{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:E22HY45TWFFSE4TYSMHKUBBKF6","short_pith_number":"pith:E22HY45T","schema_version":"1.0","canonical_sha256":"26b47c73b3b14b227278930eaa042a2f8e21b1409942988fdaa714c7a60fecac","source":{"kind":"arxiv","id":"1010.0721","version":2},"attestation_state":"computed","paper":{"title":"Entropy-expansiveness for partially hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jose L. Vieitez, Lorenzo J. Diaz, Maria J. Pacifico, Todd Fisher","submitted_at":"2010-10-04T22:19:05Z","abstract_excerpt":"We show that diffeomorphisms with a dominated splitting of the form $E^s\\oplus E^c\\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states."},"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":"1010.0721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-04T22:19:05Z","cross_cats_sorted":[],"title_canon_sha256":"eb246fe61910914de309aab65e09e721216d0d625bfc47383fbc2b0b4c74a732","abstract_canon_sha256":"1191f08a36d1efe71d0721160cc066a4f5bbb465ea5e4adfbbbbce02aed8617a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:48.332161Z","signature_b64":"2vVIQeteDaYuDlltlGEGNvRa+8MmgqPymAxgYRSZUOJbX2VTJFj7n1nC17Qmk5Vfu27ZrKqZvt+0RlBknweSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26b47c73b3b14b227278930eaa042a2f8e21b1409942988fdaa714c7a60fecac","last_reissued_at":"2026-05-18T04:10:48.331469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:48.331469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy-expansiveness for partially hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jose L. Vieitez, Lorenzo J. Diaz, Maria J. Pacifico, Todd Fisher","submitted_at":"2010-10-04T22:19:05Z","abstract_excerpt":"We show that diffeomorphisms with a dominated splitting of the form $E^s\\oplus E^c\\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0721","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":"1010.0721","created_at":"2026-05-18T04:10:48.331582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.0721v2","created_at":"2026-05-18T04:10:48.331582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0721","created_at":"2026-05-18T04:10:48.331582+00:00"},{"alias_kind":"pith_short_12","alias_value":"E22HY45TWFFS","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"E22HY45TWFFSE4TY","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"E22HY45T","created_at":"2026-05-18T12:26:06.534383+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/E22HY45TWFFSE4TYSMHKUBBKF6","json":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6.json","graph_json":"https://pith.science/api/pith-number/E22HY45TWFFSE4TYSMHKUBBKF6/graph.json","events_json":"https://pith.science/api/pith-number/E22HY45TWFFSE4TYSMHKUBBKF6/events.json","paper":"https://pith.science/paper/E22HY45T"},"agent_actions":{"view_html":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6","download_json":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6.json","view_paper":"https://pith.science/paper/E22HY45T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.0721&json=true","fetch_graph":"https://pith.science/api/pith-number/E22HY45TWFFSE4TYSMHKUBBKF6/graph.json","fetch_events":"https://pith.science/api/pith-number/E22HY45TWFFSE4TYSMHKUBBKF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6/action/storage_attestation","attest_author":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6/action/author_attestation","sign_citation":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6/action/citation_signature","submit_replication":"https://pith.science/pith/E22HY45TWFFSE4TYSMHKUBBKF6/action/replication_record"}},"created_at":"2026-05-18T04:10:48.331582+00:00","updated_at":"2026-05-18T04:10:48.331582+00:00"}