{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IAL5HKLJZA35CRIFCHSSMPIZQH","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":"7453cb39e3b4552f25799969edc1f0a52d8cfb8196286a0f3bb0670433beb553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-06-23T17:32:53Z","title_canon_sha256":"33e1d5afb68e3c0b0573beb137c91da76c0dee340491b4d8544c34176bc82590"},"schema_version":"1.0","source":{"id":"1406.5996","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5996","created_at":"2026-05-18T01:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5996v2","created_at":"2026-05-18T01:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5996","created_at":"2026-05-18T01:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"IAL5HKLJZA35","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IAL5HKLJZA35CRIF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IAL5HKLJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:cea4d04fa919f6aa85aaf57a81537f3a6127ccb588b2bb8c6cb5df4eca85e1a8","target":"graph","created_at":"2026-05-18T01:42:51Z","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":"In 2005, Bob Connelly showed that a generic framework in $\\bR^d$ is globally rigid if it has a stress matrix of maximum possible rank, and that this sufficient condition for generic global rigidity is preserved by the 1-extension operation. His results gave a key step in the characterisation of generic global rigidity in the plane. We extend these results to frameworks on surfaces in $\\bR^3$. For a framework on a family of concentric cylinders, cones or ellipsoids, we show that there is a natural surface stress matrix arising from assigning edge and vertex weights to the framework, in equilibr","authors_text":"Anthony Nixon, Bill Jackson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-06-23T17:32:53Z","title":"Stress matrices and global rigidity of frameworks on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5996","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":"sha256:44fe3879f5841a0ab31e8faa4559139187f8e630192f1a033af48e3caafbcc2c","target":"record","created_at":"2026-05-18T01:42:51Z","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":"7453cb39e3b4552f25799969edc1f0a52d8cfb8196286a0f3bb0670433beb553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-06-23T17:32:53Z","title_canon_sha256":"33e1d5afb68e3c0b0573beb137c91da76c0dee340491b4d8544c34176bc82590"},"schema_version":"1.0","source":{"id":"1406.5996","kind":"arxiv","version":2}},"canonical_sha256":"4017d3a969c837d1450511e5263d1981f43fbf31e1d6b04ce0613f44973a4f61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4017d3a969c837d1450511e5263d1981f43fbf31e1d6b04ce0613f44973a4f61","first_computed_at":"2026-05-18T01:42:51.443731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:51.443731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIpwHvlCI8XFTaRkLaEBYU0ALJlUGsIHT/Sd47+GZV+VySiL9/P+C+eqnuu22oEx/zD1mp32DteaR+RmCYT2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:51.444479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5996","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44fe3879f5841a0ab31e8faa4559139187f8e630192f1a033af48e3caafbcc2c","sha256:cea4d04fa919f6aa85aaf57a81537f3a6127ccb588b2bb8c6cb5df4eca85e1a8"],"state_sha256":"ff49a33af7fd8d163a8f1b0e24ada46bcba453d38baddccd418c64766fa315f9"}