{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AZQ52FXI7ZFWSSSPVLN3APNSY5","short_pith_number":"pith:AZQ52FXI","schema_version":"1.0","canonical_sha256":"0661dd16e8fe4b694a4faadbb03db2c769d3bd7bce2b4652d7dcbeb89e713fd5","source":{"kind":"arxiv","id":"1702.08080","version":2},"attestation_state":"computed","paper":{"title":"Unravelling the Dodecahedral Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonathan Spreer, Stephan Tillmann","submitted_at":"2017-02-26T20:30:33Z","abstract_excerpt":"The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincar\\'e homology sphere)."},"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":"1702.08080","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-26T20:30:33Z","cross_cats_sorted":[],"title_canon_sha256":"30f357cc48aa928517eda92c66c5c34e798cf1111a2989450284662292cbecda","abstract_canon_sha256":"9f49b4c79fdb9503751de2c7a114f75b97e02286e29571a9ef14066a9cae3287"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:36.541988Z","signature_b64":"6trIFhTjZQ+ZDNOBNe+R8dWuDIf3yUKms5WL41B2nyTKzRK0UczXk8CKKtj3F+APXnKtvqR3qEwkY7UsXDFzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0661dd16e8fe4b694a4faadbb03db2c769d3bd7bce2b4652d7dcbeb89e713fd5","last_reissued_at":"2026-05-18T00:02:36.541263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:36.541263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unravelling the Dodecahedral Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonathan Spreer, Stephan Tillmann","submitted_at":"2017-02-26T20:30:33Z","abstract_excerpt":"The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincar\\'e homology sphere)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08080","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":"1702.08080","created_at":"2026-05-18T00:02:36.541409+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08080v2","created_at":"2026-05-18T00:02:36.541409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08080","created_at":"2026-05-18T00:02:36.541409+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZQ52FXI7ZFW","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZQ52FXI7ZFWSSSP","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZQ52FXI","created_at":"2026-05-18T12:31:08.081275+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/AZQ52FXI7ZFWSSSPVLN3APNSY5","json":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5.json","graph_json":"https://pith.science/api/pith-number/AZQ52FXI7ZFWSSSPVLN3APNSY5/graph.json","events_json":"https://pith.science/api/pith-number/AZQ52FXI7ZFWSSSPVLN3APNSY5/events.json","paper":"https://pith.science/paper/AZQ52FXI"},"agent_actions":{"view_html":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5","download_json":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5.json","view_paper":"https://pith.science/paper/AZQ52FXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08080&json=true","fetch_graph":"https://pith.science/api/pith-number/AZQ52FXI7ZFWSSSPVLN3APNSY5/graph.json","fetch_events":"https://pith.science/api/pith-number/AZQ52FXI7ZFWSSSPVLN3APNSY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5/action/storage_attestation","attest_author":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5/action/author_attestation","sign_citation":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5/action/citation_signature","submit_replication":"https://pith.science/pith/AZQ52FXI7ZFWSSSPVLN3APNSY5/action/replication_record"}},"created_at":"2026-05-18T00:02:36.541409+00:00","updated_at":"2026-05-18T00:02:36.541409+00:00"}