{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CQTDHDIWRCNOSOCERNXQWHDCTQ","short_pith_number":"pith:CQTDHDIW","canonical_record":{"source":{"id":"1210.7073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-10-26T09:12:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"691226a3d5d47fe240af9d6b440f1ee90dbc21550a67f0dcfd5d5d3bc9136d59","abstract_canon_sha256":"445d6e79006e9d712f6853d6e48ca935ea3dae394d47f396c8000863eeafa295"},"schema_version":"1.0"},"canonical_sha256":"1426338d16889ae938448b6f0b1c629c14f1594289066564109c7fc578b4a378","source":{"kind":"arxiv","id":"1210.7073","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7073","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7073v3","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7073","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"CQTDHDIWRCNO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CQTDHDIWRCNOSOCE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CQTDHDIW","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CQTDHDIWRCNOSOCERNXQWHDCTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-10-26T09:12:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"691226a3d5d47fe240af9d6b440f1ee90dbc21550a67f0dcfd5d5d3bc9136d59","abstract_canon_sha256":"445d6e79006e9d712f6853d6e48ca935ea3dae394d47f396c8000863eeafa295"},"schema_version":"1.0"},"canonical_sha256":"1426338d16889ae938448b6f0b1c629c14f1594289066564109c7fc578b4a378","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:13.626731Z","signature_b64":"fMUXF2zYGdHFWSnAsejYhfU93OzsJkNm/bXvafPRqCFUI8fBy1XWHjpKvdHTq6vlXwUS7SZn9fRUewqBEG6qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1426338d16889ae938448b6f0b1c629c14f1594289066564109c7fc578b4a378","last_reissued_at":"2026-05-18T02:50:13.626071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:13.626071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7073","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzh2g1pthxrIC20669VNEbkZ5VYItee8bILs/zW759Erb1WCF1cKu0mQm7Ty+Zamezu1YSdjyDE2UzEyLpbtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:21:18.448750Z"},"content_sha256":"3020f152743bb083e0b4e99b98c727b546278f36c345e8eae272d2e94ca9070b","schema_version":"1.0","event_id":"sha256:3020f152743bb083e0b4e99b98c727b546278f36c345e8eae272d2e94ca9070b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CQTDHDIWRCNOSOCERNXQWHDCTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterisation of generically rigid frameworks on surfaces of revolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Anthony Nixon, John Owen, Stephen Power","submitted_at":"2012-10-26T09:12:44Z","abstract_excerpt":"A foundational theorem of Laman provides a counting characterisation of the finite simple graphs whose generic bar-joint frameworks in two dimensions are infinitesimally rigid. Recently a Laman-type characterisation was obtained for frameworks in three dimensions whose vertices are constrained to concentric spheres or to concentric cylinders. Noting that the plane and the sphere have 3 independent locally tangential infinitesimal motions while the cylinder has 2, we obtain here a Laman-Henneberg theorem for frameworks on algebraic surfaces with a 1-dimensional space of tangential motions. Such"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7073","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"noG/yiXlJp7cVOqTjYLZ8fXBGBEKZAzS1h+nn18IprLhoqdxUUkAHoid0J0OSbtjLKhlBR/a37ZGKUTjchrxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:21:18.449090Z"},"content_sha256":"2ce00c74e0efc823e8aa3a0db5d2d44daa32fe6d035b60272518d02e9115e54d","schema_version":"1.0","event_id":"sha256:2ce00c74e0efc823e8aa3a0db5d2d44daa32fe6d035b60272518d02e9115e54d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/bundle.json","state_url":"https://pith.science/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T06:21:18Z","links":{"resolver":"https://pith.science/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ","bundle":"https://pith.science/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/bundle.json","state":"https://pith.science/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQTDHDIWRCNOSOCERNXQWHDCTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CQTDHDIWRCNOSOCERNXQWHDCTQ","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":"445d6e79006e9d712f6853d6e48ca935ea3dae394d47f396c8000863eeafa295","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-10-26T09:12:44Z","title_canon_sha256":"691226a3d5d47fe240af9d6b440f1ee90dbc21550a67f0dcfd5d5d3bc9136d59"},"schema_version":"1.0","source":{"id":"1210.7073","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7073","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7073v3","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7073","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"CQTDHDIWRCNO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CQTDHDIWRCNOSOCE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CQTDHDIW","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:2ce00c74e0efc823e8aa3a0db5d2d44daa32fe6d035b60272518d02e9115e54d","target":"graph","created_at":"2026-05-18T02:50:13Z","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":"A foundational theorem of Laman provides a counting characterisation of the finite simple graphs whose generic bar-joint frameworks in two dimensions are infinitesimally rigid. Recently a Laman-type characterisation was obtained for frameworks in three dimensions whose vertices are constrained to concentric spheres or to concentric cylinders. Noting that the plane and the sphere have 3 independent locally tangential infinitesimal motions while the cylinder has 2, we obtain here a Laman-Henneberg theorem for frameworks on algebraic surfaces with a 1-dimensional space of tangential motions. Such","authors_text":"Anthony Nixon, John Owen, Stephen Power","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-10-26T09:12:44Z","title":"A characterisation of generically rigid frameworks on surfaces of revolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7073","kind":"arxiv","version":3},"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":"sha256:3020f152743bb083e0b4e99b98c727b546278f36c345e8eae272d2e94ca9070b","target":"record","created_at":"2026-05-18T02:50:13Z","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":"445d6e79006e9d712f6853d6e48ca935ea3dae394d47f396c8000863eeafa295","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-10-26T09:12:44Z","title_canon_sha256":"691226a3d5d47fe240af9d6b440f1ee90dbc21550a67f0dcfd5d5d3bc9136d59"},"schema_version":"1.0","source":{"id":"1210.7073","kind":"arxiv","version":3}},"canonical_sha256":"1426338d16889ae938448b6f0b1c629c14f1594289066564109c7fc578b4a378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1426338d16889ae938448b6f0b1c629c14f1594289066564109c7fc578b4a378","first_computed_at":"2026-05-18T02:50:13.626071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:13.626071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fMUXF2zYGdHFWSnAsejYhfU93OzsJkNm/bXvafPRqCFUI8fBy1XWHjpKvdHTq6vlXwUS7SZn9fRUewqBEG6qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:13.626731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7073","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3020f152743bb083e0b4e99b98c727b546278f36c345e8eae272d2e94ca9070b","sha256:2ce00c74e0efc823e8aa3a0db5d2d44daa32fe6d035b60272518d02e9115e54d"],"state_sha256":"02e1904216fc4d5b23e8b5fc4fe540b0baa2e1d8cfcd20714cf6b91de0863934"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HG0j39ViERnliQ4+3AUg7V8igQBybnhKeaXfT4v43ed4NTtehQCjLQd1ztWvwC3w3V6S6l11cxzWhEOkO8mNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:21:18.451185Z","bundle_sha256":"97028db3fa5d1dad0dfb67837235117b1b028a96570a96910a90984816baa6a4"}}