{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZJQ2N25DECLTKW5VT6MQUO5NEC","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":"d93ddd87fb49df4a1329e9ee30982fc6bc8fd3acffee72fb127c884095fb4f67","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-18T18:49:33Z","title_canon_sha256":"3362de18872a1de096e31015b6c75fcb0e58f80e53a8bd6ac321c59a24172dff"},"schema_version":"1.0","source":{"id":"1711.06916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06916","created_at":"2026-06-04T19:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06916v1","created_at":"2026-06-04T19:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06916","created_at":"2026-06-04T19:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZJQ2N25DECLT","created_at":"2026-06-04T19:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"ZJQ2N25DECLTKW5V","created_at":"2026-06-04T19:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"ZJQ2N25D","created_at":"2026-06-04T19:11:15Z"}],"graph_snapshots":[{"event_id":"sha256:d5f6b1a0ff0d22979c9adeb8098b6603a099355c4af050c260def1dbe044e978","target":"graph","created_at":"2026-06-04T19:11:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1711.06916/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These operators represent the infinitesimal generators of different stochastic processes, and especially their differences on a bounded domain are significant. We provide extensive numerical experiments to understand and compare their differences. We find that these four operators collapse to the classical Laplace operator as \\alpha \\to 2. The eigenvalues and eigenfunctions of these four operators are different, a","authors_text":"Hong Wang, Siwei Duo, Yanzhi Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-18T18:49:33Z","title":"A comparative study on nonlocal diffusion operators related to the fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06916","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":"sha256:50046fc32e2df421a64bdb2ada6b2454a3921a26f1d36a36932e57e7cd2356f1","target":"record","created_at":"2026-06-04T19:11:15Z","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":"d93ddd87fb49df4a1329e9ee30982fc6bc8fd3acffee72fb127c884095fb4f67","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-18T18:49:33Z","title_canon_sha256":"3362de18872a1de096e31015b6c75fcb0e58f80e53a8bd6ac321c59a24172dff"},"schema_version":"1.0","source":{"id":"1711.06916","kind":"arxiv","version":1}},"canonical_sha256":"ca61a6eba32097355bb59f990a3bad20b7e9bf530580d45c2b5f607a36cb3835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca61a6eba32097355bb59f990a3bad20b7e9bf530580d45c2b5f607a36cb3835","first_computed_at":"2026-06-04T19:11:15.505904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:15.505904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/OOhl0aQ/bQro2IogymFX+RGnOVg/LKNebHpp8MBlvRDe3BvRV3Bx6zDgUU7ao24GehIHjbCnFATuWEfKpq6BQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:15.506357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50046fc32e2df421a64bdb2ada6b2454a3921a26f1d36a36932e57e7cd2356f1","sha256:d5f6b1a0ff0d22979c9adeb8098b6603a099355c4af050c260def1dbe044e978"],"state_sha256":"f96e77ea46b262a8ab2eaaf970d61fa0b3e238d634bbcef735a46f670e225878"}