{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PIZ7LCGRK4JI6BLMSH2TELJB77","short_pith_number":"pith:PIZ7LCGR","schema_version":"1.0","canonical_sha256":"7a33f588d157128f056c91f5322d21ffc305384a7c383a3ca0cc72757af859ae","source":{"kind":"arxiv","id":"1404.6686","version":4},"attestation_state":"computed","paper":{"title":"Iterates of dynamical systems on compact metrizable countable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Uzc\\'ategui, S. Garc\\'ia-Ferreira, Y. Rodriguez-L\\'opez","submitted_at":"2014-04-26T21:29:50Z","abstract_excerpt":"Given a dynamical system $(X,f)$, we let $E(X,f)$ denote its Ellis semigroup and $E(X,f)^* = E(X,f) \\setminus \\{f^n : n \\in \\mathbb{N}\\}$. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We show that if $(X,f)$ is a dynamical system such that $X$ is a compact metric countable space and every accumulation point $X'$ is periodic, then either each function of $E(X,f)^*$ is continuous or each function of $E(X,f)^*$ is discontinuous. We describe an example of a dynamical system $(X,f)$ where $X$ is a compact metric countable space, the "},"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":"1404.6686","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-04-26T21:29:50Z","cross_cats_sorted":[],"title_canon_sha256":"6e06ce4dea657a6f008564bbc5a230d241f755919dd9b6c45d76b8d9b41721fb","abstract_canon_sha256":"1094e5b76dac8ee494e0082318e2cdeff77fc8572f5510cf7ad96ec8699b5a80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:38.079651Z","signature_b64":"GEjx5nYS2xEzHWj7msKlDfEAz0KweBLCEfkqv7LfkSxUh0WmyHmgHZHnva+h0z0mk8rcymqsu0kLJZ0Vl5U1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a33f588d157128f056c91f5322d21ffc305384a7c383a3ca0cc72757af859ae","last_reissued_at":"2026-05-18T01:21:38.078963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:38.078963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterates of dynamical systems on compact metrizable countable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Uzc\\'ategui, S. Garc\\'ia-Ferreira, Y. Rodriguez-L\\'opez","submitted_at":"2014-04-26T21:29:50Z","abstract_excerpt":"Given a dynamical system $(X,f)$, we let $E(X,f)$ denote its Ellis semigroup and $E(X,f)^* = E(X,f) \\setminus \\{f^n : n \\in \\mathbb{N}\\}$. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We show that if $(X,f)$ is a dynamical system such that $X$ is a compact metric countable space and every accumulation point $X'$ is periodic, then either each function of $E(X,f)^*$ is continuous or each function of $E(X,f)^*$ is discontinuous. We describe an example of a dynamical system $(X,f)$ where $X$ is a compact metric countable space, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6686","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":"1404.6686","created_at":"2026-05-18T01:21:38.079059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6686v4","created_at":"2026-05-18T01:21:38.079059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6686","created_at":"2026-05-18T01:21:38.079059+00:00"},{"alias_kind":"pith_short_12","alias_value":"PIZ7LCGRK4JI","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PIZ7LCGRK4JI6BLM","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PIZ7LCGR","created_at":"2026-05-18T12:28:43.426989+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/PIZ7LCGRK4JI6BLMSH2TELJB77","json":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77.json","graph_json":"https://pith.science/api/pith-number/PIZ7LCGRK4JI6BLMSH2TELJB77/graph.json","events_json":"https://pith.science/api/pith-number/PIZ7LCGRK4JI6BLMSH2TELJB77/events.json","paper":"https://pith.science/paper/PIZ7LCGR"},"agent_actions":{"view_html":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77","download_json":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77.json","view_paper":"https://pith.science/paper/PIZ7LCGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6686&json=true","fetch_graph":"https://pith.science/api/pith-number/PIZ7LCGRK4JI6BLMSH2TELJB77/graph.json","fetch_events":"https://pith.science/api/pith-number/PIZ7LCGRK4JI6BLMSH2TELJB77/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77/action/storage_attestation","attest_author":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77/action/author_attestation","sign_citation":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77/action/citation_signature","submit_replication":"https://pith.science/pith/PIZ7LCGRK4JI6BLMSH2TELJB77/action/replication_record"}},"created_at":"2026-05-18T01:21:38.079059+00:00","updated_at":"2026-05-18T01:21:38.079059+00:00"}