{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y57MNR5V4URREY5WCPZHVXAPWK","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":"1c22aee3f436d03f7ba2a87e5addc44c439ae7e2f3d6bdcdc35b82651b67a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T23:57:09Z","title_canon_sha256":"8235e2b9a329e033cb7ef405dec8d098f946cd351e2adce672f88ad0315ea39f"},"schema_version":"1.0","source":{"id":"1107.1003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1003","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1003v1","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1003","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y57MNR5V4URR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y57MNR5V4URREY5W","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y57MNR5V","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:4fff17a4711b48eee380a0598e6974b96b5542de9a521089b0cd2080ae69e8ff","target":"graph","created_at":"2026-05-18T04:18:45Z","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 the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace equation.","authors_text":"Tongkeun Chang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T23:57:09Z","title":"Boundary integral operator for the fractional Laplace equation in a bounded Lipschitz domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1003","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:de031cf2586e1b463e621705b722f60ab7d8f9c59cb2364e8f183fccd14a7d16","target":"record","created_at":"2026-05-18T04:18:45Z","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":"1c22aee3f436d03f7ba2a87e5addc44c439ae7e2f3d6bdcdc35b82651b67a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T23:57:09Z","title_canon_sha256":"8235e2b9a329e033cb7ef405dec8d098f946cd351e2adce672f88ad0315ea39f"},"schema_version":"1.0","source":{"id":"1107.1003","kind":"arxiv","version":1}},"canonical_sha256":"c77ec6c7b5e5231263b613f27adc0fb2844bbf1c0d2c0cb2bd5dd26b7473064f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c77ec6c7b5e5231263b613f27adc0fb2844bbf1c0d2c0cb2bd5dd26b7473064f","first_computed_at":"2026-05-18T04:18:45.842512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:45.842512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wyO9PEMNDWW9P6cdij0k14ap6ywT3hdU9O0AMzzwNQ+J86p1/YkgORyTHWxBuJU/nvq3Jlt2TSEVxePbtq7xDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:45.843077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de031cf2586e1b463e621705b722f60ab7d8f9c59cb2364e8f183fccd14a7d16","sha256:4fff17a4711b48eee380a0598e6974b96b5542de9a521089b0cd2080ae69e8ff"],"state_sha256":"53249b1c4d83437d44d61ee842e775807210a092443dd828ba9e64b97ab855e7"}