{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:47UT4GWWXH4LOZFFU2P5NGRGVO","short_pith_number":"pith:47UT4GWW","schema_version":"1.0","canonical_sha256":"e7e93e1ad6b9f8b764a5a69fd69a26abb6acf7946ce7f4be0788f7d65baf578c","source":{"kind":"arxiv","id":"0906.2117","version":2},"attestation_state":"computed","paper":{"title":"Grand Antiprism and Quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mehmet Koca, Mudhahir Al-Ajmi, Nazife Ozdes Koca","submitted_at":"2009-06-11T14:26:36Z","abstract_excerpt":"Vertices of the 4-dimensional semi-regular polytope, the\n  \\textit{grand antiprism} and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the \\textbf{$E_{8} $} root system which decomposes into two copies of the root system of $H_{4} $. The symmetry of the \\textit{grand antiprism} is a maximal subgroup of the Coxeter group $W(H_{4})$. It is the group $Aut(H_{2} \\oplus H'_{2})$ which is constructed in terms of 20 quaternionic roots of the Coxeter diagram $H_{2} \\oplus H'_{2}$. The root system of $H_{4} $ represe"},"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":"0906.2117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-06-11T14:26:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fbc562c72cf6368a5c734e34f3b724411841c5e6366cc87ee4ec7d65c2f241f8","abstract_canon_sha256":"943c023faa7557b79c23189a4dab5eb02b75d9cdcf0ae7eddec414e53b523f07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:38.669363Z","signature_b64":"I/pTl6nJ4fT6e3wfuz0PIHwnmeA2l7BFpOhgRrqHGOr84QyoOOBOYzxWomOP8i+fy8wQpvW3/keuS708GXhlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7e93e1ad6b9f8b764a5a69fd69a26abb6acf7946ce7f4be0788f7d65baf578c","last_reissued_at":"2026-05-18T03:59:38.668621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:38.668621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grand Antiprism and Quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mehmet Koca, Mudhahir Al-Ajmi, Nazife Ozdes Koca","submitted_at":"2009-06-11T14:26:36Z","abstract_excerpt":"Vertices of the 4-dimensional semi-regular polytope, the\n  \\textit{grand antiprism} and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the \\textbf{$E_{8} $} root system which decomposes into two copies of the root system of $H_{4} $. The symmetry of the \\textit{grand antiprism} is a maximal subgroup of the Coxeter group $W(H_{4})$. It is the group $Aut(H_{2} \\oplus H'_{2})$ which is constructed in terms of 20 quaternionic roots of the Coxeter diagram $H_{2} \\oplus H'_{2}$. The root system of $H_{4} $ represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2117","kind":"arxiv","version":2},"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":"0906.2117","created_at":"2026-05-18T03:59:38.668733+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.2117v2","created_at":"2026-05-18T03:59:38.668733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2117","created_at":"2026-05-18T03:59:38.668733+00:00"},{"alias_kind":"pith_short_12","alias_value":"47UT4GWWXH4L","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"47UT4GWWXH4LOZFF","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"47UT4GWW","created_at":"2026-05-18T12:25:58.837520+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/47UT4GWWXH4LOZFFU2P5NGRGVO","json":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO.json","graph_json":"https://pith.science/api/pith-number/47UT4GWWXH4LOZFFU2P5NGRGVO/graph.json","events_json":"https://pith.science/api/pith-number/47UT4GWWXH4LOZFFU2P5NGRGVO/events.json","paper":"https://pith.science/paper/47UT4GWW"},"agent_actions":{"view_html":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO","download_json":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO.json","view_paper":"https://pith.science/paper/47UT4GWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.2117&json=true","fetch_graph":"https://pith.science/api/pith-number/47UT4GWWXH4LOZFFU2P5NGRGVO/graph.json","fetch_events":"https://pith.science/api/pith-number/47UT4GWWXH4LOZFFU2P5NGRGVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO/action/storage_attestation","attest_author":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO/action/author_attestation","sign_citation":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO/action/citation_signature","submit_replication":"https://pith.science/pith/47UT4GWWXH4LOZFFU2P5NGRGVO/action/replication_record"}},"created_at":"2026-05-18T03:59:38.668733+00:00","updated_at":"2026-05-18T03:59:38.668733+00:00"}