{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YEROURRNBYY32ELW446TNMU6RT","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":"d4f1eccdfc4835aafe494635f78ae92a33dda14f08308a5404e9a1d3f0928e3f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-16T16:25:54Z","title_canon_sha256":"0fe4e34257d10506e88c8e2719b145e5b1c365feab52f7c52a60ef8dd2d77d1f"},"schema_version":"1.0","source":{"id":"1407.4675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4675","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4675v2","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4675","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"YEROURRNBYY3","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YEROURRNBYY32ELW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YEROURRN","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:e4e7ae80976d827980a7795a7b09d9bb70a02c5b24df38b687110243f226c41b","target":"graph","created_at":"2026-05-18T01:13:45Z","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":"A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if every continuous motion of the points and lines which preserves the constraints results in a point-line framework which can be obtained from the initial framework by a translation or a rotation. We characterise when a generic point-line framework is rigid. Our characterisation gives rise to a polynomial algorithm for solving this decision problem.","authors_text":"Bill Jackson, J. C. Owen","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-16T16:25:54Z","title":"A characterisation of the generic rigidity of 2-dimensional point-line frameworks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4675","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:e1b450fa81cc478d4b70b5abd14517f75e6b3749883fc3fb0d4e6ad06012c3aa","target":"record","created_at":"2026-05-18T01:13:45Z","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":"d4f1eccdfc4835aafe494635f78ae92a33dda14f08308a5404e9a1d3f0928e3f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-16T16:25:54Z","title_canon_sha256":"0fe4e34257d10506e88c8e2719b145e5b1c365feab52f7c52a60ef8dd2d77d1f"},"schema_version":"1.0","source":{"id":"1407.4675","kind":"arxiv","version":2}},"canonical_sha256":"c122ea462d0e31bd1176e73d36b29e8ce3f89a859c30298691789abeb648b19f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c122ea462d0e31bd1176e73d36b29e8ce3f89a859c30298691789abeb648b19f","first_computed_at":"2026-05-18T01:13:45.076262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:45.076262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+wxskOBovzfpaLWufVqhFFiepSEWAobIjW7s/sCc6KVdTr6nXuu/pkySojjnbC4jvRE3sh+As+MPNPi274edCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:45.076859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1b450fa81cc478d4b70b5abd14517f75e6b3749883fc3fb0d4e6ad06012c3aa","sha256:e4e7ae80976d827980a7795a7b09d9bb70a02c5b24df38b687110243f226c41b"],"state_sha256":"b927208ff71fd00be314bdbfe360f1c667905166baf848087fb7a90aaa2f0b46"}