{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RQZPHLKMELONEIGE7UCJKHBKUQ","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":"7046129997847eee8a5a549e0c0c97818354d57dc22b488b0f6a26ee00cb348b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-04T09:51:10Z","title_canon_sha256":"223093a4e99ef2910a4c0e55e77b5830f95ce67e2d4c7129a5e0e4da72b5d378"},"schema_version":"1.0","source":{"id":"1604.00793","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00793","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00793v3","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00793","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"RQZPHLKMELON","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RQZPHLKMELONEIGE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RQZPHLKM","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:9499a412730bd5d150f18578101ba7d630c48d1baa06d1a2d6ade6d08c1a2018","target":"graph","created_at":"2026-05-18T00:39:47Z","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":"This paper extends the theory of regular solutions ($C^1$ in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of $G$-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into $G$-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein-Uh","authors_text":"Fausto Gozzi, Salvatore Federico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-04T09:51:10Z","title":"Mild solutions of semilinear elliptic equations in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00793","kind":"arxiv","version":3},"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:b5506f3c40a968e51ed5240792046fd442e8f3b6c42023c29209c60e7e075ba3","target":"record","created_at":"2026-05-18T00:39:47Z","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":"7046129997847eee8a5a549e0c0c97818354d57dc22b488b0f6a26ee00cb348b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-04T09:51:10Z","title_canon_sha256":"223093a4e99ef2910a4c0e55e77b5830f95ce67e2d4c7129a5e0e4da72b5d378"},"schema_version":"1.0","source":{"id":"1604.00793","kind":"arxiv","version":3}},"canonical_sha256":"8c32f3ad4c22dcd220c4fd04951c2aa42b025dd554c2ec2e48a2894aa215d59a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c32f3ad4c22dcd220c4fd04951c2aa42b025dd554c2ec2e48a2894aa215d59a","first_computed_at":"2026-05-18T00:39:47.837098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:47.837098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEzfUFZYO6zCPeNKRimojWpw3N2R0QYTDH0aHxrW0xO1YUbSUhqo70ZpjglxkcTsl+bB9+AhpEYboM5wmAo4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:47.837821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00793","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5506f3c40a968e51ed5240792046fd442e8f3b6c42023c29209c60e7e075ba3","sha256:9499a412730bd5d150f18578101ba7d630c48d1baa06d1a2d6ade6d08c1a2018"],"state_sha256":"d0719a5c84664bcd11584315783cd22d1f84d9b0d43af16a11a18a08a9ae6887"}