{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RDQYJXWV7DVDBLLZ5ZA7YSKNWA","short_pith_number":"pith:RDQYJXWV","canonical_record":{"source":{"id":"1010.5440","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-26T15:55:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ad32f41467bb745d780a98b1694133fbeca4bdd010ec6273b0918e3e33ed046d","abstract_canon_sha256":"c947780ba7b69decd0b297d0dd122dc7b6474ae914898d654373e36f3939c9fb"},"schema_version":"1.0"},"canonical_sha256":"88e184ded5f8ea30ad79ee41fc494db02fbdd6594314e1a8497b066ba4c48fde","source":{"kind":"arxiv","id":"1010.5440","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5440","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5440v3","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5440","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"RDQYJXWV7DVD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RDQYJXWV7DVDBLLZ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RDQYJXWV","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RDQYJXWV7DVDBLLZ5ZA7YSKNWA","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5440","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-26T15:55:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ad32f41467bb745d780a98b1694133fbeca4bdd010ec6273b0918e3e33ed046d","abstract_canon_sha256":"c947780ba7b69decd0b297d0dd122dc7b6474ae914898d654373e36f3939c9fb"},"schema_version":"1.0"},"canonical_sha256":"88e184ded5f8ea30ad79ee41fc494db02fbdd6594314e1a8497b066ba4c48fde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:38.577385Z","signature_b64":"SDeBBwZoa1xpvd9XbI4lkU3DyGCyQtzovMBGZzUlas8rQPMHEZ+NUrtgxnAdxon4Oj/Y+FZkvGqkS7WyLqYdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e184ded5f8ea30ad79ee41fc494db02fbdd6594314e1a8497b066ba4c48fde","last_reissued_at":"2026-05-18T02:23:38.576777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:38.576777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5440","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":"2026-05-18T02:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3RQVxaZIccY3RY94czY1mNQAw4Qg/LOy4+9p0G29WgsL5cvESOe21t6X+QMgP6wbDnOTGDPja5Z3WA4V2NhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:25:01.124131Z"},"content_sha256":"3749e3fc401b9e2b4fdf4eef08c3bc20f24ea857b54fd001a2c0f2e5eed5c5ad","schema_version":"1.0","event_id":"sha256:3749e3fc401b9e2b4fdf4eef08c3bc20f24ea857b54fd001a2c0f2e5eed5c5ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RDQYJXWV7DVDBLLZ5ZA7YSKNWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite motions from periodic frameworks with added symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Bernd Schulze, Elissa Ross, Walter Whiteley","submitted_at":"2010-10-26T15:55:59Z","abstract_excerpt":"Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as an engineering type framework, or equivalently, as an idealized molecular framework. Other work has shown that for finite frameworks, introducing symmetry modifies the previous general counts, and under some circumstances this symmetrized Maxwell type count can predict added finite flexibility in the structure.\n  In this paper we combine these approaches to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5440","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":"2026-05-18T02:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Av6C2y9nROl5RYN4pKxrzvc9jp5o+AiFpfmyoc/GvQq60b8uB+qgL2+Aoj8MeZgE2o2QFIM32AIvhwNmgLmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:25:01.124520Z"},"content_sha256":"cba317f5cde40db982428d3bef69ac99a272994c9d9229453b78f94acf88eaa2","schema_version":"1.0","event_id":"sha256:cba317f5cde40db982428d3bef69ac99a272994c9d9229453b78f94acf88eaa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/bundle.json","state_url":"https://pith.science/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/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":"2026-06-24T11:25:01Z","links":{"resolver":"https://pith.science/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA","bundle":"https://pith.science/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/bundle.json","state":"https://pith.science/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDQYJXWV7DVDBLLZ5ZA7YSKNWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RDQYJXWV7DVDBLLZ5ZA7YSKNWA","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":"c947780ba7b69decd0b297d0dd122dc7b6474ae914898d654373e36f3939c9fb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-26T15:55:59Z","title_canon_sha256":"ad32f41467bb745d780a98b1694133fbeca4bdd010ec6273b0918e3e33ed046d"},"schema_version":"1.0","source":{"id":"1010.5440","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5440","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5440v3","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5440","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"RDQYJXWV7DVD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RDQYJXWV7DVDBLLZ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RDQYJXWV","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:cba317f5cde40db982428d3bef69ac99a272994c9d9229453b78f94acf88eaa2","target":"graph","created_at":"2026-05-18T02:23:38Z","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":"Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as an engineering type framework, or equivalently, as an idealized molecular framework. Other work has shown that for finite frameworks, introducing symmetry modifies the previous general counts, and under some circumstances this symmetrized Maxwell type count can predict added finite flexibility in the structure.\n  In this paper we combine these approaches to ","authors_text":"Bernd Schulze, Elissa Ross, Walter Whiteley","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-26T15:55:59Z","title":"Finite motions from periodic frameworks with added symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5440","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":"sha256:3749e3fc401b9e2b4fdf4eef08c3bc20f24ea857b54fd001a2c0f2e5eed5c5ad","target":"record","created_at":"2026-05-18T02:23:38Z","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":"c947780ba7b69decd0b297d0dd122dc7b6474ae914898d654373e36f3939c9fb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-26T15:55:59Z","title_canon_sha256":"ad32f41467bb745d780a98b1694133fbeca4bdd010ec6273b0918e3e33ed046d"},"schema_version":"1.0","source":{"id":"1010.5440","kind":"arxiv","version":3}},"canonical_sha256":"88e184ded5f8ea30ad79ee41fc494db02fbdd6594314e1a8497b066ba4c48fde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88e184ded5f8ea30ad79ee41fc494db02fbdd6594314e1a8497b066ba4c48fde","first_computed_at":"2026-05-18T02:23:38.576777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:38.576777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDeBBwZoa1xpvd9XbI4lkU3DyGCyQtzovMBGZzUlas8rQPMHEZ+NUrtgxnAdxon4Oj/Y+FZkvGqkS7WyLqYdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:38.577385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5440","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3749e3fc401b9e2b4fdf4eef08c3bc20f24ea857b54fd001a2c0f2e5eed5c5ad","sha256:cba317f5cde40db982428d3bef69ac99a272994c9d9229453b78f94acf88eaa2"],"state_sha256":"a67237944d118fcc08e47958309e5bcb9f1cb8cbe39486811e71921cf86a2177"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0hhRBjRiqQsXMQS5bh7+MrO8L6rq8coKqCPvER2myPr8VbbDWES3zmE8yl41uscvMdk9Sxo/+Iu4TL4q1Z8pAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:25:01.126391Z","bundle_sha256":"99cc976bfda5769e084323f0c8cba5d23eca4c9a55220ceba9af59356509a695"}}