{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:K4UJYC2TBF4SXTQEEWIBEMEPXE","short_pith_number":"pith:K4UJYC2T","schema_version":"1.0","canonical_sha256":"57289c0b5309792bce04259012308fb917063eec62fe4e0707e84040f698f15b","source":{"kind":"arxiv","id":"1411.2115","version":4},"attestation_state":"computed","paper":{"title":"Orbits of crystallographic embedding of non-crystallographic groups and applications to virology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG","math.MP"],"primary_cat":"math-ph","authors_text":"Emilio Zappa, Motiejus Valiunas, Reidun Twarock","submitted_at":"2014-11-08T13:00:58Z","abstract_excerpt":"The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is still lacking. We present here a group theoretical method for the construction of finite nested point set with non-crystallographic symmetry. Akin to the construction of quasicrystals, we embed a non-crystallographic group $G$ into the point group $\\mathcal{P}$ of a higher dimensional lattice and construct the chains of all $G$-containing subgroups. We determ"},"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":"1411.2115","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-08T13:00:58Z","cross_cats_sorted":["math.GR","math.MG","math.MP"],"title_canon_sha256":"c577608a213cba89d3ed03c0acce0b38be62211b8ebe38f6d1ea3846adce4abf","abstract_canon_sha256":"04cf3f9e02ed6bd26e5fabab625974a931f6e4bf78189b893a8d52a1dded1ae3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:11.786526Z","signature_b64":"+7j/P2pzWml4xYeXlOM3pVcnNpIx6y2hqaPu9H9D6/pi47jrt0Y6zwHhML/dk7XrRMyVTbpM2e3SdogMB3noDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57289c0b5309792bce04259012308fb917063eec62fe4e0707e84040f698f15b","last_reissued_at":"2026-05-18T01:35:11.785855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:11.785855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbits of crystallographic embedding of non-crystallographic groups and applications to virology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG","math.MP"],"primary_cat":"math-ph","authors_text":"Emilio Zappa, Motiejus Valiunas, Reidun Twarock","submitted_at":"2014-11-08T13:00:58Z","abstract_excerpt":"The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is still lacking. We present here a group theoretical method for the construction of finite nested point set with non-crystallographic symmetry. Akin to the construction of quasicrystals, we embed a non-crystallographic group $G$ into the point group $\\mathcal{P}$ of a higher dimensional lattice and construct the chains of all $G$-containing subgroups. We determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2115","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":"1411.2115","created_at":"2026-05-18T01:35:11.785964+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.2115v4","created_at":"2026-05-18T01:35:11.785964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2115","created_at":"2026-05-18T01:35:11.785964+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4UJYC2TBF4S","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4UJYC2TBF4SXTQE","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4UJYC2T","created_at":"2026-05-18T12:28:35.611951+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/K4UJYC2TBF4SXTQEEWIBEMEPXE","json":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE.json","graph_json":"https://pith.science/api/pith-number/K4UJYC2TBF4SXTQEEWIBEMEPXE/graph.json","events_json":"https://pith.science/api/pith-number/K4UJYC2TBF4SXTQEEWIBEMEPXE/events.json","paper":"https://pith.science/paper/K4UJYC2T"},"agent_actions":{"view_html":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE","download_json":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE.json","view_paper":"https://pith.science/paper/K4UJYC2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.2115&json=true","fetch_graph":"https://pith.science/api/pith-number/K4UJYC2TBF4SXTQEEWIBEMEPXE/graph.json","fetch_events":"https://pith.science/api/pith-number/K4UJYC2TBF4SXTQEEWIBEMEPXE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE/action/storage_attestation","attest_author":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE/action/author_attestation","sign_citation":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE/action/citation_signature","submit_replication":"https://pith.science/pith/K4UJYC2TBF4SXTQEEWIBEMEPXE/action/replication_record"}},"created_at":"2026-05-18T01:35:11.785964+00:00","updated_at":"2026-05-18T01:35:11.785964+00:00"}