{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XF7FF7KPARQDPVWOMVR2BFH27I","short_pith_number":"pith:XF7FF7KP","schema_version":"1.0","canonical_sha256":"b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a","source":{"kind":"arxiv","id":"1103.1914","version":4},"attestation_state":"computed","paper":{"title":"Crystal frameworks, symmetry and affinely periodic flexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Stephen Power","submitted_at":"2011-03-09T22:51:55Z","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"},"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":"1103.1914","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T22:51:55Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"648f0b0f32a4cdea0d3effd747a36f17eb6034c10e0f3695f3b8ff50dd80825a","abstract_canon_sha256":"df41ddae73a707827243fa74a0999da965850b40366d71aeefdd75587354296d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.361463Z","signature_b64":"2E//G3/iaa5kGQ+ZrGrzn0MVJiyPBF66hdTXQ3wexdViOLiSGjKAFSnFjoaut7rjMNyV2r+SowBo7zCKrxKvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a","last_reissued_at":"2026-05-18T02:47:51.361015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.361015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crystal frameworks, symmetry and affinely periodic flexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Stephen Power","submitted_at":"2011-03-09T22:51:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1914","kind":"arxiv","version":4},"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":"1103.1914","created_at":"2026-05-18T02:47:51.361077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1914v4","created_at":"2026-05-18T02:47:51.361077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1914","created_at":"2026-05-18T02:47:51.361077+00:00"},{"alias_kind":"pith_short_12","alias_value":"XF7FF7KPARQD","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XF7FF7KPARQDPVWO","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XF7FF7KP","created_at":"2026-05-18T12:26:44.992195+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/XF7FF7KPARQDPVWOMVR2BFH27I","json":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I.json","graph_json":"https://pith.science/api/pith-number/XF7FF7KPARQDPVWOMVR2BFH27I/graph.json","events_json":"https://pith.science/api/pith-number/XF7FF7KPARQDPVWOMVR2BFH27I/events.json","paper":"https://pith.science/paper/XF7FF7KP"},"agent_actions":{"view_html":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I","download_json":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I.json","view_paper":"https://pith.science/paper/XF7FF7KP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1914&json=true","fetch_graph":"https://pith.science/api/pith-number/XF7FF7KPARQDPVWOMVR2BFH27I/graph.json","fetch_events":"https://pith.science/api/pith-number/XF7FF7KPARQDPVWOMVR2BFH27I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I/action/storage_attestation","attest_author":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I/action/author_attestation","sign_citation":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I/action/citation_signature","submit_replication":"https://pith.science/pith/XF7FF7KPARQDPVWOMVR2BFH27I/action/replication_record"}},"created_at":"2026-05-18T02:47:51.361077+00:00","updated_at":"2026-05-18T02:47:51.361077+00:00"}