{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KT74UGJ2KYDDAUDC7QMJNXF2NI","short_pith_number":"pith:KT74UGJ2","schema_version":"1.0","canonical_sha256":"54ffca193a5606305062fc1896dcba6a0978dc5d22537dcd1abf365a053aac45","source":{"kind":"arxiv","id":"1408.6703","version":2},"attestation_state":"computed","paper":{"title":"Classification of tight regular polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Pellicer, Gabe Cunningham","submitted_at":"2014-08-28T12:34:24Z","abstract_excerpt":"A regular polyhedron of type {p, q} has at least 2pq flags, and it is called tight if it has exactly 2pq flags. The values of p and q for which there exist tight orientably regular polyhedra were previously known. We determine for which values of p and q there is a tight non-orientably regular polyhedron of type {p, q}. Furthermore, we completely classify tight regular polyhedra in terms of their automorphism groups."},"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":"1408.6703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-28T12:34:24Z","cross_cats_sorted":[],"title_canon_sha256":"c4a4d9b6c62dd1e8c2869f04613b77156f295052eae36da88f05f414be675e50","abstract_canon_sha256":"fcf3010a2c04e7c3442e400704b6c5822e9f0174e6c7f01ffb2894a4ef72d5a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:26.010841Z","signature_b64":"1KsQrm3Y5b0WEL3OPB8AsGFfBdLpOyJDZbfgrE1/GYjQIhEvfl2IWdgfK62PZIlekHtIUxZ7XwBGicls3ePaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54ffca193a5606305062fc1896dcba6a0978dc5d22537dcd1abf365a053aac45","last_reissued_at":"2026-05-18T01:17:26.010358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:26.010358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of tight regular polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Pellicer, Gabe Cunningham","submitted_at":"2014-08-28T12:34:24Z","abstract_excerpt":"A regular polyhedron of type {p, q} has at least 2pq flags, and it is called tight if it has exactly 2pq flags. The values of p and q for which there exist tight orientably regular polyhedra were previously known. We determine for which values of p and q there is a tight non-orientably regular polyhedron of type {p, q}. Furthermore, we completely classify tight regular polyhedra in terms of their automorphism groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6703","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":"1408.6703","created_at":"2026-05-18T01:17:26.010439+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.6703v2","created_at":"2026-05-18T01:17:26.010439+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6703","created_at":"2026-05-18T01:17:26.010439+00:00"},{"alias_kind":"pith_short_12","alias_value":"KT74UGJ2KYDD","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KT74UGJ2KYDDAUDC","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KT74UGJ2","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/KT74UGJ2KYDDAUDC7QMJNXF2NI","json":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI.json","graph_json":"https://pith.science/api/pith-number/KT74UGJ2KYDDAUDC7QMJNXF2NI/graph.json","events_json":"https://pith.science/api/pith-number/KT74UGJ2KYDDAUDC7QMJNXF2NI/events.json","paper":"https://pith.science/paper/KT74UGJ2"},"agent_actions":{"view_html":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI","download_json":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI.json","view_paper":"https://pith.science/paper/KT74UGJ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.6703&json=true","fetch_graph":"https://pith.science/api/pith-number/KT74UGJ2KYDDAUDC7QMJNXF2NI/graph.json","fetch_events":"https://pith.science/api/pith-number/KT74UGJ2KYDDAUDC7QMJNXF2NI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI/action/storage_attestation","attest_author":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI/action/author_attestation","sign_citation":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI/action/citation_signature","submit_replication":"https://pith.science/pith/KT74UGJ2KYDDAUDC7QMJNXF2NI/action/replication_record"}},"created_at":"2026-05-18T01:17:26.010439+00:00","updated_at":"2026-05-18T01:17:26.010439+00:00"}