{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GGMWNTZDYVLXKEALJK5VYYR25Y","short_pith_number":"pith:GGMWNTZD","schema_version":"1.0","canonical_sha256":"319966cf23c55775100b4abb5c623aee1670a49bd26cff9e8484af41eeb0d61f","source":{"kind":"arxiv","id":"1908.03802","version":2},"attestation_state":"computed","paper":{"title":"Almost-rigidity of frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Louis Theran, Miranda Holmes-Cerfon, Steven J. Gortler","submitted_at":"2019-08-10T20:35:52Z","abstract_excerpt":"We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes continuously it must remain inside a small ball, a property we call \"almost-rigidity\"; (II) any other framework with the same edge lengths must lie outside a much larger ball; (III) if the framework deforms by some given amount, its edge lengths change by a minimum amount; (IV) there is a nearby framework that is prestress stable, and thus rigid. The condition"},"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":"1908.03802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-08-10T20:35:52Z","cross_cats_sorted":[],"title_canon_sha256":"01728c771f058407b91c0974562e4d62310aae7c526ea309d2bbeea6313601d9","abstract_canon_sha256":"ec074b8081e55fa99fbb0c643ce1658739a4ad56797fab2519c44169201c00ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:34:04.628595Z","signature_b64":"LbcCA0FUyttVXHmoBDVXl5bj180HXvMIl7QSsqo25rkLyYn0gppIq0sAgju114ASOCuvFEh+Farx6/gqNXe6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"319966cf23c55775100b4abb5c623aee1670a49bd26cff9e8484af41eeb0d61f","last_reissued_at":"2026-07-05T01:34:04.627610Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:34:04.627610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost-rigidity of frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Louis Theran, Miranda Holmes-Cerfon, Steven J. Gortler","submitted_at":"2019-08-10T20:35:52Z","abstract_excerpt":"We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes continuously it must remain inside a small ball, a property we call \"almost-rigidity\"; (II) any other framework with the same edge lengths must lie outside a much larger ball; (III) if the framework deforms by some given amount, its edge lengths change by a minimum amount; (IV) there is a nearby framework that is prestress stable, and thus rigid. The condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03802","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03802/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.03802","created_at":"2026-07-05T01:34:04.628037+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03802v2","created_at":"2026-07-05T01:34:04.628037+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03802","created_at":"2026-07-05T01:34:04.628037+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGMWNTZDYVLX","created_at":"2026-07-05T01:34:04.628037+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGMWNTZDYVLXKEAL","created_at":"2026-07-05T01:34:04.628037+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGMWNTZD","created_at":"2026-07-05T01:34:04.628037+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/GGMWNTZDYVLXKEALJK5VYYR25Y","json":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y.json","graph_json":"https://pith.science/api/pith-number/GGMWNTZDYVLXKEALJK5VYYR25Y/graph.json","events_json":"https://pith.science/api/pith-number/GGMWNTZDYVLXKEALJK5VYYR25Y/events.json","paper":"https://pith.science/paper/GGMWNTZD"},"agent_actions":{"view_html":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y","download_json":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y.json","view_paper":"https://pith.science/paper/GGMWNTZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03802&json=true","fetch_graph":"https://pith.science/api/pith-number/GGMWNTZDYVLXKEALJK5VYYR25Y/graph.json","fetch_events":"https://pith.science/api/pith-number/GGMWNTZDYVLXKEALJK5VYYR25Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y/action/storage_attestation","attest_author":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y/action/author_attestation","sign_citation":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y/action/citation_signature","submit_replication":"https://pith.science/pith/GGMWNTZDYVLXKEALJK5VYYR25Y/action/replication_record"}},"created_at":"2026-07-05T01:34:04.628037+00:00","updated_at":"2026-07-05T01:34:04.628037+00:00"}