{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5S22ZFPVU6UUGJSASUJUOSDYDV","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":"70b4952664e69b383aab0cc5d1d18c6da2e194ef709b46d1c74fdac2b92948b8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-10-29T20:23:17Z","title_canon_sha256":"1359b51c49a11b0d7a86d9f7c38338e7f897b9462694cf553bb47d51c097d0bd"},"schema_version":"1.0","source":{"id":"0810.5352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.5352","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"arxiv_version","alias_value":"0810.5352v1","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.5352","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"pith_short_12","alias_value":"5S22ZFPVU6UU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5S22ZFPVU6UUGJSA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5S22ZFPV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9e519defecc6fe72a4618bd6c52e8ccbdc1bfbd5f13ae601ccc231026f9245e5","target":"graph","created_at":"2026-05-18T04:31:50Z","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":"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.","authors_text":"Daniel Carando, Ignacio Zalduendo, Silvia Lassalle","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-10-29T20:23:17Z","title":"Orthogonally additive holomorphic functions of bounded type over $C(K)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5352","kind":"arxiv","version":1},"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":"sha256:361b10f2ed1deb5bf1c70024a2c52ab5f209dbb7526f2d822a870e33ecc92e57","target":"record","created_at":"2026-05-18T04:31:50Z","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":"70b4952664e69b383aab0cc5d1d18c6da2e194ef709b46d1c74fdac2b92948b8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-10-29T20:23:17Z","title_canon_sha256":"1359b51c49a11b0d7a86d9f7c38338e7f897b9462694cf553bb47d51c097d0bd"},"schema_version":"1.0","source":{"id":"0810.5352","kind":"arxiv","version":1}},"canonical_sha256":"ecb5ac95f5a7a943264095134748781d633230675f29fef456ec5f1889094ea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecb5ac95f5a7a943264095134748781d633230675f29fef456ec5f1889094ea0","first_computed_at":"2026-05-18T04:31:50.607691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:50.607691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1erQhDvUDZXOFfypwM/pR41zdjR9p9iiJnEdUzIuugvoxnFJbmUh6r1VuemGoZKfVR3hxBY7nSR06PQQLhuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:50.608183Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.5352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:361b10f2ed1deb5bf1c70024a2c52ab5f209dbb7526f2d822a870e33ecc92e57","sha256:9e519defecc6fe72a4618bd6c52e8ccbdc1bfbd5f13ae601ccc231026f9245e5"],"state_sha256":"c172db66b121b1e06293fdacd5b23bd31d11b18c92087ca41870064df75821f6"}