{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MDPO6FGLI722E5BRGR6YISFSVX","short_pith_number":"pith:MDPO6FGL","canonical_record":{"source":{"id":"1407.1775","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T17:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"edf82e3a9648bf7fbe0338425c0b488d158cbaf0681717014d80db7fa7fc09c7","abstract_canon_sha256":"6de506f456cc2765a95dc108e97065bb5b2f0db684b17e49297eb567a0eead38"},"schema_version":"1.0"},"canonical_sha256":"60deef14cb47f5a27431347d8448b2add051e49a76a66208dc5ca787db5517cb","source":{"kind":"arxiv","id":"1407.1775","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1775","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1775v3","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1775","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"MDPO6FGLI722","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MDPO6FGLI722E5BR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MDPO6FGL","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MDPO6FGLI722E5BRGR6YISFSVX","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1775","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T17:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"edf82e3a9648bf7fbe0338425c0b488d158cbaf0681717014d80db7fa7fc09c7","abstract_canon_sha256":"6de506f456cc2765a95dc108e97065bb5b2f0db684b17e49297eb567a0eead38"},"schema_version":"1.0"},"canonical_sha256":"60deef14cb47f5a27431347d8448b2add051e49a76a66208dc5ca787db5517cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:13.644482Z","signature_b64":"zexjbNJsi2Nv94JHDWHNCFReZDVlNo60dchnsiv7OU9gZYmjMdhcwZOorVJWXEPdGBVvYROasDf6+nY44+KaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60deef14cb47f5a27431347d8448b2add051e49a76a66208dc5ca787db5517cb","last_reissued_at":"2026-05-18T02:18:13.644079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:13.644079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1775","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":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RxejkCHrn9A4xWvg0daPnHQ2oKglfFFUeKjM7FGntLenrNDRR7dLLZkATa6n5v1N6ShAt97wXaaC24NfCuECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:30:59.577663Z"},"content_sha256":"55cc83ded648fb375891e9d93b5937b2696d4c1d0af88835f73a1f0b3b5c0b71","schema_version":"1.0","event_id":"sha256:55cc83ded648fb375891e9d93b5937b2696d4c1d0af88835f73a1f0b3b5c0b71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MDPO6FGLI722E5BRGR6YISFSVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel E. Koditschek, Samuel A. Burden, Shai Revzen, S. Shankar Sastry","submitted_at":"2014-07-07T17:14:51Z","abstract_excerpt":"We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few domains of application. Under the conditions that (i) the vector field's discontinuities are locally confined to a finite number of smooth submanifolds and (ii) the vector field is transverse to these surfaces in an appropriate sense, we show that the vector field yields a well-defined flow that is Lipschitz continuous and piecewise-differentiable. This implies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1775","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":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GfNzJrlorTT7exOW+DZiOyPzkUT4Uj7hczUHXqesHBN9XrKwUfVsimVcGOA5rNcGdLToL7FHVPqJp7JAu/HJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:30:59.578152Z"},"content_sha256":"26f9218d330b0c80bdc738b39a15c5a9f012ebe96c7c6a71fd4829cd2bd64775","schema_version":"1.0","event_id":"sha256:26f9218d330b0c80bdc738b39a15c5a9f012ebe96c7c6a71fd4829cd2bd64775"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDPO6FGLI722E5BRGR6YISFSVX/bundle.json","state_url":"https://pith.science/pith/MDPO6FGLI722E5BRGR6YISFSVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDPO6FGLI722E5BRGR6YISFSVX/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":"2026-08-16T01:30:59Z","links":{"resolver":"https://pith.science/pith/MDPO6FGLI722E5BRGR6YISFSVX","bundle":"https://pith.science/pith/MDPO6FGLI722E5BRGR6YISFSVX/bundle.json","state":"https://pith.science/pith/MDPO6FGLI722E5BRGR6YISFSVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDPO6FGLI722E5BRGR6YISFSVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MDPO6FGLI722E5BRGR6YISFSVX","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":"6de506f456cc2765a95dc108e97065bb5b2f0db684b17e49297eb567a0eead38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T17:14:51Z","title_canon_sha256":"edf82e3a9648bf7fbe0338425c0b488d158cbaf0681717014d80db7fa7fc09c7"},"schema_version":"1.0","source":{"id":"1407.1775","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1775","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1775v3","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1775","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"MDPO6FGLI722","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MDPO6FGLI722E5BR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MDPO6FGL","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:26f9218d330b0c80bdc738b39a15c5a9f012ebe96c7c6a71fd4829cd2bd64775","target":"graph","created_at":"2026-05-18T02:18:13Z","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 class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few domains of application. Under the conditions that (i) the vector field's discontinuities are locally confined to a finite number of smooth submanifolds and (ii) the vector field is transverse to these surfaces in an appropriate sense, we show that the vector field yields a well-defined flow that is Lipschitz continuous and piecewise-differentiable. This implies","authors_text":"Daniel E. Koditschek, Samuel A. Burden, Shai Revzen, S. Shankar Sastry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T17:14:51Z","title":"Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1775","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":"sha256:55cc83ded648fb375891e9d93b5937b2696d4c1d0af88835f73a1f0b3b5c0b71","target":"record","created_at":"2026-05-18T02:18:13Z","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":"6de506f456cc2765a95dc108e97065bb5b2f0db684b17e49297eb567a0eead38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T17:14:51Z","title_canon_sha256":"edf82e3a9648bf7fbe0338425c0b488d158cbaf0681717014d80db7fa7fc09c7"},"schema_version":"1.0","source":{"id":"1407.1775","kind":"arxiv","version":3}},"canonical_sha256":"60deef14cb47f5a27431347d8448b2add051e49a76a66208dc5ca787db5517cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60deef14cb47f5a27431347d8448b2add051e49a76a66208dc5ca787db5517cb","first_computed_at":"2026-05-18T02:18:13.644079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:13.644079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zexjbNJsi2Nv94JHDWHNCFReZDVlNo60dchnsiv7OU9gZYmjMdhcwZOorVJWXEPdGBVvYROasDf6+nY44+KaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:13.644482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1775","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55cc83ded648fb375891e9d93b5937b2696d4c1d0af88835f73a1f0b3b5c0b71","sha256:26f9218d330b0c80bdc738b39a15c5a9f012ebe96c7c6a71fd4829cd2bd64775"],"state_sha256":"213ccb5c53b1f731edeaafe9b14268a7381e0c53ffb8b22ea959675c22ac57a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYvJvDyxHDDMYUrHpugLX4V9TtlYGV1XnaQnsCsvC6yEj7O/jMo37Js1i0TqE9XIN9HHXoT1YZJnp9ISrWQ/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:30:59.585408Z","bundle_sha256":"7819249fadfe58f53cfd46bc796f1563b30d759d37cf58062c9bf4f4ced06733"}}