{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HWRHZUW3TXFODKBAAKXTDP6FRC","short_pith_number":"pith:HWRHZUW3","schema_version":"1.0","canonical_sha256":"3da27cd2db9dcae1a82002af31bfc588996e453bd8d7f543ea381dcf75394d5b","source":{"kind":"arxiv","id":"2402.01377","version":2},"attestation_state":"computed","paper":{"title":"Shifts on trees versus classical shifts in chain recurrence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Antoni L\\'opez-Mart\\'inez, Dimitris Papathanasiou","submitted_at":"2024-02-02T13:01:56Z","abstract_excerpt":"We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This construction completely solves in the negative a problem posed by Nilson C. Bernardes Jr. and Alfred Peris on chain recurrence in Linear Dynamics. In particular: we show that the non-invertible case can be directly solved via relatively simple weighted backward shifts acting on certain unrooted directed trees; then we modify the non-invertible counterexample to addr"},"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":"2402.01377","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-02-02T13:01:56Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"863f0a9b313d3a87c0d57dda221cf07bc09a70ceec0fa4756f61ab867488f78d","abstract_canon_sha256":"187cf592c623e497aa6aea8c9116dc895695b17440f8abf65ee52b7f797ab1ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:42:57.240835Z","signature_b64":"8nUHx/DWvFYHFLJn1q4rE/aUSfHlmSwOm6Z+T/MVkIZynnUOOgTvwqV818HnJCCYKVfhAHJ3k2pe4J+07KW7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3da27cd2db9dcae1a82002af31bfc588996e453bd8d7f543ea381dcf75394d5b","last_reissued_at":"2026-07-05T10:42:57.240376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:42:57.240376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shifts on trees versus classical shifts in chain recurrence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Antoni L\\'opez-Mart\\'inez, Dimitris Papathanasiou","submitted_at":"2024-02-02T13:01:56Z","abstract_excerpt":"We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This construction completely solves in the negative a problem posed by Nilson C. Bernardes Jr. and Alfred Peris on chain recurrence in Linear Dynamics. In particular: we show that the non-invertible case can be directly solved via relatively simple weighted backward shifts acting on certain unrooted directed trees; then we modify the non-invertible counterexample to addr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.01377","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/2402.01377/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":"2402.01377","created_at":"2026-07-05T10:42:57.240431+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.01377v2","created_at":"2026-07-05T10:42:57.240431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.01377","created_at":"2026-07-05T10:42:57.240431+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWRHZUW3TXFO","created_at":"2026-07-05T10:42:57.240431+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWRHZUW3TXFODKBA","created_at":"2026-07-05T10:42:57.240431+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWRHZUW3","created_at":"2026-07-05T10:42:57.240431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.14609","citing_title":"Hypercyclic algebras for weighted shifts on trees","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC","json":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC.json","graph_json":"https://pith.science/api/pith-number/HWRHZUW3TXFODKBAAKXTDP6FRC/graph.json","events_json":"https://pith.science/api/pith-number/HWRHZUW3TXFODKBAAKXTDP6FRC/events.json","paper":"https://pith.science/paper/HWRHZUW3"},"agent_actions":{"view_html":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC","download_json":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC.json","view_paper":"https://pith.science/paper/HWRHZUW3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.01377&json=true","fetch_graph":"https://pith.science/api/pith-number/HWRHZUW3TXFODKBAAKXTDP6FRC/graph.json","fetch_events":"https://pith.science/api/pith-number/HWRHZUW3TXFODKBAAKXTDP6FRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC/action/storage_attestation","attest_author":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC/action/author_attestation","sign_citation":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC/action/citation_signature","submit_replication":"https://pith.science/pith/HWRHZUW3TXFODKBAAKXTDP6FRC/action/replication_record"}},"created_at":"2026-07-05T10:42:57.240431+00:00","updated_at":"2026-07-05T10:42:57.240431+00:00"}