{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4VWOB36JJ52NFGLRALXUXFGL3Y","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":"79af0152f674f277ae13f7edeae41bfe9bc654644ad9d5f103823b5b2f6aef22","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-07-04T00:00:04Z","title_canon_sha256":"8c1c194ea328b69e92fa138074c0beb092591618650e131e225a418bea726d23"},"schema_version":"1.0","source":{"id":"1607.00703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00703","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00703v1","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00703","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"4VWOB36JJ52N","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4VWOB36JJ52NFGLR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4VWOB36J","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:fd39d8877001cbd16e6dffe071f46da1870bfe1a555636561fd413f82a1ac0c8","target":"graph","created_at":"2026-05-17T23:56:56Z","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 introduce a variant of Farber's topological complexity, defined for smooth compact orientable Riemannian manifolds, which takes into account only motion planners with the lowest possible \"average length\" of the output paths. We prove that it never differs from topological complexity by more than $1$, thus showing that the latter invariant addresses the problem of the existence of motion planners which are \"efficient\".","authors_text":"Jos\\'e Carrasquel, Zbigniew B{\\l}aszczyk","cross_cats":["math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-07-04T00:00:04Z","title":"Topological complexity and efficiency of motion planning algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00703","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:d9a4f861f9d8960f4d7f7a2d72036ab29b3636fb75f19b30782d22174d43f6af","target":"record","created_at":"2026-05-17T23:56:56Z","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":"79af0152f674f277ae13f7edeae41bfe9bc654644ad9d5f103823b5b2f6aef22","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-07-04T00:00:04Z","title_canon_sha256":"8c1c194ea328b69e92fa138074c0beb092591618650e131e225a418bea726d23"},"schema_version":"1.0","source":{"id":"1607.00703","kind":"arxiv","version":1}},"canonical_sha256":"e56ce0efc94f74d2997102ef4b94cbde16e292c99e20e08fb79d7fadcb1c6060","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e56ce0efc94f74d2997102ef4b94cbde16e292c99e20e08fb79d7fadcb1c6060","first_computed_at":"2026-05-17T23:56:56.153167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:56.153167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmKn13HcrUhfyjoc2otAEtMIJyLrIeKDISvPDeWdjxShQlMH2m2079be1fOLvjwOWP1AxUmbf3URPGrbFMAnDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:56.153903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9a4f861f9d8960f4d7f7a2d72036ab29b3636fb75f19b30782d22174d43f6af","sha256:fd39d8877001cbd16e6dffe071f46da1870bfe1a555636561fd413f82a1ac0c8"],"state_sha256":"600e9cbc2fc609681d0ecbf3e7297915468289ba8ce434287ce9aee2167f44d6"}