{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D3A5UKLOVZN7KBJHEFNWEEBNPN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4332d257baa8c4e7888e72d3d06a75a51fc9a082e0f8acce4de8c3307dfec417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-16T21:49:24Z","title_canon_sha256":"b2225800deeec76c49dd01c4b1c6e38cb60fee04543f7e5d446cb7a37e653a2b"},"schema_version":"1.0","source":{"id":"1112.3981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3981","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3981v2","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3981","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"D3A5UKLOVZN7","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D3A5UKLOVZN7KBJH","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D3A5UKLO","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:b82921addd95f9f31d778bc6843ab76bff7def9371d12bdfb4c7ee1ad2d8090e","target":"graph","created_at":"2026-05-18T03:44:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let G be an n-dimensional crystallographic group (n-space group). If G is a Z-reducible, then the flat n-orbifold E^n/G has a nontrivial fibered orbifold structure. We prove that this structure can be described by a generalized Calabi construction, that is, E^n/G is represented as the quotient of the Cartesian product of two flat orbifolds under the diagonal action of a structure group of isometries. We determine the structure group and prove that it is finite if and only if the fibered orbifold structure has an orthogonally dual fibered orbifold structure.\n  A geometric fibration of E^n/G cor","authors_text":"John G. Ratcliffe, Steven T. Tschantz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-16T21:49:24Z","title":"Fibered orbifolds and crystallographic groups, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3981","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bc2d765380be9df38ac0e1fbc909c36ab40b493fbe41d9bb33bd4a71037f5407","target":"record","created_at":"2026-05-18T03:44:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4332d257baa8c4e7888e72d3d06a75a51fc9a082e0f8acce4de8c3307dfec417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-16T21:49:24Z","title_canon_sha256":"b2225800deeec76c49dd01c4b1c6e38cb60fee04543f7e5d446cb7a37e653a2b"},"schema_version":"1.0","source":{"id":"1112.3981","kind":"arxiv","version":2}},"canonical_sha256":"1ec1da296eae5bf50527215b62102d7b6a4c34a586aa4892197178666a7cb187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec1da296eae5bf50527215b62102d7b6a4c34a586aa4892197178666a7cb187","first_computed_at":"2026-05-18T03:44:13.604962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:13.604962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WmsKlE3BxaAotXnFFzVgvTp2u8l9FStDs0qAxNUA6Psb+iWfwtbSHHfWeGby1s8TGqrW/7hN7zqMddwn/T/KCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:13.605349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc2d765380be9df38ac0e1fbc909c36ab40b493fbe41d9bb33bd4a71037f5407","sha256:b82921addd95f9f31d778bc6843ab76bff7def9371d12bdfb4c7ee1ad2d8090e"],"state_sha256":"ed4839bbadde9e1abd76ddadc7f1dad32481616f599c4bb2bb05910796f04bcb"}