{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5JCMVZWHBOZYXLT2KZKUUPYBOA","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":"cefbadb17c9abd15e4b9b2ee9df1761418eec5a3c3ba4879fb66bdd163264531","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-20T22:56:46Z","title_canon_sha256":"8e68b0117f4289fb15c254bcdd001a9894ce5167efa5f25af45e51bb84be364e"},"schema_version":"1.0","source":{"id":"0803.3094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3094","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3094v2","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3094","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"5JCMVZWHBOZY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5JCMVZWHBOZYXLT2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5JCMVZWH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:b40d52c0a14f75556cb12329248a1988c414d087227098eb847ceb1f98fca0c3","target":"graph","created_at":"2026-05-18T04:41:05Z","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 consider an ergodic invariant measure $\\mu$ for a smooth action of $Z^k$, $k \\ge 2$, on a $(k+1)$-dimensional manifold or for a locally free smooth action of $R^k$, $k \\ge 2$ on a $(2k+1)$-dimensional manifold. We prove that if $\\mu$ is hyperbolic with the Lyapunov hyperplanes in general position and if one element of the action has positive entropy, then $\\mu$ is absolutely continuous. The main ingredient is absolute continuity of conditional measures on Lyapunov foliations which holds for a more general class of smooth actions of higher rank abelian groups.","authors_text":"Anatole Katok, Boris Kalinin, Federico Rodriguez Hertz","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-20T22:56:46Z","title":"Nonuniform measure rigidity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3094","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":"sha256:406f11e48217ff4b20ec9912152d3b786e49bf817b07c4be073653ab50ffa0e2","target":"record","created_at":"2026-05-18T04:41:05Z","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":"cefbadb17c9abd15e4b9b2ee9df1761418eec5a3c3ba4879fb66bdd163264531","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-20T22:56:46Z","title_canon_sha256":"8e68b0117f4289fb15c254bcdd001a9894ce5167efa5f25af45e51bb84be364e"},"schema_version":"1.0","source":{"id":"0803.3094","kind":"arxiv","version":2}},"canonical_sha256":"ea44cae6c70bb38bae7a56554a3f017002a282a05f427f034f7a95d4444406fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea44cae6c70bb38bae7a56554a3f017002a282a05f427f034f7a95d4444406fb","first_computed_at":"2026-05-18T04:41:05.360996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:05.360996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tC2vNG4nSUd1LHd2ELUDzPjZ+tPXYs3zgdKB+WIjlilT1kkDUVk6dKVN8JGNgVj37r7YwgWWONIIRecPdjUtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:05.361434Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:406f11e48217ff4b20ec9912152d3b786e49bf817b07c4be073653ab50ffa0e2","sha256:b40d52c0a14f75556cb12329248a1988c414d087227098eb847ceb1f98fca0c3"],"state_sha256":"dc9aaf2db2619c5c52716fd802c069f5e0fe68f202178eea628e79be2cc4f246"}