{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QW3S4DRJ6U6MSNWXJC5MTMQUTP","short_pith_number":"pith:QW3S4DRJ","schema_version":"1.0","canonical_sha256":"85b72e0e29f53cc936d748bac9b2149bd13719fd4e4a332180dbca7ff90e8046","source":{"kind":"arxiv","id":"1407.2199","version":2},"attestation_state":"computed","paper":{"title":"Graph connectivity and universal rigidity of bar frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih","submitted_at":"2014-07-08T18:34:55Z","abstract_excerpt":"Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \\leq r \\leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally rigid. The proof is constructive and is based on a theorem by Lovasz et al concerning orthogonal representations and connectivity of graphs [12,13]."},"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":"1407.2199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-08T18:34:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b9b190297e445f2e35b03b54029316dfec22b003b89e3f25e125c5cda4c5109c","abstract_canon_sha256":"07fe033e6ba306caeda3ecce1601b7bd9d66adbf2b4c5accd1479a30406a65b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:12.032693Z","signature_b64":"GqusUhhro67gBIkyQDp5en3dc1YbmBrGok9T5P3zocFBolOV9Dr245UOw9Gy672TSzAR3tzcCQGKtiZx+RNYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b72e0e29f53cc936d748bac9b2149bd13719fd4e4a332180dbca7ff90e8046","last_reissued_at":"2026-05-18T02:45:12.032093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:12.032093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph connectivity and universal rigidity of bar frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih","submitted_at":"2014-07-08T18:34:55Z","abstract_excerpt":"Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \\leq r \\leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally rigid. The proof is constructive and is based on a theorem by Lovasz et al concerning orthogonal representations and connectivity of graphs [12,13]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2199","kind":"arxiv","version":2},"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":"1407.2199","created_at":"2026-05-18T02:45:12.032181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2199v2","created_at":"2026-05-18T02:45:12.032181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2199","created_at":"2026-05-18T02:45:12.032181+00:00"},{"alias_kind":"pith_short_12","alias_value":"QW3S4DRJ6U6M","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QW3S4DRJ6U6MSNWX","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QW3S4DRJ","created_at":"2026-05-18T12:28:46.137349+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/QW3S4DRJ6U6MSNWXJC5MTMQUTP","json":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP.json","graph_json":"https://pith.science/api/pith-number/QW3S4DRJ6U6MSNWXJC5MTMQUTP/graph.json","events_json":"https://pith.science/api/pith-number/QW3S4DRJ6U6MSNWXJC5MTMQUTP/events.json","paper":"https://pith.science/paper/QW3S4DRJ"},"agent_actions":{"view_html":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP","download_json":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP.json","view_paper":"https://pith.science/paper/QW3S4DRJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2199&json=true","fetch_graph":"https://pith.science/api/pith-number/QW3S4DRJ6U6MSNWXJC5MTMQUTP/graph.json","fetch_events":"https://pith.science/api/pith-number/QW3S4DRJ6U6MSNWXJC5MTMQUTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP/action/storage_attestation","attest_author":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP/action/author_attestation","sign_citation":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP/action/citation_signature","submit_replication":"https://pith.science/pith/QW3S4DRJ6U6MSNWXJC5MTMQUTP/action/replication_record"}},"created_at":"2026-05-18T02:45:12.032181+00:00","updated_at":"2026-05-18T02:45:12.032181+00:00"}