{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JMNNXEUM4LP34ZNG2EIF63Z77G","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":"697ef262b17dcaf9174e5d877781d89a8862d52aaac3039f5e8d28db58c8db36","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-02T20:10:30Z","title_canon_sha256":"17b0da547d6c14ee03a6d5e9831663bb3f8cefbcaa401f4badb34f0dc706dfec"},"schema_version":"1.0","source":{"id":"1510.00723","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00723","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00723v4","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00723","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"JMNNXEUM4LP3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JMNNXEUM4LP34ZNG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JMNNXEUM","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:ab6cc4e3c52197a11b3d0b5075c8803b78b0b7f0f1624b6ac7bafa27fbb135fe","target":"graph","created_at":"2026-05-17T23:52:34Z","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 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","authors_text":"Pierre-Antoine Guih\\'eneuf","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-02T20:10:30Z","title":"Degree of recurrence of generic diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00723","kind":"arxiv","version":4},"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":"sha256:8307517d87c39abfe4c7e63193537e720de0c7ad15d19a4ec8e653b24808153b","target":"record","created_at":"2026-05-17T23:52:34Z","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":"697ef262b17dcaf9174e5d877781d89a8862d52aaac3039f5e8d28db58c8db36","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-02T20:10:30Z","title_canon_sha256":"17b0da547d6c14ee03a6d5e9831663bb3f8cefbcaa401f4badb34f0dc706dfec"},"schema_version":"1.0","source":{"id":"1510.00723","kind":"arxiv","version":4}},"canonical_sha256":"4b1adb928ce2dfbe65a6d1105f6f3ff998a471773e746021692024724a19b45e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b1adb928ce2dfbe65a6d1105f6f3ff998a471773e746021692024724a19b45e","first_computed_at":"2026-05-17T23:52:34.518964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:34.518964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5yMkuhDxof4c5iPzq+yb/5ATh5K/oveOkOAsaNEK7ZoLv+/uwIvCwPWCXIEOqzjPJwk6pD9B0Snem6rFwVprDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:34.519450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00723","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8307517d87c39abfe4c7e63193537e720de0c7ad15d19a4ec8e653b24808153b","sha256:ab6cc4e3c52197a11b3d0b5075c8803b78b0b7f0f1624b6ac7bafa27fbb135fe"],"state_sha256":"cb841aedac6e525d5c89ca586320347905eb35b7b0215e64ce90131142b71a6e"}