{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:U5SHVEVYDXVSBLNPITSZQUQTZG","short_pith_number":"pith:U5SHVEVY","canonical_record":{"source":{"id":"2109.10443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-09-21T22:09:32Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"8388e422363d8b70b473c24e11b53468e00c61b8b1f97cfddc8da40e9b13a6df","abstract_canon_sha256":"d9448f13aa224a48ecc57f3a73d4aa1cf80f4dbaf2fff3b269d8c592c5bd315f"},"schema_version":"1.0"},"canonical_sha256":"a7647a92b81deb20adaf44e5985213c98cc6b1c2e4e76916d7b95e01f813b100","source":{"kind":"arxiv","id":"2109.10443","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10443","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10443v2","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10443","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"U5SHVEVYDXVS","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_16","alias_value":"U5SHVEVYDXVSBLNP","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_8","alias_value":"U5SHVEVY","created_at":"2026-07-05T03:49:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:U5SHVEVYDXVSBLNPITSZQUQTZG","target":"record","payload":{"canonical_record":{"source":{"id":"2109.10443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-09-21T22:09:32Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"8388e422363d8b70b473c24e11b53468e00c61b8b1f97cfddc8da40e9b13a6df","abstract_canon_sha256":"d9448f13aa224a48ecc57f3a73d4aa1cf80f4dbaf2fff3b269d8c592c5bd315f"},"schema_version":"1.0"},"canonical_sha256":"a7647a92b81deb20adaf44e5985213c98cc6b1c2e4e76916d7b95e01f813b100","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:42.387577Z","signature_b64":"TPeH4ZrsXMH/oyY3+8eh/9s1XNWIqsPyo/rCYqJTvlNxDnydOzfI14wJ122bg7FDyEkYq1BX5hxMbLJB2Z+XAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7647a92b81deb20adaf44e5985213c98cc6b1c2e4e76916d7b95e01f813b100","last_reissued_at":"2026-07-05T03:49:42.387053Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:42.387053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.10443","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhIv27RQEcAg/jA7J3YRM1LkrCoitsdErQKe2sTNeP/hUW9ZEyN1599VCgWkx5WFW0LRJeQ4x9pUN5PXUI21CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:32:31.830409Z"},"content_sha256":"ea99fbb9595c260c9578e051ccbc957d871256a10fc1548359aae9a4ce377b64","schema_version":"1.0","event_id":"sha256:ea99fbb9595c260c9578e051ccbc957d871256a10fc1548359aae9a4ce377b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:U5SHVEVYDXVSBLNPITSZQUQTZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.RO","authors_text":"Anqi Li, Balakumar Sundaralingam, Bryan Peele, Buck Babich, Byron Boots, Dieter Fox, Iretiayo Akinola, Karl Van Wyk, Mandy Xie, Muhammad Asif Rana, Nathan D. Ratliff, Qian Wan","submitted_at":"2021-09-21T22:09:32Z","abstract_excerpt":"Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical stability guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10443","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.10443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1iuAlt26h5zcMcvqe7Njz4COfAvQVfKlFIgqCdY5fMwGtGIoD6bvZK/JTi2zF9wKa66DBs0xxpYjYv/cHX60DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:32:31.830932Z"},"content_sha256":"d11f9815f7eed016dcf9b2609c045538ccb3da2c44817bdcd4590bd6ffe9901e","schema_version":"1.0","event_id":"sha256:d11f9815f7eed016dcf9b2609c045538ccb3da2c44817bdcd4590bd6ffe9901e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/bundle.json","state_url":"https://pith.science/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/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":"2026-08-05T02:32:31Z","links":{"resolver":"https://pith.science/pith/U5SHVEVYDXVSBLNPITSZQUQTZG","bundle":"https://pith.science/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/bundle.json","state":"https://pith.science/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5SHVEVYDXVSBLNPITSZQUQTZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:U5SHVEVYDXVSBLNPITSZQUQTZG","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":"d9448f13aa224a48ecc57f3a73d4aa1cf80f4dbaf2fff3b269d8c592c5bd315f","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-09-21T22:09:32Z","title_canon_sha256":"8388e422363d8b70b473c24e11b53468e00c61b8b1f97cfddc8da40e9b13a6df"},"schema_version":"1.0","source":{"id":"2109.10443","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10443","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10443v2","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10443","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"U5SHVEVYDXVS","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_16","alias_value":"U5SHVEVYDXVSBLNP","created_at":"2026-07-05T03:49:42Z"},{"alias_kind":"pith_short_8","alias_value":"U5SHVEVY","created_at":"2026-07-05T03:49:42Z"}],"graph_snapshots":[{"event_id":"sha256:d11f9815f7eed016dcf9b2609c045538ccb3da2c44817bdcd4590bd6ffe9901e","target":"graph","created_at":"2026-07-05T03:49:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.10443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical stability guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics","authors_text":"Anqi Li, Balakumar Sundaralingam, Bryan Peele, Buck Babich, Byron Boots, Dieter Fox, Iretiayo Akinola, Karl Van Wyk, Mandy Xie, Muhammad Asif Rana, Nathan D. Ratliff, Qian Wan","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-09-21T22:09:32Z","title":"Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10443","kind":"arxiv","version":2},"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:ea99fbb9595c260c9578e051ccbc957d871256a10fc1548359aae9a4ce377b64","target":"record","created_at":"2026-07-05T03:49:42Z","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":"d9448f13aa224a48ecc57f3a73d4aa1cf80f4dbaf2fff3b269d8c592c5bd315f","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-09-21T22:09:32Z","title_canon_sha256":"8388e422363d8b70b473c24e11b53468e00c61b8b1f97cfddc8da40e9b13a6df"},"schema_version":"1.0","source":{"id":"2109.10443","kind":"arxiv","version":2}},"canonical_sha256":"a7647a92b81deb20adaf44e5985213c98cc6b1c2e4e76916d7b95e01f813b100","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7647a92b81deb20adaf44e5985213c98cc6b1c2e4e76916d7b95e01f813b100","first_computed_at":"2026-07-05T03:49:42.387053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:49:42.387053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPeH4ZrsXMH/oyY3+8eh/9s1XNWIqsPyo/rCYqJTvlNxDnydOzfI14wJ122bg7FDyEkYq1BX5hxMbLJB2Z+XAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:49:42.387577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.10443","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea99fbb9595c260c9578e051ccbc957d871256a10fc1548359aae9a4ce377b64","sha256:d11f9815f7eed016dcf9b2609c045538ccb3da2c44817bdcd4590bd6ffe9901e"],"state_sha256":"5d848127303e7964ec2ec752a112583e0d0526d77b29473b80b53c7dcc4713ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtg3RQ3WDWYfhfh/rGk+euNOih3H5S/baV9OMuyNpMpK2pdvQqhv57X1IMFcoObYtOww0jeOFOJ5QhIm6IrTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:32:31.838454Z","bundle_sha256":"78c81749e49facf227b99b753640c1c868bf721de7a51215af0898794f024396"}}