{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KNREF35F7D2TEJEOVXVCLIPLDJ","short_pith_number":"pith:KNREF35F","schema_version":"1.0","canonical_sha256":"536242efa5f8f532248eadea25a1eb1a6357686885b6ca5e6793dad99e18baff","source":{"kind":"arxiv","id":"1201.4806","version":2},"attestation_state":"computed","paper":{"title":"Robust Transitivity for Endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cristina Lizana, Enrique Pujals","submitted_at":"2012-01-23T18:40:51Z","abstract_excerpt":"We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large class of examples, for endomorphisms on the n-dimensional torus to be robustly transitive: the endomorphism must be volume expanding and any large connected arc must contain a point such that its future orbit belong to an expanding region."},"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":"1201.4806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-23T18:40:51Z","cross_cats_sorted":[],"title_canon_sha256":"795687b51a72aac766f6496e1d3ca49d2f64515fb2be2d5003ff360f1cf22ffa","abstract_canon_sha256":"04f5537e797225f5cf740b0ab7bd10f983de16be610a8203a9b4be5b079a5196"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.088190Z","signature_b64":"aJENtBxkhfz6ybdWZtImRyhK5i3gTYUs+zYUxMU7aOolM+4usm0yk3R+vz31wDP2tgsN+7afbOAzeKsnAAbjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"536242efa5f8f532248eadea25a1eb1a6357686885b6ca5e6793dad99e18baff","last_reissued_at":"2026-05-18T03:59:49.087822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.087822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust Transitivity for Endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cristina Lizana, Enrique Pujals","submitted_at":"2012-01-23T18:40:51Z","abstract_excerpt":"We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large class of examples, for endomorphisms on the n-dimensional torus to be robustly transitive: the endomorphism must be volume expanding and any large connected arc must contain a point such that its future orbit belong to an expanding region."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4806","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":"1201.4806","created_at":"2026-05-18T03:59:49.087876+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4806v2","created_at":"2026-05-18T03:59:49.087876+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4806","created_at":"2026-05-18T03:59:49.087876+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNREF35F7D2T","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNREF35F7D2TEJEO","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNREF35F","created_at":"2026-05-18T12:27:11.947152+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/KNREF35F7D2TEJEOVXVCLIPLDJ","json":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ.json","graph_json":"https://pith.science/api/pith-number/KNREF35F7D2TEJEOVXVCLIPLDJ/graph.json","events_json":"https://pith.science/api/pith-number/KNREF35F7D2TEJEOVXVCLIPLDJ/events.json","paper":"https://pith.science/paper/KNREF35F"},"agent_actions":{"view_html":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ","download_json":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ.json","view_paper":"https://pith.science/paper/KNREF35F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4806&json=true","fetch_graph":"https://pith.science/api/pith-number/KNREF35F7D2TEJEOVXVCLIPLDJ/graph.json","fetch_events":"https://pith.science/api/pith-number/KNREF35F7D2TEJEOVXVCLIPLDJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ/action/storage_attestation","attest_author":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ/action/author_attestation","sign_citation":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ/action/citation_signature","submit_replication":"https://pith.science/pith/KNREF35F7D2TEJEOVXVCLIPLDJ/action/replication_record"}},"created_at":"2026-05-18T03:59:49.087876+00:00","updated_at":"2026-05-18T03:59:49.087876+00:00"}