{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HUTBRWYV2C4FAFYZBPYEYJ7V4G","short_pith_number":"pith:HUTBRWYV","schema_version":"1.0","canonical_sha256":"3d2618db15d0b85017190bf04c27f5e1a301a70de96712de7cdbd59a2d2edcd8","source":{"kind":"arxiv","id":"1804.10458","version":1},"attestation_state":"computed","paper":{"title":"Sufficient connectivity conditions for rigidity of symmetric frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernd Schulze, Viktoria E. Kaszanitzky","submitted_at":"2018-04-27T12:02:53Z","abstract_excerpt":"It is a famous result of Lovasz and Yemini (1982) that 6-connected graphs are rigid in the plane. This was recently improved by Jackson and Jordan (2009) who showed that 6-mixed connectivity is also sufficient for rigidity. Here we give sufficient graph connectivity conditions for both `forced symmetric' and `incidentally symmetric' infinitesimal rigidity in the plane."},"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":"1804.10458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-27T12:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"ee88ab65d7bb8224a328b345e4961c9bd271e05b2d3777b72641f142695f037f","abstract_canon_sha256":"1206b182df3cb5e51ddc53a6caa5328ac3787f27db6a80e0da1ee50e6e76eb1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:20.699885Z","signature_b64":"9ASG83MrnQQSBhu032zll5dGc6FhNhvVlakMu7aUdOW+rsh3l6X8xePpWnIqhSWVwKix8RCXSEYT2nTguttPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d2618db15d0b85017190bf04c27f5e1a301a70de96712de7cdbd59a2d2edcd8","last_reissued_at":"2026-05-18T00:17:20.699233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:20.699233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sufficient connectivity conditions for rigidity of symmetric frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernd Schulze, Viktoria E. Kaszanitzky","submitted_at":"2018-04-27T12:02:53Z","abstract_excerpt":"It is a famous result of Lovasz and Yemini (1982) that 6-connected graphs are rigid in the plane. This was recently improved by Jackson and Jordan (2009) who showed that 6-mixed connectivity is also sufficient for rigidity. Here we give sufficient graph connectivity conditions for both `forced symmetric' and `incidentally symmetric' infinitesimal rigidity in the plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10458","kind":"arxiv","version":1},"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":"1804.10458","created_at":"2026-05-18T00:17:20.699349+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.10458v1","created_at":"2026-05-18T00:17:20.699349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10458","created_at":"2026-05-18T00:17:20.699349+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUTBRWYV2C4F","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUTBRWYV2C4FAFYZ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUTBRWYV","created_at":"2026-05-18T12:32:28.185984+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/HUTBRWYV2C4FAFYZBPYEYJ7V4G","json":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G.json","graph_json":"https://pith.science/api/pith-number/HUTBRWYV2C4FAFYZBPYEYJ7V4G/graph.json","events_json":"https://pith.science/api/pith-number/HUTBRWYV2C4FAFYZBPYEYJ7V4G/events.json","paper":"https://pith.science/paper/HUTBRWYV"},"agent_actions":{"view_html":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G","download_json":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G.json","view_paper":"https://pith.science/paper/HUTBRWYV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.10458&json=true","fetch_graph":"https://pith.science/api/pith-number/HUTBRWYV2C4FAFYZBPYEYJ7V4G/graph.json","fetch_events":"https://pith.science/api/pith-number/HUTBRWYV2C4FAFYZBPYEYJ7V4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G/action/storage_attestation","attest_author":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G/action/author_attestation","sign_citation":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G/action/citation_signature","submit_replication":"https://pith.science/pith/HUTBRWYV2C4FAFYZBPYEYJ7V4G/action/replication_record"}},"created_at":"2026-05-18T00:17:20.699349+00:00","updated_at":"2026-05-18T00:17:20.699349+00:00"}