{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EEBN5OXWFO4GXZI7H7YN2LJ756","short_pith_number":"pith:EEBN5OXW","schema_version":"1.0","canonical_sha256":"2102debaf62bb86be51f3ff0dd2d3fefa7d75408a2e6d2f266e108dcdb84639f","source":{"kind":"arxiv","id":"1604.07475","version":4},"attestation_state":"computed","paper":{"title":"Generically globally rigid graphs have generic universally rigid frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Louis Theran, Robert Connelly, Steven J. Gortler","submitted_at":"2016-04-25T23:30:43Z","abstract_excerpt":"We show that any graph that is generically globally rigid in $\\mathbb{R}^d$ has a realization in $\\mathbb{R}^d$ that is both generic and universally rigid. This also implies that the graph also must have a realization in $\\mathbb{R}^d$ that is both infinitesimally rigid and universally rigid; such a realization serves as a certificate of generic global rigidity.\n  Our approach involves an algorithm by Lov\\'asz, Saks and Schrijver that, for a sufficiently connected graph, constructs a general position orthogonal representation of the vertices, and a result of Alfakih that shows how this represe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.07475","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-04-25T23:30:43Z","cross_cats_sorted":[],"title_canon_sha256":"1d1360b658c7323a3b3ccd2bd411dcb2d38593c48bdb59f757cce4fd92a43ee8","abstract_canon_sha256":"ba1a626ddf006d0b31880e226ada79c04b18e44dc941ced9df279d722ebd5a62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:16.361331Z","signature_b64":"6xBQ4i9fTh1BbydKKe5mmlrvk4ZHdgolGM0pvQw8jDdpc5ZLmga2PXu5kM/nnothefIdWFXq0n2bRLX9dkThCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2102debaf62bb86be51f3ff0dd2d3fefa7d75408a2e6d2f266e108dcdb84639f","last_reissued_at":"2026-05-18T00:08:16.360889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:16.360889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generically globally rigid graphs have generic universally rigid frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Louis Theran, Robert Connelly, Steven J. Gortler","submitted_at":"2016-04-25T23:30:43Z","abstract_excerpt":"We show that any graph that is generically globally rigid in $\\mathbb{R}^d$ has a realization in $\\mathbb{R}^d$ that is both generic and universally rigid. This also implies that the graph also must have a realization in $\\mathbb{R}^d$ that is both infinitesimally rigid and universally rigid; such a realization serves as a certificate of generic global rigidity.\n  Our approach involves an algorithm by Lov\\'asz, Saks and Schrijver that, for a sufficiently connected graph, constructs a general position orthogonal representation of the vertices, and a result of Alfakih that shows how this represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07475","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.07475","created_at":"2026-05-18T00:08:16.360952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07475v4","created_at":"2026-05-18T00:08:16.360952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07475","created_at":"2026-05-18T00:08:16.360952+00:00"},{"alias_kind":"pith_short_12","alias_value":"EEBN5OXWFO4G","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EEBN5OXWFO4GXZI7","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EEBN5OXW","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756","json":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756.json","graph_json":"https://pith.science/api/pith-number/EEBN5OXWFO4GXZI7H7YN2LJ756/graph.json","events_json":"https://pith.science/api/pith-number/EEBN5OXWFO4GXZI7H7YN2LJ756/events.json","paper":"https://pith.science/paper/EEBN5OXW"},"agent_actions":{"view_html":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756","download_json":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756.json","view_paper":"https://pith.science/paper/EEBN5OXW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07475&json=true","fetch_graph":"https://pith.science/api/pith-number/EEBN5OXWFO4GXZI7H7YN2LJ756/graph.json","fetch_events":"https://pith.science/api/pith-number/EEBN5OXWFO4GXZI7H7YN2LJ756/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756/action/storage_attestation","attest_author":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756/action/author_attestation","sign_citation":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756/action/citation_signature","submit_replication":"https://pith.science/pith/EEBN5OXWFO4GXZI7H7YN2LJ756/action/replication_record"}},"created_at":"2026-05-18T00:08:16.360952+00:00","updated_at":"2026-05-18T00:08:16.360952+00:00"}