{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GGN47HPRMOI7XYBBAQVWLHFK7E","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":"2abe62f8a45df3fdd91162a33c3d7ff5c6de0c81e8b23e3aa28d783ed8c1f478","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-22T10:35:44Z","title_canon_sha256":"adea0fe197685e0f3bd751c9597c1db22f8d9d3b40b98b6d8ad66f5d2f26ed29"},"schema_version":"1.0","source":{"id":"1004.3885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3885","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3885v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3885","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"GGN47HPRMOI7","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GGN47HPRMOI7XYBB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GGN47HPR","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:4a510bb44d9690d170e003b5511b15a0f363a62d199a0e5adde2e5911b88971d","target":"graph","created_at":"2026-05-18T02:26:53Z","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, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of $\\mathbb{C}^d$, improving earlier results where the extension was shown for a strip. Moreover, exponential decay for such extended solutions is also proved. The results apply, in particular, to solitary wave solutions of many classical nonlinear evolution equations.","authors_text":"Fabio Nicola, Marco Cappiello","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-22T10:35:44Z","title":"Holomorphic extension of solutions of semilinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3885","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":"sha256:787ecbcd981e218cc00f5afb17c82aeab7522cef0cd275ac33de393d13680574","target":"record","created_at":"2026-05-18T02:26:53Z","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":"2abe62f8a45df3fdd91162a33c3d7ff5c6de0c81e8b23e3aa28d783ed8c1f478","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-22T10:35:44Z","title_canon_sha256":"adea0fe197685e0f3bd751c9597c1db22f8d9d3b40b98b6d8ad66f5d2f26ed29"},"schema_version":"1.0","source":{"id":"1004.3885","kind":"arxiv","version":1}},"canonical_sha256":"319bcf9df16391fbe021042b659caaf91b2c9a8462ce457bcb287f1ea7ca38e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"319bcf9df16391fbe021042b659caaf91b2c9a8462ce457bcb287f1ea7ca38e9","first_computed_at":"2026-05-18T02:26:53.257615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:53.257615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LO2y15S9SQM/3prwt+KCC5evvnb9zL7xyv/89K7/wrWsBZvIaOEa7mDQJZOTJR9D2swcTQP5dy/GtC+1pzsgDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:53.257984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:787ecbcd981e218cc00f5afb17c82aeab7522cef0cd275ac33de393d13680574","sha256:4a510bb44d9690d170e003b5511b15a0f363a62d199a0e5adde2e5911b88971d"],"state_sha256":"b388b7f9fa86b4de1ea71b5a72ef7f13a7e456eafdff3a79aa27d374c33edbe1"}