{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6R5JSO3EYBFCI7IE7UTPEOFBXQ","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":"d97d64dcd7b2830b36bcc9b2d6734ea693017805992ca03c4167759a16d052f0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:15:13Z","title_canon_sha256":"c7d5e4d9bcfb9956bedac48580ad0faed3da78c8a8e39bb3036468cc0a1c2d3e"},"schema_version":"1.0","source":{"id":"1310.0951","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0951","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0951v5","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0951","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"6R5JSO3EYBFC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6R5JSO3EYBFCI7IE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6R5JSO3E","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:66ee854adac1612af6ec56465ea85b770b6c1262832d92f48eab3d7b595069b9","target":"graph","created_at":"2026-05-18T02:38:46Z","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":"Let $P$ be a classical pseudodifferential operator of complex order $m$ on an $n$-dimensional smooth manifold $\\Omega_1$. For the truncation $P_\\Omega$ to a smooth subset $\\Omega$ there is a well-known theory of boundary value problems when $P_\\Omega$ has the transmission property (preserves $C^\\infty (\\bar\\Omega)$) and is of integer order; the calculus of Boutet de Monvel. Many interesting operators, such as for example complex powers of the Laplacian $(-\\Delta)^\\mu $ with noninteger mu, are not covered. They have instead the mu-transmission property defined in H\\\"ormander's books, mapping $x","authors_text":"Gerd Grubb","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:15:13Z","title":"Fractional Laplacians on domains, a development of H\\\"ormander's theory of mu-transmission pseudodifferential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0951","kind":"arxiv","version":5},"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":"sha256:03d765926ba54b0c21a5c1e6e6c2f4da0a9efbb54ec794bc70a69f0f6fdad4df","target":"record","created_at":"2026-05-18T02:38:46Z","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":"d97d64dcd7b2830b36bcc9b2d6734ea693017805992ca03c4167759a16d052f0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:15:13Z","title_canon_sha256":"c7d5e4d9bcfb9956bedac48580ad0faed3da78c8a8e39bb3036468cc0a1c2d3e"},"schema_version":"1.0","source":{"id":"1310.0951","kind":"arxiv","version":5}},"canonical_sha256":"f47a993b64c04a247d04fd26f238a1bc085983edfbdbb5ac37f2df3910148f20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47a993b64c04a247d04fd26f238a1bc085983edfbdbb5ac37f2df3910148f20","first_computed_at":"2026-05-18T02:38:46.218057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:46.218057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvBBXMS/IupnaapubeVQGsBewej0l6raCHiHjPSKXtCss5YxyJajUKWFMhILwDet43xOB8AG6KFoS/85XDyPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:46.218654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0951","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03d765926ba54b0c21a5c1e6e6c2f4da0a9efbb54ec794bc70a69f0f6fdad4df","sha256:66ee854adac1612af6ec56465ea85b770b6c1262832d92f48eab3d7b595069b9"],"state_sha256":"0c918d3a54f89525b52ebf84713bc0b7111845d80745e80627ec626a06b5b713"}