{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OW642RZE6WOIX47KZNOJR4LBLB","short_pith_number":"pith:OW642RZE","canonical_record":{"source":{"id":"1612.01193","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-04T22:09:35Z","cross_cats_sorted":["cs.SY","math.OC","nlin.CD"],"title_canon_sha256":"8ae051b9c72cc6f6cf5ce2187d37a3b2df79f1c829b066e39d6b865183c97bd8","abstract_canon_sha256":"31c95177d2964a8a758c95412b40b396dbacfa2b4452030c6c950cfbb036cf2b"},"schema_version":"1.0"},"canonical_sha256":"75bdcd4724f59c8bf3eacb5c98f16158586864eb37073bf37867b51ea366c8be","source":{"kind":"arxiv","id":"1612.01193","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01193","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01193v3","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01193","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"OW642RZE6WOI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OW642RZE6WOIX47K","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OW642RZE","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OW642RZE6WOIX47KZNOJR4LBLB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01193","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-04T22:09:35Z","cross_cats_sorted":["cs.SY","math.OC","nlin.CD"],"title_canon_sha256":"8ae051b9c72cc6f6cf5ce2187d37a3b2df79f1c829b066e39d6b865183c97bd8","abstract_canon_sha256":"31c95177d2964a8a758c95412b40b396dbacfa2b4452030c6c950cfbb036cf2b"},"schema_version":"1.0"},"canonical_sha256":"75bdcd4724f59c8bf3eacb5c98f16158586864eb37073bf37867b51ea366c8be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:54.401770Z","signature_b64":"Z//Xl147X3FB2vG9B0NvsndTvrCYrcyC8hjz+kpMdXBLwRuKV8/6ts+cviQCEu0yiUlYWgRBgO89s5e8Wl/aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75bdcd4724f59c8bf3eacb5c98f16158586864eb37073bf37867b51ea366c8be","last_reissued_at":"2026-05-17T23:57:54.401075Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:54.401075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01193","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sAppr6V3ZSptP6KFhe+f2oHVcbRQglBg2FNc2F2hnpg5z6ALBJCGQ3SnaLLCecLKNCUY++6FtzsGGMKWBc5+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:31:24.205593Z"},"content_sha256":"c1e21eeebdab2cfa8e37d75bd190d070d16c7e6daa2144d869c2aec0c6006d94","schema_version":"1.0","event_id":"sha256:c1e21eeebdab2cfa8e37d75bd190d070d16c7e6daa2144d869c2aec0c6006d94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OW642RZE6WOIX47KZNOJR4LBLB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal transport over nonlinear systems via infinitesimal generators on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC","nlin.CD"],"primary_cat":"math.DS","authors_text":"Karthik Elamvazhuthi, Piyush Grover","submitted_at":"2016-12-04T22:09:35Z","abstract_excerpt":"We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a final distribution in prescribed finite time for the case of non-autonomous nonlinear control-affine systems, while minimizing a quadratic control cost. The resulting control law can be used to obtain approximate feedback laws for individual agents in a swarm control application. Using infinitesimal generators, the optimal control problem is reduced to a modifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01193","kind":"arxiv","version":3},"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":"2026-05-17T23:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVsrU+PiyJ7BDdAomtGWSe1jbQqjCLNEb7jasrdb86hIenfqZjhkKlRreMueSOJSffn/tyu8TT3Ut2/SAte6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:31:24.206313Z"},"content_sha256":"86739ef9a2c2c2ea7eb45dd7c781d3eaa760d7e2c698c65626799dac69ea99cd","schema_version":"1.0","event_id":"sha256:86739ef9a2c2c2ea7eb45dd7c781d3eaa760d7e2c698c65626799dac69ea99cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OW642RZE6WOIX47KZNOJR4LBLB/bundle.json","state_url":"https://pith.science/pith/OW642RZE6WOIX47KZNOJR4LBLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OW642RZE6WOIX47KZNOJR4LBLB/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":"2026-06-05T20:31:24Z","links":{"resolver":"https://pith.science/pith/OW642RZE6WOIX47KZNOJR4LBLB","bundle":"https://pith.science/pith/OW642RZE6WOIX47KZNOJR4LBLB/bundle.json","state":"https://pith.science/pith/OW642RZE6WOIX47KZNOJR4LBLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OW642RZE6WOIX47KZNOJR4LBLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OW642RZE6WOIX47KZNOJR4LBLB","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":"31c95177d2964a8a758c95412b40b396dbacfa2b4452030c6c950cfbb036cf2b","cross_cats_sorted":["cs.SY","math.OC","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-04T22:09:35Z","title_canon_sha256":"8ae051b9c72cc6f6cf5ce2187d37a3b2df79f1c829b066e39d6b865183c97bd8"},"schema_version":"1.0","source":{"id":"1612.01193","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01193","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01193v3","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01193","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"OW642RZE6WOI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OW642RZE6WOIX47K","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OW642RZE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:86739ef9a2c2c2ea7eb45dd7c781d3eaa760d7e2c698c65626799dac69ea99cd","target":"graph","created_at":"2026-05-17T23:57:54Z","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 present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a final distribution in prescribed finite time for the case of non-autonomous nonlinear control-affine systems, while minimizing a quadratic control cost. The resulting control law can be used to obtain approximate feedback laws for individual agents in a swarm control application. Using infinitesimal generators, the optimal control problem is reduced to a modifi","authors_text":"Karthik Elamvazhuthi, Piyush Grover","cross_cats":["cs.SY","math.OC","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-04T22:09:35Z","title":"Optimal transport over nonlinear systems via infinitesimal generators on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01193","kind":"arxiv","version":3},"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:c1e21eeebdab2cfa8e37d75bd190d070d16c7e6daa2144d869c2aec0c6006d94","target":"record","created_at":"2026-05-17T23:57:54Z","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":"31c95177d2964a8a758c95412b40b396dbacfa2b4452030c6c950cfbb036cf2b","cross_cats_sorted":["cs.SY","math.OC","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-04T22:09:35Z","title_canon_sha256":"8ae051b9c72cc6f6cf5ce2187d37a3b2df79f1c829b066e39d6b865183c97bd8"},"schema_version":"1.0","source":{"id":"1612.01193","kind":"arxiv","version":3}},"canonical_sha256":"75bdcd4724f59c8bf3eacb5c98f16158586864eb37073bf37867b51ea366c8be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75bdcd4724f59c8bf3eacb5c98f16158586864eb37073bf37867b51ea366c8be","first_computed_at":"2026-05-17T23:57:54.401075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:54.401075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z//Xl147X3FB2vG9B0NvsndTvrCYrcyC8hjz+kpMdXBLwRuKV8/6ts+cviQCEu0yiUlYWgRBgO89s5e8Wl/aAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:54.401770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01193","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e21eeebdab2cfa8e37d75bd190d070d16c7e6daa2144d869c2aec0c6006d94","sha256:86739ef9a2c2c2ea7eb45dd7c781d3eaa760d7e2c698c65626799dac69ea99cd"],"state_sha256":"c195023f908095e316add0a6bf318b9871c6f83047c2ebc53f8b26c047b9811e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWhG9ZEWEX1cvb6GJUYBhg4y/Sknw07wOEf7/IovufMEP3Bnj87HiZvav8kP7n66B5uPfr3vP3WAbc2Ykd0xAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:31:24.210285Z","bundle_sha256":"96ce6f13c6f3629bb2fdbcdd6056c07b23103765313f41ac7ed7a587893e4d49"}}