{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7UGVJGAYMQMNMNSMVFANYSZJGD","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":"be0cc72dc3f573ebb564c38490fd66bd947d32db896ce3f33e4bbabe3c033e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-07-14T06:16:49Z","title_canon_sha256":"6f84a8719aef59e82da340f24b255d3f08e88a4aa190b358bf1202b00ee90d57"},"schema_version":"1.0","source":{"id":"1607.04005","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04005","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04005v4","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04005","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"7UGVJGAYMQMN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7UGVJGAYMQMNMNSM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7UGVJGAY","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:202f9f2a327b16f028a7ac546a4b0e24dfab6d15cd14c1116a6aa8376775b470","target":"graph","created_at":"2026-05-18T00:52:25Z","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 the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization of a shortest collision-avoiding motion for all initial and final configurations of the robots. The individual paths are composed of at most six (straight or circular-arc) segments, and their total length can be expressed as a simple integral with a closed form solution depending only on the initial and final configuration of the robots. Furthermore, the pat","authors_text":"David Kirkpatrick, Paul Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-07-14T06:16:49Z","title":"Characterizing minimum-length coordinated motions for two discs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04005","kind":"arxiv","version":4},"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":"sha256:1c94e0c90b48e1546cd55a3b1be8a829bb9f37a9998c998595113ea1e31d44af","target":"record","created_at":"2026-05-18T00:52:25Z","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":"be0cc72dc3f573ebb564c38490fd66bd947d32db896ce3f33e4bbabe3c033e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-07-14T06:16:49Z","title_canon_sha256":"6f84a8719aef59e82da340f24b255d3f08e88a4aa190b358bf1202b00ee90d57"},"schema_version":"1.0","source":{"id":"1607.04005","kind":"arxiv","version":4}},"canonical_sha256":"fd0d5498186418d6364ca940dc4b2930f9f7c365007da132a1c479cdaea57606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0d5498186418d6364ca940dc4b2930f9f7c365007da132a1c479cdaea57606","first_computed_at":"2026-05-18T00:52:25.414706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:25.414706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhVL/U1ByLgLm2q0qRQQKhmFC8Ni8rzg9oZRJU8+mmRpIVymVN8M2YG4JRgbqR9BEBVcRYUAgV38JZs2mDPcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:25.415268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04005","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c94e0c90b48e1546cd55a3b1be8a829bb9f37a9998c998595113ea1e31d44af","sha256:202f9f2a327b16f028a7ac546a4b0e24dfab6d15cd14c1116a6aa8376775b470"],"state_sha256":"4383ba33a5c0642fcc405ec1178a9c45c8d1fa93df5791fcf6fe354a471792e1"}