{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WUNRQMJ7I3D5AZABZ62ZSZW57S","short_pith_number":"pith:WUNRQMJ7","canonical_record":{"source":{"id":"1706.01127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-06-04T18:42:19Z","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"title_canon_sha256":"0349479f5f3d78696bc94d7f11ad767b4dc0997cbc2bc44ef4cf0c78c3fc875c","abstract_canon_sha256":"84fa842c32640badd90e5f0f4464e15dac180d0876c89ddcc38710b1b901c7d7"},"schema_version":"1.0"},"canonical_sha256":"b51b18313f46c7d06401cfb59966ddfc8cbb05f49e844ca35e18546e149df0e5","source":{"kind":"arxiv","id":"1706.01127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01127","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01127v1","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01127","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"WUNRQMJ7I3D5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WUNRQMJ7I3D5AZAB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WUNRQMJ7","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WUNRQMJ7I3D5AZABZ62ZSZW57S","target":"record","payload":{"canonical_record":{"source":{"id":"1706.01127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-06-04T18:42:19Z","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"title_canon_sha256":"0349479f5f3d78696bc94d7f11ad767b4dc0997cbc2bc44ef4cf0c78c3fc875c","abstract_canon_sha256":"84fa842c32640badd90e5f0f4464e15dac180d0876c89ddcc38710b1b901c7d7"},"schema_version":"1.0"},"canonical_sha256":"b51b18313f46c7d06401cfb59966ddfc8cbb05f49e844ca35e18546e149df0e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:04.414264Z","signature_b64":"/el5E5pETlP/bKOK8+sv4bZ0UOR0+7PfzaoId+G4an2nDgp3Iloy55kOQPq2cudVLhrdZiEH1IaZgPmeyW+YBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b51b18313f46c7d06401cfb59966ddfc8cbb05f49e844ca35e18546e149df0e5","last_reissued_at":"2026-05-18T00:43:04.413482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:04.413482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.01127","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":"2026-05-18T00:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KvFZV24Z7KCnChtFsNL2Kkg+aNT6XuFKFlu3WrROpADZwN3nX+hWJLPCJMGkDXt1gj8eCiUPJRz8NGZq9mYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:35:33.421158Z"},"content_sha256":"f5123e6b1c5321344ef367d4375d25e14ebf925b139178077d19f3e039dd9ae7","schema_version":"1.0","event_id":"sha256:f5123e6b1c5321344ef367d4375d25e14ebf925b139178077d19f3e039dd9ae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WUNRQMJ7I3D5AZABZ62ZSZW57S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.DS","math.OC"],"primary_cat":"cs.RO","authors_text":"Christine Chevallereau, Jessy W Grizzle","submitted_at":"2017-06-04T18:42:19Z","abstract_excerpt":"Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01127","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":"2026-05-18T00:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iaAp1Z7GvmHQUjxo9aaefMtuprpSLaZaXoLqZm2zoftZc9Cor7cZpfaU6DzD5b3M4+RQ/cszhwTGMqBLXc84Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:35:33.421594Z"},"content_sha256":"6048f381116c1c2fb7a38af94cf825777890114e420c220b56c7b28616e54d9a","schema_version":"1.0","event_id":"sha256:6048f381116c1c2fb7a38af94cf825777890114e420c220b56c7b28616e54d9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/bundle.json","state_url":"https://pith.science/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/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":"2026-05-31T11:35:33Z","links":{"resolver":"https://pith.science/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S","bundle":"https://pith.science/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/bundle.json","state":"https://pith.science/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUNRQMJ7I3D5AZABZ62ZSZW57S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WUNRQMJ7I3D5AZABZ62ZSZW57S","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":"84fa842c32640badd90e5f0f4464e15dac180d0876c89ddcc38710b1b901c7d7","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-06-04T18:42:19Z","title_canon_sha256":"0349479f5f3d78696bc94d7f11ad767b4dc0997cbc2bc44ef4cf0c78c3fc875c"},"schema_version":"1.0","source":{"id":"1706.01127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01127","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01127v1","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01127","created_at":"2026-05-18T00:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"WUNRQMJ7I3D5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WUNRQMJ7I3D5AZAB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WUNRQMJ7","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:6048f381116c1c2fb7a38af94cf825777890114e420c220b56c7b28616e54d9a","target":"graph","created_at":"2026-05-18T00:43:04Z","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":"Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to i","authors_text":"Christine Chevallereau, Jessy W Grizzle","cross_cats":["cs.SY","math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-06-04T18:42:19Z","title":"Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01127","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:f5123e6b1c5321344ef367d4375d25e14ebf925b139178077d19f3e039dd9ae7","target":"record","created_at":"2026-05-18T00:43:04Z","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":"84fa842c32640badd90e5f0f4464e15dac180d0876c89ddcc38710b1b901c7d7","cross_cats_sorted":["cs.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-06-04T18:42:19Z","title_canon_sha256":"0349479f5f3d78696bc94d7f11ad767b4dc0997cbc2bc44ef4cf0c78c3fc875c"},"schema_version":"1.0","source":{"id":"1706.01127","kind":"arxiv","version":1}},"canonical_sha256":"b51b18313f46c7d06401cfb59966ddfc8cbb05f49e844ca35e18546e149df0e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b51b18313f46c7d06401cfb59966ddfc8cbb05f49e844ca35e18546e149df0e5","first_computed_at":"2026-05-18T00:43:04.413482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:04.413482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/el5E5pETlP/bKOK8+sv4bZ0UOR0+7PfzaoId+G4an2nDgp3Iloy55kOQPq2cudVLhrdZiEH1IaZgPmeyW+YBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:04.414264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5123e6b1c5321344ef367d4375d25e14ebf925b139178077d19f3e039dd9ae7","sha256:6048f381116c1c2fb7a38af94cf825777890114e420c220b56c7b28616e54d9a"],"state_sha256":"2adce95c0e4ef28468f04a645dc92063e5298fbca34b4907213bdbc36e106b65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKNEjFZEx9MPtaLU/apQSzoRZCgo22zoXCjWTdRzUU3/ZbFjwGO92cc5gm0Ej7jUgcAzzb+awiOt/mUX9FU7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:35:33.424417Z","bundle_sha256":"089338cbc96cba683aa6ba90041a6729eea652424cbe3c4fccf46e202b5f558f"}}