{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2J5EMQ32VXPVNUO2TR3NS7VZON","short_pith_number":"pith:2J5EMQ32","canonical_record":{"source":{"id":"1407.3421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-07-12T23:54:54Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"7913a25dc12071396d05cf58fbf2e40629de6a514091d51c60c7ceab58c6c7ab","abstract_canon_sha256":"abc6ab9c3cc235571f32a0f585f75d4ece578939d7483ccf1e4e553377aa18dd"},"schema_version":"1.0"},"canonical_sha256":"d27a46437aaddf56d1da9c76d97eb9737cabf04e0b3e1cf127cd25d679907004","source":{"kind":"arxiv","id":"1407.3421","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3421","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3421v1","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3421","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"2J5EMQ32VXPV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2J5EMQ32VXPVNUO2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2J5EMQ32","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2J5EMQ32VXPVNUO2TR3NS7VZON","target":"record","payload":{"canonical_record":{"source":{"id":"1407.3421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-07-12T23:54:54Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"7913a25dc12071396d05cf58fbf2e40629de6a514091d51c60c7ceab58c6c7ab","abstract_canon_sha256":"abc6ab9c3cc235571f32a0f585f75d4ece578939d7483ccf1e4e553377aa18dd"},"schema_version":"1.0"},"canonical_sha256":"d27a46437aaddf56d1da9c76d97eb9737cabf04e0b3e1cf127cd25d679907004","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:42.938667Z","signature_b64":"sPzSjBTpMUkDoXNPBmCjAQzBj1whcVKbaCfq6n92kqIm9U5QYaeSvwvZXwYwioiK/zYTuJvh9KQOWsiYFaorAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d27a46437aaddf56d1da9c76d97eb9737cabf04e0b3e1cf127cd25d679907004","last_reissued_at":"2026-05-18T02:47:42.937886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:42.937886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.3421","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":"2026-05-18T02:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opoTaofCyBct9NlacDampHGgiaTCinqrbkDHdHXbF2PUTLwnZPYwyho8J6DNRpUTPNi8Xcep+U+KXQu/bHdBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:38:44.113053Z"},"content_sha256":"c417b88808e819a578b0369909ddd5c023e26fb934261956bb72689dce6cac94","schema_version":"1.0","event_id":"sha256:c417b88808e819a578b0369909ddd5c023e26fb934261956bb72689dce6cac94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2J5EMQ32VXPVNUO2TR3NS7VZON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic bridges of linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cs.SY","authors_text":"Tryphon Georgiou, Yongxin Chen","submitted_at":"2014-07-12T23:54:54Z","abstract_excerpt":"We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed to have known states at the boundary. Thus, the movement of the particles can be modeled as an Ornstein-Uhlenbeck process conditioned on position and velocity measurements at the two end-points. It is shown that optimal stochastic control provides a stochastic differential equation (SDE) that generates such a bridge as a degenerate diffusion process. Genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3421","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":"2026-05-18T02:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjVwXIUlVryf2fYkfQTPFZdcXf+MpjscrEEy2Y8IduqWdiep0iArje3xLZbZYTqPfimIgvV/liFLpBezMeKACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:38:44.113428Z"},"content_sha256":"166ccf3123520a153f116a0dd7d65031e89b2ad6bf5174378c629ff164e2dc11","schema_version":"1.0","event_id":"sha256:166ccf3123520a153f116a0dd7d65031e89b2ad6bf5174378c629ff164e2dc11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/bundle.json","state_url":"https://pith.science/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/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":"2026-06-09T09:38:44Z","links":{"resolver":"https://pith.science/pith/2J5EMQ32VXPVNUO2TR3NS7VZON","bundle":"https://pith.science/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/bundle.json","state":"https://pith.science/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2J5EMQ32VXPVNUO2TR3NS7VZON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2J5EMQ32VXPVNUO2TR3NS7VZON","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":"abc6ab9c3cc235571f32a0f585f75d4ece578939d7483ccf1e4e553377aa18dd","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-07-12T23:54:54Z","title_canon_sha256":"7913a25dc12071396d05cf58fbf2e40629de6a514091d51c60c7ceab58c6c7ab"},"schema_version":"1.0","source":{"id":"1407.3421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3421","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3421v1","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3421","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"2J5EMQ32VXPV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2J5EMQ32VXPVNUO2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2J5EMQ32","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:166ccf3123520a153f116a0dd7d65031e89b2ad6bf5174378c629ff164e2dc11","target":"graph","created_at":"2026-05-18T02:47:42Z","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 study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed to have known states at the boundary. Thus, the movement of the particles can be modeled as an Ornstein-Uhlenbeck process conditioned on position and velocity measurements at the two end-points. It is shown that optimal stochastic control provides a stochastic differential equation (SDE) that generates such a bridge as a degenerate diffusion process. Genera","authors_text":"Tryphon Georgiou, Yongxin Chen","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-07-12T23:54:54Z","title":"Stochastic bridges of linear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3421","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:c417b88808e819a578b0369909ddd5c023e26fb934261956bb72689dce6cac94","target":"record","created_at":"2026-05-18T02:47:42Z","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":"abc6ab9c3cc235571f32a0f585f75d4ece578939d7483ccf1e4e553377aa18dd","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-07-12T23:54:54Z","title_canon_sha256":"7913a25dc12071396d05cf58fbf2e40629de6a514091d51c60c7ceab58c6c7ab"},"schema_version":"1.0","source":{"id":"1407.3421","kind":"arxiv","version":1}},"canonical_sha256":"d27a46437aaddf56d1da9c76d97eb9737cabf04e0b3e1cf127cd25d679907004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d27a46437aaddf56d1da9c76d97eb9737cabf04e0b3e1cf127cd25d679907004","first_computed_at":"2026-05-18T02:47:42.937886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:42.937886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sPzSjBTpMUkDoXNPBmCjAQzBj1whcVKbaCfq6n92kqIm9U5QYaeSvwvZXwYwioiK/zYTuJvh9KQOWsiYFaorAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:42.938667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c417b88808e819a578b0369909ddd5c023e26fb934261956bb72689dce6cac94","sha256:166ccf3123520a153f116a0dd7d65031e89b2ad6bf5174378c629ff164e2dc11"],"state_sha256":"00ea9f58010c05cb783f6cda916c5c68e9ec33b9fbae11849fe88b436ca84676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pWf+WDz0Zm87/DY1awQS7AtH2iU3LqFVOmLjRQei8pgzRyRtrmfMyQalejxyo5NIQ3LPBQZ91tPOuyCFOJtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:38:44.115370Z","bundle_sha256":"fb89894cfe888d6a63c92d01f5c22bb1df9a890f5327ef60fe82b7b6fee1f538"}}