{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5SKLR3VJNOL7BTHY4BYHRJTVYC","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":"a56b273999faf5265b5d940c0e69b2d25bc44e0bbec1d31d2ced7e918665ea9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-25T17:33:41Z","title_canon_sha256":"322d426cf5cd48389173b875e39efae4cf154ab41efb7fde1329dcf7132ed964"},"schema_version":"1.0","source":{"id":"1403.6431","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6431","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6431v2","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6431","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"5SKLR3VJNOL7","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5SKLR3VJNOL7BTHY","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5SKLR3VJ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:88849d9e4b99022d50ead914ea770f1834fbedaabc32b7d04dbea01ceaed8402","target":"graph","created_at":"2026-05-18T02:19:36Z","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":"Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(\\beta)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases wh","authors_text":"Daniel Carando, Martin Mazzitelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-25T17:33:41Z","title":"Bounded holomorphic functions attaining their norms in the bidual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6431","kind":"arxiv","version":2},"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":"sha256:49504b0299915872ffcef0f898fa58051b55ebf3d8cbe94c2296a5c13101b19c","target":"record","created_at":"2026-05-18T02:19:36Z","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":"a56b273999faf5265b5d940c0e69b2d25bc44e0bbec1d31d2ced7e918665ea9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-25T17:33:41Z","title_canon_sha256":"322d426cf5cd48389173b875e39efae4cf154ab41efb7fde1329dcf7132ed964"},"schema_version":"1.0","source":{"id":"1403.6431","kind":"arxiv","version":2}},"canonical_sha256":"ec94b8eea96b97f0ccf8e07078a675c0820a6d7af8b4f59e9cfbc48c3cb48c14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec94b8eea96b97f0ccf8e07078a675c0820a6d7af8b4f59e9cfbc48c3cb48c14","first_computed_at":"2026-05-18T02:19:36.243407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:36.243407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mxo/FbGdsj2YJwySMR0evbZalOy/VnXeZGR76ZTbZEW7nQ6ezHM/4EwIzmaOzIbKBeOURgH+WSqm2M4n8SIgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:36.244049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6431","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49504b0299915872ffcef0f898fa58051b55ebf3d8cbe94c2296a5c13101b19c","sha256:88849d9e4b99022d50ead914ea770f1834fbedaabc32b7d04dbea01ceaed8402"],"state_sha256":"65f76e8e3a2a5be547d13175014404009727342ed6e9f67ff6ecd1e923ecbad7"}