{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:5JCMVZWHBOZYXLT2KZKUUPYBOA","short_pith_number":"pith:5JCMVZWH","schema_version":"1.0","canonical_sha256":"ea44cae6c70bb38bae7a56554a3f017002a282a05f427f034f7a95d4444406fb","source":{"kind":"arxiv","id":"0803.3094","version":2},"attestation_state":"computed","paper":{"title":"Nonuniform measure rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Anatole Katok, Boris Kalinin, Federico Rodriguez Hertz","submitted_at":"2008-03-20T22:56:46Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0803.3094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-20T22:56:46Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"8e68b0117f4289fb15c254bcdd001a9894ce5167efa5f25af45e51bb84be364e","abstract_canon_sha256":"cefbadb17c9abd15e4b9b2ee9df1761418eec5a3c3ba4879fb66bdd163264531"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:05.361434Z","signature_b64":"tC2vNG4nSUd1LHd2ELUDzPjZ+tPXYs3zgdKB+WIjlilT1kkDUVk6dKVN8JGNgVj37r7YwgWWONIIRecPdjUtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea44cae6c70bb38bae7a56554a3f017002a282a05f427f034f7a95d4444406fb","last_reissued_at":"2026-05-18T04:41:05.360996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:05.360996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonuniform measure rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Anatole Katok, Boris Kalinin, Federico Rodriguez Hertz","submitted_at":"2008-03-20T22:56:46Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3094","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0803.3094","created_at":"2026-05-18T04:41:05.361062+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.3094v2","created_at":"2026-05-18T04:41:05.361062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3094","created_at":"2026-05-18T04:41:05.361062+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JCMVZWHBOZY","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JCMVZWHBOZYXLT2","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JCMVZWH","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA","json":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA.json","graph_json":"https://pith.science/api/pith-number/5JCMVZWHBOZYXLT2KZKUUPYBOA/graph.json","events_json":"https://pith.science/api/pith-number/5JCMVZWHBOZYXLT2KZKUUPYBOA/events.json","paper":"https://pith.science/paper/5JCMVZWH"},"agent_actions":{"view_html":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA","download_json":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA.json","view_paper":"https://pith.science/paper/5JCMVZWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.3094&json=true","fetch_graph":"https://pith.science/api/pith-number/5JCMVZWHBOZYXLT2KZKUUPYBOA/graph.json","fetch_events":"https://pith.science/api/pith-number/5JCMVZWHBOZYXLT2KZKUUPYBOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA/action/storage_attestation","attest_author":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA/action/author_attestation","sign_citation":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA/action/citation_signature","submit_replication":"https://pith.science/pith/5JCMVZWHBOZYXLT2KZKUUPYBOA/action/replication_record"}},"created_at":"2026-05-18T04:41:05.361062+00:00","updated_at":"2026-05-18T04:41:05.361062+00:00"}