{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LDL7SPG33GEUC54QJDK3AXHWLK","short_pith_number":"pith:LDL7SPG3","schema_version":"1.0","canonical_sha256":"58d7f93cdbd98941779048d5b05cf65aba670881b79d6194591f47a8bfa3c621","source":{"kind":"arxiv","id":"2401.01131","version":2},"attestation_state":"computed","paper":{"title":"Strong universality, recurrence, and analytic P-ideals in dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti","submitted_at":"2024-01-02T10:13:15Z","abstract_excerpt":"Given a dynamical system $(X,T)$ and a family $\\mathsf{I}\\subseteq \\mathcal{P}(\\omega)$ of \"small\" sets of nonnegative integers, a point $x \\in X$ is said to be $\\mathsf{I}$-strong universal if for each $y \\in X$ there exists a subsequence $(T^nx: n \\in A)$ of its orbit which is convergent to $y$ and, in addition, the set of indexes $A$ is \"not small,\" that is, $A\\notin \\mathsf{I}$. An analoguous definition is given for $\\mathsf{I}$-strong recurrence. In this work, we provide several structural properties and relationships between $\\mathsf{I}$-strong universality, $\\mathsf{I}$-strong recurrenc"},"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":"2401.01131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-01-02T10:13:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a2f302391edee9e9de571111226d8e36309bd1fc6e4809df672064c39ba0dcb0","abstract_canon_sha256":"a84d79d1d48158c7f3e5104796d9975c4992fe008413e233e54a1906453cd7eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:00:36.041477Z","signature_b64":"QTv4Q6CqMfSaFkDvKzeJ7k/goWUvZoKFOk9+S37tIBRLBHlEWXIehzivWV/cmf6uZArUL7B1//pzNklZB5VNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d7f93cdbd98941779048d5b05cf65aba670881b79d6194591f47a8bfa3c621","last_reissued_at":"2026-07-05T11:00:36.040936Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:00:36.040936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong universality, recurrence, and analytic P-ideals in dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti","submitted_at":"2024-01-02T10:13:15Z","abstract_excerpt":"Given a dynamical system $(X,T)$ and a family $\\mathsf{I}\\subseteq \\mathcal{P}(\\omega)$ of \"small\" sets of nonnegative integers, a point $x \\in X$ is said to be $\\mathsf{I}$-strong universal if for each $y \\in X$ there exists a subsequence $(T^nx: n \\in A)$ of its orbit which is convergent to $y$ and, in addition, the set of indexes $A$ is \"not small,\" that is, $A\\notin \\mathsf{I}$. An analoguous definition is given for $\\mathsf{I}$-strong recurrence. In this work, we provide several structural properties and relationships between $\\mathsf{I}$-strong universality, $\\mathsf{I}$-strong recurrenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01131","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.01131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2401.01131","created_at":"2026-07-05T11:00:36.041002+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.01131v2","created_at":"2026-07-05T11:00:36.041002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01131","created_at":"2026-07-05T11:00:36.041002+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDL7SPG33GEU","created_at":"2026-07-05T11:00:36.041002+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDL7SPG33GEUC54Q","created_at":"2026-07-05T11:00:36.041002+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDL7SPG3","created_at":"2026-07-05T11:00:36.041002+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.22341","citing_title":"On the complexity of upper frequently hypercyclic vectors","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK","json":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK.json","graph_json":"https://pith.science/api/pith-number/LDL7SPG33GEUC54QJDK3AXHWLK/graph.json","events_json":"https://pith.science/api/pith-number/LDL7SPG33GEUC54QJDK3AXHWLK/events.json","paper":"https://pith.science/paper/LDL7SPG3"},"agent_actions":{"view_html":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK","download_json":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK.json","view_paper":"https://pith.science/paper/LDL7SPG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.01131&json=true","fetch_graph":"https://pith.science/api/pith-number/LDL7SPG33GEUC54QJDK3AXHWLK/graph.json","fetch_events":"https://pith.science/api/pith-number/LDL7SPG33GEUC54QJDK3AXHWLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK/action/storage_attestation","attest_author":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK/action/author_attestation","sign_citation":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK/action/citation_signature","submit_replication":"https://pith.science/pith/LDL7SPG33GEUC54QJDK3AXHWLK/action/replication_record"}},"created_at":"2026-07-05T11:00:36.041002+00:00","updated_at":"2026-07-05T11:00:36.041002+00:00"}