{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NNFYR52T3R4R5SXBUMXYTCNGVE","short_pith_number":"pith:NNFYR52T","canonical_record":{"source":{"id":"1610.07755","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-25T07:27:47Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a06fba4263637c6d2a5bbb8addf1c35429972c20f9322f20b910ce81e25765ad","abstract_canon_sha256":"75e390756587f00b1acad88d22836200258de8ee0ac40f1f68105e4e7235d866"},"schema_version":"1.0"},"canonical_sha256":"6b4b88f753dc791ecae1a32f8989a6a9315fccca2d1b1df882203f887c247d5a","source":{"kind":"arxiv","id":"1610.07755","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07755","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07755v3","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07755","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"NNFYR52T3R4R","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNFYR52T3R4R5SXB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNFYR52T","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NNFYR52T3R4R5SXBUMXYTCNGVE","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07755","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-25T07:27:47Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a06fba4263637c6d2a5bbb8addf1c35429972c20f9322f20b910ce81e25765ad","abstract_canon_sha256":"75e390756587f00b1acad88d22836200258de8ee0ac40f1f68105e4e7235d866"},"schema_version":"1.0"},"canonical_sha256":"6b4b88f753dc791ecae1a32f8989a6a9315fccca2d1b1df882203f887c247d5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:25.288841Z","signature_b64":"faUW2rf4IP1mxauBJCOWqU6LF4MakzM9BHVBxfh84WBpdqG2aJYPzfsqUNXnjQ9dx5fO6pQfaxcG/QbrcINtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b4b88f753dc791ecae1a32f8989a6a9315fccca2d1b1df882203f887c247d5a","last_reissued_at":"2026-05-18T00:03:25.288243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:25.288243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07755","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":"2026-05-18T00:03:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UWxQ5xaj8HU4GEiDVHxRU31MTg8FNV2ZkHX4QT3OjTeu3SAcLpqjc2gYEAjMPCQ/y+KIL72YvqY16q/NLlKxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:58:16.514710Z"},"content_sha256":"48d410820e76094c2ecc2c821bf891750c1082f6fd734d590ba8888c89eb54f0","schema_version":"1.0","event_id":"sha256:48d410820e76094c2ecc2c821bf891750c1082f6fd734d590ba8888c89eb54f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NNFYR52T3R4R5SXBUMXYTCNGVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global rigidity of generic frameworks on the cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Anthony Nixon, Bill Jackson","submitted_at":"2016-10-25T07:27:47Z","abstract_excerpt":"We show that a generic framework $(G,p)$ on the cylinder is globally rigid if and only if $G$ is a complete graph on at most four vertices or $G$ is both redundantly rigid and $2$-connected. To prove the theorem we also derive a new recursive construction of circuits in the simple $(2,2)$-sparse matroid, and a characterisation of rigidity for generic frameworks on the cylinder when a single designated vertex is allowed to move off the cylinder."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07755","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":"2026-05-18T00:03:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5el+aT/8HlGLEgUDmQP06R8MRIwWaxQz1BpjwftwhOonHyI03/1ZwpLWjlJjkcEMbGKeqUXQareeGKtRo23DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:58:16.515388Z"},"content_sha256":"b2f711be0b021e5d4c534213f75a500dff286d27c8d173b663082a24456ee7d8","schema_version":"1.0","event_id":"sha256:b2f711be0b021e5d4c534213f75a500dff286d27c8d173b663082a24456ee7d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/bundle.json","state_url":"https://pith.science/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/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":"2026-05-26T17:58:16Z","links":{"resolver":"https://pith.science/pith/NNFYR52T3R4R5SXBUMXYTCNGVE","bundle":"https://pith.science/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/bundle.json","state":"https://pith.science/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNFYR52T3R4R5SXBUMXYTCNGVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NNFYR52T3R4R5SXBUMXYTCNGVE","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":"75e390756587f00b1acad88d22836200258de8ee0ac40f1f68105e4e7235d866","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-25T07:27:47Z","title_canon_sha256":"a06fba4263637c6d2a5bbb8addf1c35429972c20f9322f20b910ce81e25765ad"},"schema_version":"1.0","source":{"id":"1610.07755","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07755","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07755v3","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07755","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"NNFYR52T3R4R","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNFYR52T3R4R5SXB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNFYR52T","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:b2f711be0b021e5d4c534213f75a500dff286d27c8d173b663082a24456ee7d8","target":"graph","created_at":"2026-05-18T00:03:25Z","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":"We show that a generic framework $(G,p)$ on the cylinder is globally rigid if and only if $G$ is a complete graph on at most four vertices or $G$ is both redundantly rigid and $2$-connected. To prove the theorem we also derive a new recursive construction of circuits in the simple $(2,2)$-sparse matroid, and a characterisation of rigidity for generic frameworks on the cylinder when a single designated vertex is allowed to move off the cylinder.","authors_text":"Anthony Nixon, Bill Jackson","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-25T07:27:47Z","title":"Global rigidity of generic frameworks on the cylinder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07755","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":"sha256:48d410820e76094c2ecc2c821bf891750c1082f6fd734d590ba8888c89eb54f0","target":"record","created_at":"2026-05-18T00:03:25Z","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":"75e390756587f00b1acad88d22836200258de8ee0ac40f1f68105e4e7235d866","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-25T07:27:47Z","title_canon_sha256":"a06fba4263637c6d2a5bbb8addf1c35429972c20f9322f20b910ce81e25765ad"},"schema_version":"1.0","source":{"id":"1610.07755","kind":"arxiv","version":3}},"canonical_sha256":"6b4b88f753dc791ecae1a32f8989a6a9315fccca2d1b1df882203f887c247d5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b4b88f753dc791ecae1a32f8989a6a9315fccca2d1b1df882203f887c247d5a","first_computed_at":"2026-05-18T00:03:25.288243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:25.288243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"faUW2rf4IP1mxauBJCOWqU6LF4MakzM9BHVBxfh84WBpdqG2aJYPzfsqUNXnjQ9dx5fO6pQfaxcG/QbrcINtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:25.288841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07755","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d410820e76094c2ecc2c821bf891750c1082f6fd734d590ba8888c89eb54f0","sha256:b2f711be0b021e5d4c534213f75a500dff286d27c8d173b663082a24456ee7d8"],"state_sha256":"4e330f19700d6a4c4c2d83c62c015acfbd62814c8111d5b3cd2e7cb4b78fe3eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJ++ldmjbdEB5Ix1N71cldd3WJnInai0nV2eBYDF+GdMdA92+glZnItniSFHg10m/Gz4RkFbmERg2eeKI9JqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:58:16.518837Z","bundle_sha256":"319e503995222c26741d4a5cf3c976f3212606a93a3dc89214b514707fd70b2f"}}