{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SRWSQQCBXKE3RJVUXAX4YCBJZO","short_pith_number":"pith:SRWSQQCB","canonical_record":{"source":{"id":"1608.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-01T18:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"388af16f580a4b8bfcdba3b9ffb66967c90d90cff168edfe7a9fc90d36ee9c71","abstract_canon_sha256":"0606f2f9da65ffa93a9d19acbb94202dbec59425b38659632b77e225921716cf"},"schema_version":"1.0"},"canonical_sha256":"946d284041ba89b8a6b4b82fcc0829cbaf6760e4273104224ae0b509b2d98b88","source":{"kind":"arxiv","id":"1608.00511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00511","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00511v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00511","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"SRWSQQCBXKE3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRWSQQCBXKE3RJVU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRWSQQCB","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SRWSQQCBXKE3RJVUXAX4YCBJZO","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-01T18:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"388af16f580a4b8bfcdba3b9ffb66967c90d90cff168edfe7a9fc90d36ee9c71","abstract_canon_sha256":"0606f2f9da65ffa93a9d19acbb94202dbec59425b38659632b77e225921716cf"},"schema_version":"1.0"},"canonical_sha256":"946d284041ba89b8a6b4b82fcc0829cbaf6760e4273104224ae0b509b2d98b88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.648002Z","signature_b64":"776gj58R8TLylW55t4ftlK6ol6msW557Jvn2C7UK/RiqIvxDQx3uNy/6Ns0rUdPymR8oszmc+my7ymR2m+LMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"946d284041ba89b8a6b4b82fcc0829cbaf6760e4273104224ae0b509b2d98b88","last_reissued_at":"2026-05-18T01:10:11.647623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.647623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00511","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVXGOUcaklHc5Xe6NFJaYay2u2PuIb5gY0hu81J8bECzVHhYAEOkhJTlA8bHz9lNlOiMAlGJf7AbbgDWE7PNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:07.593841Z"},"content_sha256":"cd450122896aef5e14873d186f31bfab13f0bc03afc4b1e78e787259ce43c8ce","schema_version":"1.0","event_id":"sha256:cd450122896aef5e14873d186f31bfab13f0bc03afc4b1e78e787259ce43c8ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SRWSQQCBXKE3RJVUXAX4YCBJZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Finite difference schemes for partial integro-differential equations of L\\'evy type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Konstantinos Dareiotis","submitted_at":"2016-08-01T18:09:26Z","abstract_excerpt":"In this article we introduce a finite difference approximation for integro-differential operators of L\\'evy type. We approximate solutions of integro-differential equations, where the second order operator is allowed to degenerate. In the existing literature, the L\\'evy operator is treated as a zero/first order operator outside of a centered ball of radius $\\delta$, leading to error estimates of order $\\xi (\\delta)+N(\\delta)(h+\\sqrt{\\tau})$, where $h$ and $\\tau$ are the spatial and temporal discretization parameters respectively. In these estimates $\\xi (\\delta) \\downarrow 0$, but $N(\\delta )\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00511","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KyJ9aVSLcbCaV2crw9twBZrMN1bONybnZntfolTXPPYUd6rTISkR3dWBEgizlo3/P30zZTJNR+m8/7NCW7SQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:07.594392Z"},"content_sha256":"5afb317ec7bac7d7df04ea3ffa8e57c06eab322de0d3204ea32915eb07a67339","schema_version":"1.0","event_id":"sha256:5afb317ec7bac7d7df04ea3ffa8e57c06eab322de0d3204ea32915eb07a67339"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/bundle.json","state_url":"https://pith.science/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T20:24:07Z","links":{"resolver":"https://pith.science/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO","bundle":"https://pith.science/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/bundle.json","state":"https://pith.science/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRWSQQCBXKE3RJVUXAX4YCBJZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SRWSQQCBXKE3RJVUXAX4YCBJZO","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":"0606f2f9da65ffa93a9d19acbb94202dbec59425b38659632b77e225921716cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-01T18:09:26Z","title_canon_sha256":"388af16f580a4b8bfcdba3b9ffb66967c90d90cff168edfe7a9fc90d36ee9c71"},"schema_version":"1.0","source":{"id":"1608.00511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00511","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00511v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00511","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"SRWSQQCBXKE3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRWSQQCBXKE3RJVU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRWSQQCB","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:5afb317ec7bac7d7df04ea3ffa8e57c06eab322de0d3204ea32915eb07a67339","target":"graph","created_at":"2026-05-18T01:10:11Z","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 article we introduce a finite difference approximation for integro-differential operators of L\\'evy type. We approximate solutions of integro-differential equations, where the second order operator is allowed to degenerate. In the existing literature, the L\\'evy operator is treated as a zero/first order operator outside of a centered ball of radius $\\delta$, leading to error estimates of order $\\xi (\\delta)+N(\\delta)(h+\\sqrt{\\tau})$, where $h$ and $\\tau$ are the spatial and temporal discretization parameters respectively. In these estimates $\\xi (\\delta) \\downarrow 0$, but $N(\\delta )\\","authors_text":"Konstantinos Dareiotis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-01T18:09:26Z","title":"On Finite difference schemes for partial integro-differential equations of L\\'evy type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00511","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:cd450122896aef5e14873d186f31bfab13f0bc03afc4b1e78e787259ce43c8ce","target":"record","created_at":"2026-05-18T01:10:11Z","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":"0606f2f9da65ffa93a9d19acbb94202dbec59425b38659632b77e225921716cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-01T18:09:26Z","title_canon_sha256":"388af16f580a4b8bfcdba3b9ffb66967c90d90cff168edfe7a9fc90d36ee9c71"},"schema_version":"1.0","source":{"id":"1608.00511","kind":"arxiv","version":1}},"canonical_sha256":"946d284041ba89b8a6b4b82fcc0829cbaf6760e4273104224ae0b509b2d98b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"946d284041ba89b8a6b4b82fcc0829cbaf6760e4273104224ae0b509b2d98b88","first_computed_at":"2026-05-18T01:10:11.647623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.647623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"776gj58R8TLylW55t4ftlK6ol6msW557Jvn2C7UK/RiqIvxDQx3uNy/6Ns0rUdPymR8oszmc+my7ymR2m+LMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.648002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd450122896aef5e14873d186f31bfab13f0bc03afc4b1e78e787259ce43c8ce","sha256:5afb317ec7bac7d7df04ea3ffa8e57c06eab322de0d3204ea32915eb07a67339"],"state_sha256":"38dee9bab0e6e698db3297cbcb5b249846196652ec654bfb78099ee7f62bdc84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EOInu5LOgriS3/6Cxm8RcQUREOe+L+7ZbHIyEMW/820pNXQ8m3bM0fdBL9NpeWbwZkKJJb+FB8pdgNvMjoUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:24:07.597143Z","bundle_sha256":"e231ff6b9298b6d75488b66d218c5d4bac02e178c46be1fbf5593125924883e6"}}