{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HPVTQKREQ2RZC3J2GPA7B7EH4I","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":"58f25bfe318123a1c6a3febbf992ad18cad5cf7590266fbd4386167f45052a0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-14T13:59:06Z","title_canon_sha256":"8b6d349a3fd30419f84160df3d63bacbd55bf5631b39e232faebd75efe3c5c56"},"schema_version":"1.0","source":{"id":"1201.3013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3013","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3013v1","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3013","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"HPVTQKREQ2RZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HPVTQKREQ2RZC3J2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HPVTQKRE","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:b16aab4aa3403e3bffd781101922e650f582c3365ca150e646aad7938d42193b","target":"graph","created_at":"2026-05-18T04:04:32Z","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 configuration p in r-dimensional Euclidean space is a finite collection of labeled points p^1,p^2,...,p^n in R^r that affinely span R^r. Each configuration p defines a Euclidean distance matrix D_p = (d_ij) = (||p^i-p^j||^2), where ||.|| denotes the Euclidean norm. A fundamental problem in distance geometry is to find out whether or not, a given proper subset of the entries of D_p suffices to uniquely determine the entire matrix D_p. This problem is known as the universal rigidity problem of bar frameworks. In this chapter, we present a unified approach for the universal rigidity of bar fram","authors_text":"A. Y. Alfakih","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-14T13:59:06Z","title":"Universal rigidity of bar frameworks in general position: a Euclidean distance matrix approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3013","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:fd8aa091ab4c64a3a35e2a96cee4e9048ee1ae87e2d31a85b63074ae55f55a04","target":"record","created_at":"2026-05-18T04:04:32Z","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":"58f25bfe318123a1c6a3febbf992ad18cad5cf7590266fbd4386167f45052a0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-14T13:59:06Z","title_canon_sha256":"8b6d349a3fd30419f84160df3d63bacbd55bf5631b39e232faebd75efe3c5c56"},"schema_version":"1.0","source":{"id":"1201.3013","kind":"arxiv","version":1}},"canonical_sha256":"3beb382a2486a3916d3a33c1f0fc87e205ea7b4f02e5acd5d20854c1c496f450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3beb382a2486a3916d3a33c1f0fc87e205ea7b4f02e5acd5d20854c1c496f450","first_computed_at":"2026-05-18T04:04:32.496353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:32.496353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZD92tqQ4p0W3uwOArXejG7oelmrqx34EWBdfYMBF3Ut3HDvATXuhkMcp37D0YrCyz0s6N7Ezv5cHp2gxJF90Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:32.497021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd8aa091ab4c64a3a35e2a96cee4e9048ee1ae87e2d31a85b63074ae55f55a04","sha256:b16aab4aa3403e3bffd781101922e650f582c3365ca150e646aad7938d42193b"],"state_sha256":"1a0c5a2ffa4c6ee4e6eda400ed400547cc6dee8d634f26f1d0dae0a438d1c543"}