{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U7J6HDR35IYXOXPAHG3JPAW2LQ","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":"3c73b6779c5a58ffb7361df067e38d8cfb9d42c95e5f9578d2f5ef60caf14992","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-16T19:51:37Z","title_canon_sha256":"14dc0e349f6a0b3db369b711b5972133e07f272f58608a08ec8402fd455d9a18"},"schema_version":"1.0","source":{"id":"1804.05913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05913","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05913v2","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05913","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"pith_short_12","alias_value":"U7J6HDR35IYX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U7J6HDR35IYXOXPA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U7J6HDR3","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:ed5d1a2a9e515c1e0c447d142fd961c55293d669a538a20cca465833b30a1c45","target":"graph","created_at":"2026-05-17T23:42:58Z","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 study $C^1$-robustly transitive and nonhyperbolic diffeomorphisms having a partially hyperbolic splitting with one-dimensional central bundle whose strong un-/stable foliations are both minimal. {In dimension $3$, an important class of examples of such systems is given by those with a simple closed periodic curve tangent to the central bundle.} We prove that there is a $C^1$-open and dense subset of such diffeomorphisms such that every nonhyperbolic ergodic measure (i.e. with zero central exponent) can be approximated in the weak$\\ast$ topology and in entropy by measures supported in basic ","authors_text":"Bruno Santiago, Katrin Gelfert, Lorenzo J. D\\'iaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-16T19:51:37Z","title":"Weak* and entropy approximation of nonhyperbolic measures: a geometrical approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05913","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:dbdc587f1ff661bc0c18bd4f2fe2a67561466a7dc611f1074f8c05bb541020af","target":"record","created_at":"2026-05-17T23:42:58Z","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":"3c73b6779c5a58ffb7361df067e38d8cfb9d42c95e5f9578d2f5ef60caf14992","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-16T19:51:37Z","title_canon_sha256":"14dc0e349f6a0b3db369b711b5972133e07f272f58608a08ec8402fd455d9a18"},"schema_version":"1.0","source":{"id":"1804.05913","kind":"arxiv","version":2}},"canonical_sha256":"a7d3e38e3bea31775de039b69782da5c1d200e7311ca4e6ea6389d60358f4f8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7d3e38e3bea31775de039b69782da5c1d200e7311ca4e6ea6389d60358f4f8d","first_computed_at":"2026-05-17T23:42:58.968336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:58.968336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IbYZn+oGtLeHzGEm3lakuN3AIYSdskHQO0CwUlgm3RvTWmyXY9u8NpvidcMxLggvuuULRNyGp6MRRzQx7OLZBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:58.968786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbdc587f1ff661bc0c18bd4f2fe2a67561466a7dc611f1074f8c05bb541020af","sha256:ed5d1a2a9e515c1e0c447d142fd961c55293d669a538a20cca465833b30a1c45"],"state_sha256":"9868585bdd812f582f98596b80b4183ab6c8ddb6f0422de3d6f1661aac70bf0d"}