{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FPFQDZXPG2EMGUVVDAK7WDBQQF","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":"bb022f925ad26ff7398a7156121cebe9417d58f099ba59f2c541abf80058f725","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-13T04:23:36Z","title_canon_sha256":"07c0880f2db45076ad569d379cedc59d45b707544a5ba2192c4bfb5d1479a330"},"schema_version":"1.0","source":{"id":"1003.2674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2674","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2674v1","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2674","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"FPFQDZXPG2EM","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FPFQDZXPG2EMGUVV","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FPFQDZXP","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:f55105be70a480a78d0122680f7100e6b9a35795036f40d2cf0d62c3b6a0be7b","target":"graph","created_at":"2026-05-18T04:19:41Z","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 the   topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We   consider those maps satisfying  the \"separation property\":  different continuity pieces have disjoint images. The continuity pieces act as stable topological manifolds while the points in the discontinuity lines, separating  different continuity pieces, act as topological saddles   with an infinite expanding rate. We prove that C0 generically  such systems exhibit one and at most a finite number of persistent periodic sinks  attract","authors_text":"Eleonora Catsigeras, Ruben Budelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-13T04:23:36Z","title":"Topological dynamics of generic piecewise continuous contractive maps in n dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2674","kind":"arxiv","version":1},"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:cf833cc1f107477c8062083d90e1e477fe8d5ab11c7123fe1b6c6f0a8b30f98a","target":"record","created_at":"2026-05-18T04:19:41Z","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":"bb022f925ad26ff7398a7156121cebe9417d58f099ba59f2c541abf80058f725","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-13T04:23:36Z","title_canon_sha256":"07c0880f2db45076ad569d379cedc59d45b707544a5ba2192c4bfb5d1479a330"},"schema_version":"1.0","source":{"id":"1003.2674","kind":"arxiv","version":1}},"canonical_sha256":"2bcb01e6ef3688c352b51815fb0c30815c1a3b631895cd3cd7b25e120c5d0cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bcb01e6ef3688c352b51815fb0c30815c1a3b631895cd3cd7b25e120c5d0cdf","first_computed_at":"2026-05-18T04:19:41.281584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:41.281584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e48TuYp0Yq3PCRV5Nra3Wzt4XxO5Zc3tFWaYHWhKE9F8/fG252USYJD0XammHYsbhFBf48Key1orY+9GResBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:41.282014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf833cc1f107477c8062083d90e1e477fe8d5ab11c7123fe1b6c6f0a8b30f98a","sha256:f55105be70a480a78d0122680f7100e6b9a35795036f40d2cf0d62c3b6a0be7b"],"state_sha256":"c1a19d509db13b17d6038a4d2f9542b6ee860d708485e21bbb003157ba290727"}