781acba0997827ba70f64c124e2d23dfabb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-09T11:12:08Z","title_canon_sha256":"cc462a8983f30499108efc194e737c328d3e012ad99b673b0fb8373375571529"},"schema_version":"1.0","source":{"id":"1204.1856","kind":"arxiv","version":1}},"canonical_sha256":"918b4e6a8a830bf649338238f0a7615b4f45b92164fae024dbbdbcdfe0b1fd3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"918b4e6a8a830bf649338238f0a7615b4f45b92164fae024dbbdbcdfe0b1fd3d","first_computed_at":"2026-05-18T03:58:14.885061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:14.885061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kNeCUdeNVwDLlqHGS5FzUAyq9tow4MRX4qbdZGaRhO76cQhEw31hgrTJnSeHA5Z4w1TdsD2cU92qrSnPxcBuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:14.885572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ccab1d37b563cf2fd01c14a998e3c4c547a57fe4bedc8b8c9c6d5be40e6d84b","sha256:13598f838d94c8cf695c3590e68e4865a9f576b51808a8c33f2a00c8ecb8caf7"],"state_sha256":"b0929a83cb4146159a722dda710562b80fbcdb2026f2cfd108e84a3cc4c8a688"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4gcm188F4MslazOujCr1LogParugnYZF9rwyo0V/42lfzqeRFgstq27mEC4QA3eSZtS3HK7fqWkPsS1G58YCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:55:43.937532Z","bundle_sha256":"cde9915141050704c1c2dd7b7d59f3b7d34aa3fae287acaec0f7fda759d123e8"}}