{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VH2BLD5DYMVJVQ6HWW2LXHQVFM","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":"542e6ceb901d9c37a035d687418c411ddf0c598b0dbe354d82aede5229e8aa0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T14:04:00Z","title_canon_sha256":"71e39e73c314607574bd3edbaee48e127a8cc5c24dfbddaddb7fa7d83e3753e2"},"schema_version":"1.0","source":{"id":"1805.09685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09685","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09685v1","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09685","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"VH2BLD5DYMVJ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VH2BLD5DYMVJVQ6H","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VH2BLD5D","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:dd45019cd703c834938a8786b1514ddd99275b4b483999f79684837656324a94","target":"graph","created_at":"2026-05-18T00:15:03Z","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":"We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are following a different approach than the results obtained in [11], more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case.","authors_text":"Gerhard Schindl, Javier Jim\\'enez-Garrido, Javier Sanz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T14:04:00Z","title":"Sectorial extensions for ultraholomorphic classes defined by weight functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09685","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:fc63303148eef7cb7b00f3fd380ed48be82e0ff156fa3f866d02d5c9e3c4038f","target":"record","created_at":"2026-05-18T00:15:03Z","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":"542e6ceb901d9c37a035d687418c411ddf0c598b0dbe354d82aede5229e8aa0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T14:04:00Z","title_canon_sha256":"71e39e73c314607574bd3edbaee48e127a8cc5c24dfbddaddb7fa7d83e3753e2"},"schema_version":"1.0","source":{"id":"1805.09685","kind":"arxiv","version":1}},"canonical_sha256":"a9f4158fa3c32a9ac3c7b5b4bb9e152b1eed231a68bc9f9afe068497873ec4b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9f4158fa3c32a9ac3c7b5b4bb9e152b1eed231a68bc9f9afe068497873ec4b0","first_computed_at":"2026-05-18T00:15:03.144779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:03.144779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SEjFFAGppmf6vVPDXXf3MMwviAz44BeKfqWuxoEtTYi99lQW1Y8RRbux+3dHAv/AlL4v8zwzZnM1PaU6VHinBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:03.145410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc63303148eef7cb7b00f3fd380ed48be82e0ff156fa3f866d02d5c9e3c4038f","sha256:dd45019cd703c834938a8786b1514ddd99275b4b483999f79684837656324a94"],"state_sha256":"09849a31c61b1ddc9b6be0469fc4e740a2bd0870abcdfd6ebac773cfe7e725a8"}