{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OPMCCKOAGFQPCF4DG75KDW7UDG","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":"9adf03dfb8c5a756f9b7e31bbf2c0b58bb02cf4736907500036048494c0b04ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T12:51:49Z","title_canon_sha256":"2844431adc0509b4e68ea6a216cfd3d1260d581df09fc7cb6af405dbe454e4fe"},"schema_version":"1.0","source":{"id":"1504.00831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00831","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00831v1","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00831","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"OPMCCKOAGFQP","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OPMCCKOAGFQPCF4D","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OPMCCKOA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:7e05e2b7f1a96dec145918e027418e2fa40c367e63a5fb6b866ea82ffe629785","target":"graph","created_at":"2026-05-18T02:19:36Z","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":"We prove for some singular kernels $K(x,y)$ that viscosity solutions of the integro-differential equation $\\int_{\\mathbb{R}^n} \\left[u(x+y)+u(x-y)-2u(x)\\right]\\,K(x,y)dy=f(x)$ locally belong to some Gevrey class if so does $f$. The fractional Laplacian equation is included in this framework as a special case.","authors_text":"Alessio Fiscella, Enrico Valdinoci, Guglielmo Albanese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T12:51:49Z","title":"Gevrey regularity for integro-differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00831","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":"sha256:6733f5fceb7b8a642fedfc70c070f55bb7e387bfa29f026866c7614d81da0ed7","target":"record","created_at":"2026-05-18T02:19:36Z","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":"9adf03dfb8c5a756f9b7e31bbf2c0b58bb02cf4736907500036048494c0b04ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T12:51:49Z","title_canon_sha256":"2844431adc0509b4e68ea6a216cfd3d1260d581df09fc7cb6af405dbe454e4fe"},"schema_version":"1.0","source":{"id":"1504.00831","kind":"arxiv","version":1}},"canonical_sha256":"73d82129c03160f1178337faa1dbf4198b3fb1c2ffc99ae5b4b448f427729775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73d82129c03160f1178337faa1dbf4198b3fb1c2ffc99ae5b4b448f427729775","first_computed_at":"2026-05-18T02:19:36.943673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:36.943673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Th9/67GzIkBUD8yGQlzpYPbmlMWOvTqq7cj0QiRx89i2lXJbjVDV5SzbaQf7u5wPSD8JXaKyKa41hYtw1MFRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:36.944152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6733f5fceb7b8a642fedfc70c070f55bb7e387bfa29f026866c7614d81da0ed7","sha256:7e05e2b7f1a96dec145918e027418e2fa40c367e63a5fb6b866ea82ffe629785"],"state_sha256":"29ab39f5a2d280bd23b58a3c123b09fd4ef96082bdd6f385e3bfdad757d933aa"}