{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6O2TKOC2WNP4N7I2TZDGQ6EKZE","short_pith_number":"pith:6O2TKOC2","schema_version":"1.0","canonical_sha256":"f3b535385ab35fc6fd1a9e4668788ac91fa6ab35d9500a7f22a5290ac82ff7f4","source":{"kind":"arxiv","id":"1705.03619","version":1},"attestation_state":"computed","paper":{"title":"Weak-2-local isometries on uniform algebras and Lipschitz algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Antonio M. Peralta, Lei Li, Liguang Wang, Ya-Shu Wang","submitted_at":"2017-05-10T06:35:36Z","abstract_excerpt":"We establish spherical variants of the Gleason-Kahane-Zelazko and Kowalski-S{\\l}odkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka and H. Takagi in 2007.\n  Another application is given in the setting of weak-2-local isometries between Lipschitz algebras by showing that given two metric spaces $E$ and $F$ such that the set Iso$((\\hbox{Lip}(E),\\|.\\|),(\\hbox{Lip}(F),\\|.\\|))$ is canonical, then every\\hyphenation{every} weak-2-local Iso"},"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":"1705.03619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-10T06:35:36Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cc9c48ea386e1e10ce94768e3f23e29094e06c09bb7827e1ae03be984e189110","abstract_canon_sha256":"5a750c3786ad4cd54bf3e89b4c2d535952ac680c464858fad8d656ef9abbcd3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:43.427139Z","signature_b64":"2LqhH0Uze536FrHwCwvXd1JGNN2qRDYLpaMA1Htw7dh5p1LfRBIsXoNZ+lQ+loXLXKCZFPWngYbuxHGzGutgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3b535385ab35fc6fd1a9e4668788ac91fa6ab35d9500a7f22a5290ac82ff7f4","last_reissued_at":"2026-05-18T00:44:43.426571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:43.426571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak-2-local isometries on uniform algebras and Lipschitz algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Antonio M. Peralta, Lei Li, Liguang Wang, Ya-Shu Wang","submitted_at":"2017-05-10T06:35:36Z","abstract_excerpt":"We establish spherical variants of the Gleason-Kahane-Zelazko and Kowalski-S{\\l}odkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka and H. Takagi in 2007.\n  Another application is given in the setting of weak-2-local isometries between Lipschitz algebras by showing that given two metric spaces $E$ and $F$ such that the set Iso$((\\hbox{Lip}(E),\\|.\\|),(\\hbox{Lip}(F),\\|.\\|))$ is canonical, then every\\hyphenation{every} weak-2-local Iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03619","kind":"arxiv","version":1},"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":"1705.03619","created_at":"2026-05-18T00:44:43.426663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03619v1","created_at":"2026-05-18T00:44:43.426663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03619","created_at":"2026-05-18T00:44:43.426663+00:00"},{"alias_kind":"pith_short_12","alias_value":"6O2TKOC2WNP4","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6O2TKOC2WNP4N7I2","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6O2TKOC2","created_at":"2026-05-18T12:31:03.183658+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/6O2TKOC2WNP4N7I2TZDGQ6EKZE","json":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE.json","graph_json":"https://pith.science/api/pith-number/6O2TKOC2WNP4N7I2TZDGQ6EKZE/graph.json","events_json":"https://pith.science/api/pith-number/6O2TKOC2WNP4N7I2TZDGQ6EKZE/events.json","paper":"https://pith.science/paper/6O2TKOC2"},"agent_actions":{"view_html":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE","download_json":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE.json","view_paper":"https://pith.science/paper/6O2TKOC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03619&json=true","fetch_graph":"https://pith.science/api/pith-number/6O2TKOC2WNP4N7I2TZDGQ6EKZE/graph.json","fetch_events":"https://pith.science/api/pith-number/6O2TKOC2WNP4N7I2TZDGQ6EKZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE/action/storage_attestation","attest_author":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE/action/author_attestation","sign_citation":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE/action/citation_signature","submit_replication":"https://pith.science/pith/6O2TKOC2WNP4N7I2TZDGQ6EKZE/action/replication_record"}},"created_at":"2026-05-18T00:44:43.426663+00:00","updated_at":"2026-05-18T00:44:43.426663+00:00"}