{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FSOI6NKL2Y4Q6TG3WIVZ43FJHR","short_pith_number":"pith:FSOI6NKL","canonical_record":{"source":{"id":"1502.01265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-04T17:40:11Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"2784523e620044f5d1327a804ebf47a1145852af9b5eec793e767c7c31e79e19","abstract_canon_sha256":"b837f804079e6b7b8b1b48f3051363af966d85a367d46c98325cffc6d6f709ff"},"schema_version":"1.0"},"canonical_sha256":"2c9c8f354bd6390f4cdbb22b9e6ca93c4a29234f3361a14c2efbb7bb108aa659","source":{"kind":"arxiv","id":"1502.01265","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01265","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01265v1","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01265","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"FSOI6NKL2Y4Q","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FSOI6NKL2Y4Q6TG3","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FSOI6NKL","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FSOI6NKL2Y4Q6TG3WIVZ43FJHR","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-04T17:40:11Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"2784523e620044f5d1327a804ebf47a1145852af9b5eec793e767c7c31e79e19","abstract_canon_sha256":"b837f804079e6b7b8b1b48f3051363af966d85a367d46c98325cffc6d6f709ff"},"schema_version":"1.0"},"canonical_sha256":"2c9c8f354bd6390f4cdbb22b9e6ca93c4a29234f3361a14c2efbb7bb108aa659","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:57.650404Z","signature_b64":"URWeJHuExn6qFs86hlUyEUHL/wFrNlIQMAu5lkHPaxDy/wYv+1rR3DcXkxLt6AQ02v4C1yYY+1IzHXDX7r1iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c9c8f354bd6390f4cdbb22b9e6ca93c4a29234f3361a14c2efbb7bb108aa659","last_reissued_at":"2026-05-18T02:27:57.649906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:57.649906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01265","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":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+iSmsxsCefdeWEw0dDYt9zUtijYOwEcrgNxEzilx1xsmaNLrRTErTcdScIjwXw1i0yJEEl+cddQZsqQ2QcgyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:55.863781Z"},"content_sha256":"291ae5223a8ff1475b6d53a80b8f1feac7af852d876288c0a47c97205f6194e7","schema_version":"1.0","event_id":"sha256:291ae5223a8ff1475b6d53a80b8f1feac7af852d876288c0a47c97205f6194e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FSOI6NKL2Y4Q6TG3WIVZ43FJHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal transport over a linear dynamical system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Michele Pavon, Tryphon Georgiou, Yongxin Chen","submitted_at":"2015-02-04T17:40:11Z","abstract_excerpt":"We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01265","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":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIrO7CHel0Uhvc5ZLTJrAgeNBMIbo/iMng90Wxth2RIfil2hZDeA5g2HqKNzlYcRzGP5J8ic2L7juWXzT0SHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:55.864544Z"},"content_sha256":"6c111e4f5e9167cf7397718eda72e73c47ba9d81d3eb9d34144469f15b765ed5","schema_version":"1.0","event_id":"sha256:6c111e4f5e9167cf7397718eda72e73c47ba9d81d3eb9d34144469f15b765ed5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/bundle.json","state_url":"https://pith.science/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/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":"2026-06-09T07:46:55Z","links":{"resolver":"https://pith.science/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR","bundle":"https://pith.science/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/bundle.json","state":"https://pith.science/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSOI6NKL2Y4Q6TG3WIVZ43FJHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FSOI6NKL2Y4Q6TG3WIVZ43FJHR","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":"b837f804079e6b7b8b1b48f3051363af966d85a367d46c98325cffc6d6f709ff","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-04T17:40:11Z","title_canon_sha256":"2784523e620044f5d1327a804ebf47a1145852af9b5eec793e767c7c31e79e19"},"schema_version":"1.0","source":{"id":"1502.01265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01265","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01265v1","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01265","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"FSOI6NKL2Y4Q","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FSOI6NKL2Y4Q6TG3","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FSOI6NKL","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:6c111e4f5e9167cf7397718eda72e73c47ba9d81d3eb9d34144469f15b765ed5","target":"graph","created_at":"2026-05-18T02:27:57Z","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 the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a S","authors_text":"Michele Pavon, Tryphon Georgiou, Yongxin Chen","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-04T17:40:11Z","title":"Optimal transport over a linear dynamical system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01265","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":"sha256:291ae5223a8ff1475b6d53a80b8f1feac7af852d876288c0a47c97205f6194e7","target":"record","created_at":"2026-05-18T02:27:57Z","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":"b837f804079e6b7b8b1b48f3051363af966d85a367d46c98325cffc6d6f709ff","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-04T17:40:11Z","title_canon_sha256":"2784523e620044f5d1327a804ebf47a1145852af9b5eec793e767c7c31e79e19"},"schema_version":"1.0","source":{"id":"1502.01265","kind":"arxiv","version":1}},"canonical_sha256":"2c9c8f354bd6390f4cdbb22b9e6ca93c4a29234f3361a14c2efbb7bb108aa659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c9c8f354bd6390f4cdbb22b9e6ca93c4a29234f3361a14c2efbb7bb108aa659","first_computed_at":"2026-05-18T02:27:57.649906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.649906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"URWeJHuExn6qFs86hlUyEUHL/wFrNlIQMAu5lkHPaxDy/wYv+1rR3DcXkxLt6AQ02v4C1yYY+1IzHXDX7r1iBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.650404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:291ae5223a8ff1475b6d53a80b8f1feac7af852d876288c0a47c97205f6194e7","sha256:6c111e4f5e9167cf7397718eda72e73c47ba9d81d3eb9d34144469f15b765ed5"],"state_sha256":"f299478dff3036958e4c30214624dfc0f86fa37316974ef746f48fb4edb5298a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtH0Ol/dKdaa+0QkgyiioqvSjbukaWPXwM7Kw5gzT4LiZ0Qv7/n2kJIChsBwGvgm3tU/cgfQ4Lym4AnrjbZsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:46:55.868389Z","bundle_sha256":"1b504160b2de08acf08dfd23c7375939e811744c85ab0bdbf642e7b67cf3589b"}}