{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PL2S6QGIIGBE2CAWALTEWPKMFH","short_pith_number":"pith:PL2S6QGI","schema_version":"1.0","canonical_sha256":"7af52f40c841824d081602e64b3d4c29eb4c86f02dfb96c4da51b1053df22d5c","source":{"kind":"arxiv","id":"1709.04983","version":1},"attestation_state":"computed","paper":{"title":"$C^1$ density of stable ergodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Avila, A. Wilkinson, S. Crovisier","submitted_at":"2017-09-14T21:29:51Z","abstract_excerpt":"We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense.\n  To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of \"superblenders\" from hyperbolic sets with large entropy."},"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":"1709.04983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-14T21:29:51Z","cross_cats_sorted":[],"title_canon_sha256":"fe2925d2ec331e8d1828e9de986ba8f86033f1b5464da25e2f992f970af1fe2f","abstract_canon_sha256":"2fb1002ce5e7173092118ecd826e5b9f9fe7c5947fff3978804910eacbc482f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:08.679720Z","signature_b64":"MLLma/fDTAeF2lXRwt9N1HXJlbBmld1rUaXGJEwRJ+TmJXWuToXvUUNyRjJepYQVb+/sX4wfzvf9U1Vq8E7gBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af52f40c841824d081602e64b3d4c29eb4c86f02dfb96c4da51b1053df22d5c","last_reissued_at":"2026-05-18T00:35:08.679359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:08.679359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C^1$ density of stable ergodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Avila, A. Wilkinson, S. Crovisier","submitted_at":"2017-09-14T21:29:51Z","abstract_excerpt":"We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense.\n  To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of \"superblenders\" from hyperbolic sets with large entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04983","kind":"arxiv","version":1},"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":"1709.04983","created_at":"2026-05-18T00:35:08.679419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04983v1","created_at":"2026-05-18T00:35:08.679419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04983","created_at":"2026-05-18T00:35:08.679419+00:00"},{"alias_kind":"pith_short_12","alias_value":"PL2S6QGIIGBE","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PL2S6QGIIGBE2CAW","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PL2S6QGI","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.04755","citing_title":"Ergodicity and partial hyperbolicity on Seifert manifolds","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH","json":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH.json","graph_json":"https://pith.science/api/pith-number/PL2S6QGIIGBE2CAWALTEWPKMFH/graph.json","events_json":"https://pith.science/api/pith-number/PL2S6QGIIGBE2CAWALTEWPKMFH/events.json","paper":"https://pith.science/paper/PL2S6QGI"},"agent_actions":{"view_html":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH","download_json":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH.json","view_paper":"https://pith.science/paper/PL2S6QGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04983&json=true","fetch_graph":"https://pith.science/api/pith-number/PL2S6QGIIGBE2CAWALTEWPKMFH/graph.json","fetch_events":"https://pith.science/api/pith-number/PL2S6QGIIGBE2CAWALTEWPKMFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH/action/storage_attestation","attest_author":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH/action/author_attestation","sign_citation":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH/action/citation_signature","submit_replication":"https://pith.science/pith/PL2S6QGIIGBE2CAWALTEWPKMFH/action/replication_record"}},"created_at":"2026-05-18T00:35:08.679419+00:00","updated_at":"2026-05-18T00:35:08.679419+00:00"}