{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TDKRBK74UES6YDW52EWHHLIV5A","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":"51fafc8a856d42ea06dab4192fcc27cc3309b21af3c4a3387477ae91b99ab909","cross_cats_sorted":["math-ph","math.MP","math.NA","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-15T17:37:17Z","title_canon_sha256":"523885c7d42a300d8fd835cf7d22dfd9abf1802fabf479a6bae06485e5bb3d9f"},"schema_version":"1.0","source":{"id":"1810.07028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07028","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07028v2","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07028","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"TDKRBK74UES6","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TDKRBK74UES6YDW5","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TDKRBK74","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:e4ece005543b164ba83b050634c479efdb7b7bdb253bc95579f66e369f17b680","target":"graph","created_at":"2026-05-17T23:47:59Z","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":"The fractional Laplacian $(- \\Delta)^{\\alpha /2}$, $\\alpha \\in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to ","authors_text":"P. Garbaczewski, V. A. Stephanovich","cross_cats":["math-ph","math.MP","math.NA","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-15T17:37:17Z","title":"Fractional Laplacians in bounded domains: Killed, reflected, censored and taboo L\\'evy flights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07028","kind":"arxiv","version":2},"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:fc906336ed6046df42a5782e727b5177749b1d317d9d2978cf7f5e9b010973f9","target":"record","created_at":"2026-05-17T23:47:59Z","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":"51fafc8a856d42ea06dab4192fcc27cc3309b21af3c4a3387477ae91b99ab909","cross_cats_sorted":["math-ph","math.MP","math.NA","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-15T17:37:17Z","title_canon_sha256":"523885c7d42a300d8fd835cf7d22dfd9abf1802fabf479a6bae06485e5bb3d9f"},"schema_version":"1.0","source":{"id":"1810.07028","kind":"arxiv","version":2}},"canonical_sha256":"98d510abfca125ec0eddd12c73ad15e824e42d681b84e4585197abed936b60f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98d510abfca125ec0eddd12c73ad15e824e42d681b84e4585197abed936b60f1","first_computed_at":"2026-05-17T23:47:59.380373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:59.380373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A1KlC1uJ1gdBI3bWjQXzLoaZ/GpPRNUR20Td3LhPVbzdefabMlM0XVEROoAopktW24/cKCplCV8cip143CRlBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:59.380872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc906336ed6046df42a5782e727b5177749b1d317d9d2978cf7f5e9b010973f9","sha256:e4ece005543b164ba83b050634c479efdb7b7bdb253bc95579f66e369f17b680"],"state_sha256":"e21b0880b22ffb160e91294c17aeb77ab4a60cecf5a70f1a9377ed928e498a3b"}