{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XF7FF7KPARQDPVWOMVR2BFH27I","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":"df41ddae73a707827243fa74a0999da965850b40366d71aeefdd75587354296d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T22:51:55Z","title_canon_sha256":"648f0b0f32a4cdea0d3effd747a36f17eb6034c10e0f3695f3b8ff50dd80825a"},"schema_version":"1.0","source":{"id":"1103.1914","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1914","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1914v4","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1914","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"pith_short_12","alias_value":"XF7FF7KPARQD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XF7FF7KPARQDPVWO","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XF7FF7KP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:8c77822b3df1937115d6f63ffc296d12bd3beb1ef07f2172000c35d234bbae39","target":"graph","created_at":"2026-05-18T02:47:51Z","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":"Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework $\\C$ in $\\bR^d$. These equations are used to derive symmetry-adapted Maxwell-Calladine counting formulae for periodic self-stresses and affinely periodic infinitesimal mechanisms. The symmetry equations also lead to general Fowler-Guest formulae connecting the character lists of subrepresentations of the crystallographic space and point groups which are associated with bonds, nodes, stresses, flexes and rigid motions. A new derivation","authors_text":"Stephen Power","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T22:51:55Z","title":"Crystal frameworks, symmetry and affinely periodic flexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1914","kind":"arxiv","version":4},"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:d66c079fc4d62f393ab08fb4f5b9c641b1f2c827c7f4848596177adeea9ace81","target":"record","created_at":"2026-05-18T02:47:51Z","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":"df41ddae73a707827243fa74a0999da965850b40366d71aeefdd75587354296d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T22:51:55Z","title_canon_sha256":"648f0b0f32a4cdea0d3effd747a36f17eb6034c10e0f3695f3b8ff50dd80825a"},"schema_version":"1.0","source":{"id":"1103.1914","kind":"arxiv","version":4}},"canonical_sha256":"b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a","first_computed_at":"2026-05-18T02:47:51.361015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:51.361015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2E//G3/iaa5kGQ+ZrGrzn0MVJiyPBF66hdTXQ3wexdViOLiSGjKAFSnFjoaut7rjMNyV2r+SowBo7zCKrxKvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:51.361463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1914","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d66c079fc4d62f393ab08fb4f5b9c641b1f2c827c7f4848596177adeea9ace81","sha256:8c77822b3df1937115d6f63ffc296d12bd3beb1ef07f2172000c35d234bbae39"],"state_sha256":"5dd52f2d3d7a988b91bee967771983d104dac3ffc5f8abfdb2d908cfbc7a141f"}