{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JMNNXEUM4LP34ZNG2EIF63Z77G","short_pith_number":"pith:JMNNXEUM","schema_version":"1.0","canonical_sha256":"4b1adb928ce2dfbe65a6d1105f6f3ff998a471773e746021692024724a19b45e","source":{"kind":"arxiv","id":"1510.00723","version":4},"attestation_state":"computed","paper":{"title":"Degree of recurrence of generic diffeomorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.DS","authors_text":"Pierre-Antoine Guih\\'eneuf","submitted_at":"2015-10-02T20:10:30Z","abstract_excerpt":"We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of orbits with a fixed number of digits. We show that for every $r\\ge 1$, the dynamics of the discretizations of a $C^r$ generic conservative diffeomorphism of the torus is very different from that observed in the $C^0$ regularity. The proof of our results involves in particular a local-global formula for discretizations, as well as a study of the corresponding li"},"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":"1510.00723","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-02T20:10:30Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"17b0da547d6c14ee03a6d5e9831663bb3f8cefbcaa401f4badb34f0dc706dfec","abstract_canon_sha256":"697ef262b17dcaf9174e5d877781d89a8862d52aaac3039f5e8d28db58c8db36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:34.519450Z","signature_b64":"5yMkuhDxof4c5iPzq+yb/5ATh5K/oveOkOAsaNEK7ZoLv+/uwIvCwPWCXIEOqzjPJwk6pD9B0Snem6rFwVprDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b1adb928ce2dfbe65a6d1105f6f3ff998a471773e746021692024724a19b45e","last_reissued_at":"2026-05-17T23:52:34.518964Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:34.518964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degree of recurrence of generic diffeomorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.DS","authors_text":"Pierre-Antoine Guih\\'eneuf","submitted_at":"2015-10-02T20:10:30Z","abstract_excerpt":"We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of orbits with a fixed number of digits. We show that for every $r\\ge 1$, the dynamics of the discretizations of a $C^r$ generic conservative diffeomorphism of the torus is very different from that observed in the $C^0$ regularity. The proof of our results involves in particular a local-global formula for discretizations, as well as a study of the corresponding li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00723","kind":"arxiv","version":4},"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":"1510.00723","created_at":"2026-05-17T23:52:34.519035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00723v4","created_at":"2026-05-17T23:52:34.519035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00723","created_at":"2026-05-17T23:52:34.519035+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMNNXEUM4LP3","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMNNXEUM4LP34ZNG","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMNNXEUM","created_at":"2026-05-18T12:29:27.538025+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/JMNNXEUM4LP34ZNG2EIF63Z77G","json":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G.json","graph_json":"https://pith.science/api/pith-number/JMNNXEUM4LP34ZNG2EIF63Z77G/graph.json","events_json":"https://pith.science/api/pith-number/JMNNXEUM4LP34ZNG2EIF63Z77G/events.json","paper":"https://pith.science/paper/JMNNXEUM"},"agent_actions":{"view_html":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G","download_json":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G.json","view_paper":"https://pith.science/paper/JMNNXEUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00723&json=true","fetch_graph":"https://pith.science/api/pith-number/JMNNXEUM4LP34ZNG2EIF63Z77G/graph.json","fetch_events":"https://pith.science/api/pith-number/JMNNXEUM4LP34ZNG2EIF63Z77G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G/action/storage_attestation","attest_author":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G/action/author_attestation","sign_citation":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G/action/citation_signature","submit_replication":"https://pith.science/pith/JMNNXEUM4LP34ZNG2EIF63Z77G/action/replication_record"}},"created_at":"2026-05-17T23:52:34.519035+00:00","updated_at":"2026-05-17T23:52:34.519035+00:00"}