{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:JEEERJ77TV7HDG4GLRVHQDR4FD","short_pith_number":"pith:JEEERJ77","canonical_record":{"source":{"id":"2209.11869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2022-09-23T21:35:48Z","cross_cats_sorted":["math.DG","math.OC"],"title_canon_sha256":"4dae7bafcdd9b2c911035633b14cba4bf39dc916da193dcc1b27557c32eac4b6","abstract_canon_sha256":"d8204c7cd0e44d8619a617df1b1b89dcdb419f92ce391bf8c1e2ed78719e0c17"},"schema_version":"1.0"},"canonical_sha256":"490848a7ff9d7e719b865c6a780e3c28ed556674a0eb72930e939056c98c1e49","source":{"kind":"arxiv","id":"2209.11869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.11869","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"2209.11869v2","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.11869","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"JEEERJ77TV7H","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_16","alias_value":"JEEERJ77TV7HDG4G","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_8","alias_value":"JEEERJ77","created_at":"2026-07-05T05:55:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:JEEERJ77TV7HDG4GLRVHQDR4FD","target":"record","payload":{"canonical_record":{"source":{"id":"2209.11869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2022-09-23T21:35:48Z","cross_cats_sorted":["math.DG","math.OC"],"title_canon_sha256":"4dae7bafcdd9b2c911035633b14cba4bf39dc916da193dcc1b27557c32eac4b6","abstract_canon_sha256":"d8204c7cd0e44d8619a617df1b1b89dcdb419f92ce391bf8c1e2ed78719e0c17"},"schema_version":"1.0"},"canonical_sha256":"490848a7ff9d7e719b865c6a780e3c28ed556674a0eb72930e939056c98c1e49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:55:11.987583Z","signature_b64":"t6xThGF2ll93AcjjSgOV4oCpl3aF2bzfhuKmXZMbpjmJ6WMLr6sYQByvmwuhkZ7irTtCG3YGdI72giL47gynDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"490848a7ff9d7e719b865c6a780e3c28ed556674a0eb72930e939056c98c1e49","last_reissued_at":"2026-07-05T05:55:11.986999Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:55:11.986999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.11869","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":"2026-07-05T05:55:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oT1MYDknJWftM7lVAN5H8NSgC5AP+hLkdN6aGR5eccbYBC0Hp8aEdPawOYp0GXQeQ/r7DEWqW9HFoU3N+HcUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:54:02.227809Z"},"content_sha256":"d52ee6e2f115e72181f2d7fd4f6a13d82052d8114843bd452ffacce2e48cdf6f","schema_version":"1.0","event_id":"sha256:d52ee6e2f115e72181f2d7fd4f6a13d82052d8114843bd452ffacce2e48cdf6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:JEEERJ77TV7HDG4GLRVHQDR4FD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Role of Symmetry in Constructing Geometric Flat Outputs for Free-Flying Robotic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.OC"],"primary_cat":"cs.RO","authors_text":"Jake Welde, Matthew D. Kvalheim, Vijay Kumar","submitted_at":"2022-09-23T21:35:48Z","abstract_excerpt":"Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the locomotion of many robotic and biological systems. On the other hand, the property of differential flatness has enabled efficient, effective planning and control algorithms for various robotic systems. Yet, a practical means of finding a flat output for an arbitrary robotic system remains an open question. In this work, we demonstrate surprising new connections"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.11869","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/2209.11869/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":"2026-07-05T05:55:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylYA+lI7ov1aSO64SeuZln3xwZ/LaemDfmYKl18jfcHBf6OS3ZhfjbBliDMnivUQeBhgMZpYj2nsg8BAr6OzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:54:02.228227Z"},"content_sha256":"3d5954bdaf28e9cf897332dec65c0969574ec76a6c7d389e8e03fef937221ae2","schema_version":"1.0","event_id":"sha256:3d5954bdaf28e9cf897332dec65c0969574ec76a6c7d389e8e03fef937221ae2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/bundle.json","state_url":"https://pith.science/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/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":"2026-08-05T22:54:02Z","links":{"resolver":"https://pith.science/pith/JEEERJ77TV7HDG4GLRVHQDR4FD","bundle":"https://pith.science/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/bundle.json","state":"https://pith.science/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEEERJ77TV7HDG4GLRVHQDR4FD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JEEERJ77TV7HDG4GLRVHQDR4FD","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":"d8204c7cd0e44d8619a617df1b1b89dcdb419f92ce391bf8c1e2ed78719e0c17","cross_cats_sorted":["math.DG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2022-09-23T21:35:48Z","title_canon_sha256":"4dae7bafcdd9b2c911035633b14cba4bf39dc916da193dcc1b27557c32eac4b6"},"schema_version":"1.0","source":{"id":"2209.11869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.11869","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"2209.11869v2","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.11869","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"JEEERJ77TV7H","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_16","alias_value":"JEEERJ77TV7HDG4G","created_at":"2026-07-05T05:55:11Z"},{"alias_kind":"pith_short_8","alias_value":"JEEERJ77","created_at":"2026-07-05T05:55:11Z"}],"graph_snapshots":[{"event_id":"sha256:3d5954bdaf28e9cf897332dec65c0969574ec76a6c7d389e8e03fef937221ae2","target":"graph","created_at":"2026-07-05T05:55:11Z","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/2209.11869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the locomotion of many robotic and biological systems. On the other hand, the property of differential flatness has enabled efficient, effective planning and control algorithms for various robotic systems. Yet, a practical means of finding a flat output for an arbitrary robotic system remains an open question. In this work, we demonstrate surprising new connections","authors_text":"Jake Welde, Matthew D. Kvalheim, Vijay Kumar","cross_cats":["math.DG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2022-09-23T21:35:48Z","title":"The Role of Symmetry in Constructing Geometric Flat Outputs for Free-Flying Robotic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.11869","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:d52ee6e2f115e72181f2d7fd4f6a13d82052d8114843bd452ffacce2e48cdf6f","target":"record","created_at":"2026-07-05T05:55:11Z","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":"d8204c7cd0e44d8619a617df1b1b89dcdb419f92ce391bf8c1e2ed78719e0c17","cross_cats_sorted":["math.DG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2022-09-23T21:35:48Z","title_canon_sha256":"4dae7bafcdd9b2c911035633b14cba4bf39dc916da193dcc1b27557c32eac4b6"},"schema_version":"1.0","source":{"id":"2209.11869","kind":"arxiv","version":2}},"canonical_sha256":"490848a7ff9d7e719b865c6a780e3c28ed556674a0eb72930e939056c98c1e49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"490848a7ff9d7e719b865c6a780e3c28ed556674a0eb72930e939056c98c1e49","first_computed_at":"2026-07-05T05:55:11.986999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:55:11.986999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6xThGF2ll93AcjjSgOV4oCpl3aF2bzfhuKmXZMbpjmJ6WMLr6sYQByvmwuhkZ7irTtCG3YGdI72giL47gynDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:55:11.987583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.11869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d52ee6e2f115e72181f2d7fd4f6a13d82052d8114843bd452ffacce2e48cdf6f","sha256:3d5954bdaf28e9cf897332dec65c0969574ec76a6c7d389e8e03fef937221ae2"],"state_sha256":"479a07c3ddc92db0c1014e5579faf12a78c287bf6dd457ec45ca2786a4a4bc97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHyGmai+PzpTvh5+5DxzcUr879jFCR+jxAGLMNTfj6TXBvoICyYs/fEq1M1J7x4Tu324Wl06TV0tGtb9GQaxDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T22:54:02.231245Z","bundle_sha256":"0a0cec6d054ce45cd0ad485e3783c1e73e6aa3ae54a74eeebe4754314145a8c6"}}