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We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic functions of bounded type $f$ over $C(K)$ is of the form $$ f(x)=\\int_K h(x) d\\mu $$ for some $\\mu$ and holomorphic $h\\colon C(K) \\to L^1(\\mu)$ of bounded type."},"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":"0810.5352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-10-29T20:23:17Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1359b51c49a11b0d7a86d9f7c38338e7f897b9462694cf553bb47d51c097d0bd","abstract_canon_sha256":"70b4952664e69b383aab0cc5d1d18c6da2e194ef709b46d1c74fdac2b92948b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:50.608183Z","signature_b64":"g1erQhDvUDZXOFfypwM/pR41zdjR9p9iiJnEdUzIuugvoxnFJbmUh6r1VuemGoZKfVR3hxBY7nSR06PQQLhuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecb5ac95f5a7a943264095134748781d633230675f29fef456ec5f1889094ea0","last_reissued_at":"2026-05-18T04:31:50.607691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:50.607691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonally additive holomorphic functions of bounded type over $C(K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Daniel Carando, Ignacio Zalduendo, Silvia Lassalle","submitted_at":"2008-10-29T20:23:17Z","abstract_excerpt":"It is known that all $k$-homogeneous orthogonally additive polynomials $P$ over $C(K)$ are of the form $$ P(x)=\\int_K x^k d\\mu . $$ Thus $x\\mapsto x^k$ factors all orthogonally additive polynomials through some linear form $\\mu$. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic functions of bounded type $f$ over $C(K)$ is of the form $$ f(x)=\\int_K h(x) d\\mu $$ for some $\\mu$ and holomorphic $h\\colon C(K) \\to L^1(\\mu)$ of bounded type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5352","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":"0810.5352","created_at":"2026-05-18T04:31:50.607754+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.5352v1","created_at":"2026-05-18T04:31:50.607754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.5352","created_at":"2026-05-18T04:31:50.607754+00:00"},{"alias_kind":"pith_short_12","alias_value":"5S22ZFPVU6UU","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"5S22ZFPVU6UUGJSA","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"5S22ZFPV","created_at":"2026-05-18T12:25:56.245647+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/5S22ZFPVU6UUGJSASUJUOSDYDV","json":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV.json","graph_json":"https://pith.science/api/pith-number/5S22ZFPVU6UUGJSASUJUOSDYDV/graph.json","events_json":"https://pith.science/api/pith-number/5S22ZFPVU6UUGJSASUJUOSDYDV/events.json","paper":"https://pith.science/paper/5S22ZFPV"},"agent_actions":{"view_html":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV","download_json":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV.json","view_paper":"https://pith.science/paper/5S22ZFPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.5352&json=true","fetch_graph":"https://pith.science/api/pith-number/5S22ZFPVU6UUGJSASUJUOSDYDV/graph.json","fetch_events":"https://pith.science/api/pith-number/5S22ZFPVU6UUGJSASUJUOSDYDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV/action/storage_attestation","attest_author":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV/action/author_attestation","sign_citation":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV/action/citation_signature","submit_replication":"https://pith.science/pith/5S22ZFPVU6UUGJSASUJUOSDYDV/action/replication_record"}},"created_at":"2026-05-18T04:31:50.607754+00:00","updated_at":"2026-05-18T04:31:50.607754+00:00"}