{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WXEP32Y62MQYD2UHHKS4MT64FL","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":"f59e8a6f168541bea514b5cb8c55fe80d4dc404397ad83a80e65ee73dfa57fc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:24:42Z","title_canon_sha256":"f9b9edf2357743ff2ecedb4f009f7ab5366b06129512d78e2961aceffb55297e"},"schema_version":"1.0","source":{"id":"1707.00969","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00969","created_at":"2026-05-18T00:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00969v1","created_at":"2026-05-18T00:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00969","created_at":"2026-05-18T00:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"WXEP32Y62MQY","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXEP32Y62MQYD2UH","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXEP32Y6","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:23d7cfd1086f31e23fa029bfd34df13b79c14bb590a31a29609df8f2d41d0a29","target":"graph","created_at":"2026-05-18T00:40:56Z","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 study a nonlocal Venttsel' problem in a non-convex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out and optimal a priori error estimates are obtained.","authors_text":"Maria Rosaria Lancia, Massimo Cefalo, Paola Vernole, Simone Creo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:24:42Z","title":"Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00969","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":"sha256:773076aaa1934a1fda8a0dfa3948580d775509d767d66d77da162838d8828e0b","target":"record","created_at":"2026-05-18T00:40:56Z","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":"f59e8a6f168541bea514b5cb8c55fe80d4dc404397ad83a80e65ee73dfa57fc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:24:42Z","title_canon_sha256":"f9b9edf2357743ff2ecedb4f009f7ab5366b06129512d78e2961aceffb55297e"},"schema_version":"1.0","source":{"id":"1707.00969","kind":"arxiv","version":1}},"canonical_sha256":"b5c8fdeb1ed32181ea873aa5c64fdc2acb6d9c106fd9a39652e21077f8bca75a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c8fdeb1ed32181ea873aa5c64fdc2acb6d9c106fd9a39652e21077f8bca75a","first_computed_at":"2026-05-18T00:40:56.513360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:56.513360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGrOUGUBltAFjxoZjZtUOWNDUAtDiQN6htiqnOTrC8Djemjd8iXv482Q4GdvqUsqmssH+Xc/liYW/AMoz3NFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:56.514060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00969","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:773076aaa1934a1fda8a0dfa3948580d775509d767d66d77da162838d8828e0b","sha256:23d7cfd1086f31e23fa029bfd34df13b79c14bb590a31a29609df8f2d41d0a29"],"state_sha256":"6a199c521a6dae18237acc438586930470a84f6ec90d467d42dc224be524060b"}