{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NKBGCLGH73HZHFUPEKRP6NE6I5","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":"93a76bd509a4406f03ff471c0f12a0bdaf221a40a60faba2b5f9d573216e6051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T10:56:52Z","title_canon_sha256":"f7b18048f59f5a95d85a33a76887d3113caa7a76379913eb465fc7f39ae9301e"},"schema_version":"1.0","source":{"id":"1802.00239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00239","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00239v1","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00239","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"NKBGCLGH73HZ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NKBGCLGH73HZHFUP","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NKBGCLGH","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:482d56ee782b2bfc721b647546ba8b13a4477edfa6782f3d37cd87c3f27f55c6","target":"graph","created_at":"2026-05-18T00:24:36Z","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":"Let $G$ be a compact group, let $X$ be a Banach space, and let $P\\colon L^1(G)\\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $\\Phi\\colon L^1(G)\\to X$ such that $P(f)=\\Phi \\bigl(f\\ast\\stackrel{n}{\\cdots}\\ast f \\bigr)$ for each $f\\in L^1(G)$. We also seek analogues of this result about $L^1(G)$ for various other convolution algebras, including $L^p(G)$, for $1< p\\le\\infty$, and $C(G)$.","authors_text":"A. R. Villena, J. Alaminos, J. Extremera, M. L. C. Godoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T10:56:52Z","title":"Orthogonally additive polynomials on convolution algebras associated with a compact group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00239","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":"sha256:25afab0ae30353f9cdf952626d23ea43cc00bf7cd6a43dc14ca44c54cc156329","target":"record","created_at":"2026-05-18T00:24:36Z","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":"93a76bd509a4406f03ff471c0f12a0bdaf221a40a60faba2b5f9d573216e6051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T10:56:52Z","title_canon_sha256":"f7b18048f59f5a95d85a33a76887d3113caa7a76379913eb465fc7f39ae9301e"},"schema_version":"1.0","source":{"id":"1802.00239","kind":"arxiv","version":1}},"canonical_sha256":"6a82612cc7fecf93968f22a2ff349e475716760d8fbeeb083e18dd86eed686fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a82612cc7fecf93968f22a2ff349e475716760d8fbeeb083e18dd86eed686fe","first_computed_at":"2026-05-18T00:24:36.467866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:36.467866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5zwSCihzgOJ6F3nZ0dfO4grlDYcqnokBpvsiF3QLYNqVorV6+5y+W6ABP4Jv3FWTcpY67q+M1HDWwOeMLH2aDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:36.468295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25afab0ae30353f9cdf952626d23ea43cc00bf7cd6a43dc14ca44c54cc156329","sha256:482d56ee782b2bfc721b647546ba8b13a4477edfa6782f3d37cd87c3f27f55c6"],"state_sha256":"0b092c0c6b8c5c4baeec6659e558e435461cdf33e7896b6b2ef167a1188838c9"}