{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MKMK3RNDDECEMD5R52KVI3BYNZ","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":"c534e57030c0b13bec5e843ef8e369d3082cad775a4c02701650821836a09a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-21T19:52:09Z","title_canon_sha256":"a475a1f14d184f77208d6476a24cd79802fc2bea9ffe22f457cf7fb59430a0a8"},"schema_version":"1.0","source":{"id":"1410.5804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5804","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5804v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5804","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"MKMK3RNDDECE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MKMK3RNDDECEMD5R","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MKMK3RND","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:c77836c51f361a7f9053afeaee5fe4ba36fe3ab9dd9d6c8261857eca04fff1dc","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"Crooked planes are piecewise linear surfaces that were introduced by Drumm in the early 1990s to construct fundamental domains for properly discontinuous actions of free groups on Minkowski 3-space. In a previous paper, we introduced analogues of these surfaces, called AdS crooked planes, in the 3-dimensional anti-de Sitter space AdS^3; we showed that many properly discontinuous actions of free groups on AdS^3 admit fundamental domains bounded by AdS crooked planes. Here we study further the question of which proper actions on AdS^3 admit crooked fundamental domains, and show that some do not,","authors_text":"Fanny Kassel, Fran\\c{c}ois Gu\\'eritaud, Jeffrey Danciger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-21T19:52:09Z","title":"Fundamental domains for free groups acting on anti-de Sitter 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5804","kind":"arxiv","version":1},"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:e5a51d18fcfc3fda2af37c4bbf470be076793f3efe5854217f37bc8fcc08c19f","target":"record","created_at":"2026-05-18T02:39:39Z","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":"c534e57030c0b13bec5e843ef8e369d3082cad775a4c02701650821836a09a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-21T19:52:09Z","title_canon_sha256":"a475a1f14d184f77208d6476a24cd79802fc2bea9ffe22f457cf7fb59430a0a8"},"schema_version":"1.0","source":{"id":"1410.5804","kind":"arxiv","version":1}},"canonical_sha256":"6298adc5a31904460fb1ee95546c386e5afc31aaae74625fb956b850d3b5bd33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6298adc5a31904460fb1ee95546c386e5afc31aaae74625fb956b850d3b5bd33","first_computed_at":"2026-05-18T02:39:39.079840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.079840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C20n4Ylv/5EHTGSaTwcosrd1GdALtyo/m+0B4w1ct2uUbjcJ8WkDCeWFU/ApSiu8vb4f5W0Fu0gF8a8UrPZYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.080377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5a51d18fcfc3fda2af37c4bbf470be076793f3efe5854217f37bc8fcc08c19f","sha256:c77836c51f361a7f9053afeaee5fe4ba36fe3ab9dd9d6c8261857eca04fff1dc"],"state_sha256":"f05e8749af909a357c3e6dba20d58d0468349457583227a1784897318c43bdec"}