{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PK7VBEKYMB6PPRUBFZVDHR5FJ5","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":"ac6fd7e1b831f846c36ff257626268a0a5a678f90cf0013cd3450743a4d77102","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T01:50:37Z","title_canon_sha256":"f85f7b382cfefc9aaa2c868aed974e6d8baf732f157d9ff082d166cee101a3df"},"schema_version":"1.0","source":{"id":"1111.4712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4712","created_at":"2026-05-18T04:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4712v1","created_at":"2026-05-18T04:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4712","created_at":"2026-05-18T04:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"PK7VBEKYMB6P","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PK7VBEKYMB6PPRUB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PK7VBEKY","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:9d8b3f252248e65075bd5b5a2c467523963dbb3a11c3e697d777edd4eaf0901f","target":"graph","created_at":"2026-05-18T04:08:02Z","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":"In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\\'evy processes.","authors_text":"Kyeong-Hun Kim, Panki Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T01:50:37Z","title":"An L_p-theory of stochastic parabolic equations with the random fractional Laplacian driven by L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4712","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":"sha256:865989d869902c00cf0818a97952917d4a0c8f494f7c49338d1f49e092a3f161","target":"record","created_at":"2026-05-18T04:08:02Z","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":"ac6fd7e1b831f846c36ff257626268a0a5a678f90cf0013cd3450743a4d77102","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T01:50:37Z","title_canon_sha256":"f85f7b382cfefc9aaa2c868aed974e6d8baf732f157d9ff082d166cee101a3df"},"schema_version":"1.0","source":{"id":"1111.4712","kind":"arxiv","version":1}},"canonical_sha256":"7abf509158607cf7c6812e6a33c7a54f7037c2012cb0faab5ebb7da452810f1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7abf509158607cf7c6812e6a33c7a54f7037c2012cb0faab5ebb7da452810f1b","first_computed_at":"2026-05-18T04:08:02.783871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:02.783871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qJZq+8Iw3lAJdmy+9xWeg6lgiVWtIcHCR7dtuYbgaPN9bq4i0UbKDdrZhH44mKSC3o5laf+8GrkYNvURoScVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:02.784305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:865989d869902c00cf0818a97952917d4a0c8f494f7c49338d1f49e092a3f161","sha256:9d8b3f252248e65075bd5b5a2c467523963dbb3a11c3e697d777edd4eaf0901f"],"state_sha256":"fbccbf5b2baea5f88150d21774eac32bfa04ab2115e3ba8033ac039c32017fa0"}