{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PSIZX5GDFDZHBTPOBETMPZ2M5Z","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":"f75163d621ee0d17b79e35aa8b75db497e51aff5f1d925c4780e72350ae2dfa2","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-27T14:29:24Z","title_canon_sha256":"704d33dc788f27d2fa399fa95d559741eb73991d34cd0a0007023194d0cf43de"},"schema_version":"1.0","source":{"id":"1609.08474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08474","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08474v1","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08474","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"PSIZX5GDFDZH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSIZX5GDFDZHBTPO","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSIZX5GD","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:a090bca4b09dffc60b76ef9ee69bf1344d5219606cfbedcf6a64f0fc9222c16a","target":"graph","created_at":"2026-05-17T23:42:31Z","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":"We prove that a K\\\"ahler group which is cubulable, i.e. which acts properly discontinuously and cocompactly on a CAT(0) cubical complex, has a finite index subgroup isomorphic to a direct product of surface groups, possibly with a free Abelian factor. Similarly, we prove that a closed aspherical K\\\"ahler manifold with a cubulable fundamental group has a finite cover which is biholomorphic to a topologically trivial principal torus bundle over a product of Riemann surfaces. Along the way, we prove a factorization result for essential actions of K\\\"ahler groups on irreducible, locally finite CAT","authors_text":"Pierre Py, Thomas Delzant","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-27T14:29:24Z","title":"Cubulable K\\\"ahler groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08474","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:cc0885096c775812ea624c267b9b415c96e5ac5e29bcc1f1b16a750a97dd8df5","target":"record","created_at":"2026-05-17T23:42:31Z","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":"f75163d621ee0d17b79e35aa8b75db497e51aff5f1d925c4780e72350ae2dfa2","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-27T14:29:24Z","title_canon_sha256":"704d33dc788f27d2fa399fa95d559741eb73991d34cd0a0007023194d0cf43de"},"schema_version":"1.0","source":{"id":"1609.08474","kind":"arxiv","version":1}},"canonical_sha256":"7c919bf4c328f270cdee0926c7e74cee4e1c6ee6d975724a08de7e9633a6ecbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c919bf4c328f270cdee0926c7e74cee4e1c6ee6d975724a08de7e9633a6ecbb","first_computed_at":"2026-05-17T23:42:31.224582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:31.224582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JGSyEtgCC13hhTqdv9J+F2EVvKyMKWihfQ8nnrWo97iQv1INFR995GdHiHDOdgmq18RneNPNZz9Jg9Lun6t7Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:31.225250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc0885096c775812ea624c267b9b415c96e5ac5e29bcc1f1b16a750a97dd8df5","sha256:a090bca4b09dffc60b76ef9ee69bf1344d5219606cfbedcf6a64f0fc9222c16a"],"state_sha256":"f87c4d2275c78295ed306f4e05990d3a7fef8d53d7a563fabc55d23d1fedf574"}