{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ATXEB4HYWBWCLA7XAKH5POUCPR","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":"963883df6a059c34293557521b77ea9f338f3f100f80be3f3f3c11166e9ce8c0","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-10T16:58:01Z","title_canon_sha256":"7fbda57cc225fba03fac8898b331a3e9f87ef1081c4932d08632a021dfd91cd2"},"schema_version":"1.0","source":{"id":"1312.2872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2872","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2872v2","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2872","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"ATXEB4HYWBWC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ATXEB4HYWBWCLA7X","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ATXEB4HY","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:0a9db14ba9b3976ba7e36a2353d006abd2df84801798cd07f16e386948551994","target":"graph","created_at":"2026-05-18T02:29:39Z","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":"It is conjectured that every manifold admitting an Anosov diffeomorphism is, up to homeomorphism, finitely covered by a nilmanifold. Motivated by this conjecture, an important problem is to determine which nilmanifolds admit an Anosov diffeomorphism. The main theorem of this article gives a general method for constructing Anosov diffeomorphisms on nilmanifolds. As a consequence, we give counterexamples to a corollary of the classification of low-dimensional nilmanifolds with Anosov diffeomorphisms and a correction to this statement is proven. This method also answers some open questions about ","authors_text":"Jonas Der\\'e","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-10T16:58:01Z","title":"A new method for constructing Anosov Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2872","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":"sha256:2afc0f824edc6d9a0363c8d344b86e7d3734d949127079f143fdf290c50c07a6","target":"record","created_at":"2026-05-18T02:29:39Z","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":"963883df6a059c34293557521b77ea9f338f3f100f80be3f3f3c11166e9ce8c0","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-10T16:58:01Z","title_canon_sha256":"7fbda57cc225fba03fac8898b331a3e9f87ef1081c4932d08632a021dfd91cd2"},"schema_version":"1.0","source":{"id":"1312.2872","kind":"arxiv","version":2}},"canonical_sha256":"04ee40f0f8b06c2583f7028fd7ba827c7e73ffe187cf36b07c48d0b868837685","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04ee40f0f8b06c2583f7028fd7ba827c7e73ffe187cf36b07c48d0b868837685","first_computed_at":"2026-05-18T02:29:39.200097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:39.200097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AgJ1Nc7mpLXZeNPRQuIRT+Z+HWC8IGjMDwizKLXMNxjh0SNLv/ixAtWlR0UYn5B/kMHFoBJhF1Rp2l/EB+/vDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:39.200497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2afc0f824edc6d9a0363c8d344b86e7d3734d949127079f143fdf290c50c07a6","sha256:0a9db14ba9b3976ba7e36a2353d006abd2df84801798cd07f16e386948551994"],"state_sha256":"6a4685b5474a581671bf61fc8aaf0a5bb93241777766c167c86cb7a77c0e99d9"}