{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NQU77WKK52Z66FUO73Y6M3JE6C","short_pith_number":"pith:NQU77WKK","canonical_record":{"source":{"id":"1605.05481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-18T08:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"fa23bc8e22be00a6b308b35c76a19594beefee653714340083f9efd31b20cfbe","abstract_canon_sha256":"3234193b6f530d1d04c3bc825400125c3dfcb633663589f4de4773c6b33a3f8a"},"schema_version":"1.0"},"canonical_sha256":"6c29ffd94aeeb3ef168efef1e66d24f0959ddf84079fc3a826ed683bf827f779","source":{"kind":"arxiv","id":"1605.05481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05481","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05481v1","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05481","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"NQU77WKK52Z6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQU77WKK52Z66FUO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQU77WKK","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NQU77WKK52Z66FUO73Y6M3JE6C","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-18T08:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"fa23bc8e22be00a6b308b35c76a19594beefee653714340083f9efd31b20cfbe","abstract_canon_sha256":"3234193b6f530d1d04c3bc825400125c3dfcb633663589f4de4773c6b33a3f8a"},"schema_version":"1.0"},"canonical_sha256":"6c29ffd94aeeb3ef168efef1e66d24f0959ddf84079fc3a826ed683bf827f779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:33.327144Z","signature_b64":"Yf36KlxSXftMwAWgG+wp9qX4WPxthEZaQJfQIURjnzXo1eGgQ7nXAclGiyxYvh8KJr0iBn2NEHNgeUPZJnypBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c29ffd94aeeb3ef168efef1e66d24f0959ddf84079fc3a826ed683bf827f779","last_reissued_at":"2026-05-18T00:36:33.326732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:33.326732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05481","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":"2026-05-18T00:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJCEWWa/NILvvWFw22Yo46CR4VbCrdskGV2h+1U19Pc4qbPKpWH04rDoN7iWhA7O3WLWSLZDnkb3rk8uDbHIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:06:16.550430Z"},"content_sha256":"5103430df8cef3eccc2b69c99df586e0a65773b1551815fc44e848cbb08fe357","schema_version":"1.0","event_id":"sha256:5103430df8cef3eccc2b69c99df586e0a65773b1551815fc44e848cbb08fe357"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NQU77WKK52Z66FUO73Y6M3JE6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence proof for the multigrid method of the nonlocal model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Minghua Chen, Weihua Deng","submitted_at":"2016-05-18T08:59:46Z","abstract_excerpt":"Recently, nonlocal models attract the wide interests of scientist. They mainly come from two applied scientific fields: peridyanmics and anomalous diffusion. Even though the matrices of the algebraic equation corresponding the nonlocal models are usually Toeplitz (denote a0 as the principal diagonal element, a1 as the trailing diagonal element, etc). There are still some differences for the models in these two fields. For the model of anomalous diffusion, a0/a1 is uniformly bounded; most of the time, a0/a1 of the model for peridyanmics is unbounded as the stepsize h tends to zero. Based on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05481","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":"2026-05-18T00:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxzyDJ735lIZ4RXHTMtejIzMVKIZAOVv99OkdziYlNIXMwP/zpNvbfOCyIo98DPt3o6tXun9SFwN9IEP9JwmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:06:16.550769Z"},"content_sha256":"0c70963ff6eb6a02edb42b120cae271faeecafe3cad0879390eebd59f14a7051","schema_version":"1.0","event_id":"sha256:0c70963ff6eb6a02edb42b120cae271faeecafe3cad0879390eebd59f14a7051"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQU77WKK52Z66FUO73Y6M3JE6C/bundle.json","state_url":"https://pith.science/pith/NQU77WKK52Z66FUO73Y6M3JE6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQU77WKK52Z66FUO73Y6M3JE6C/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":"2026-06-09T00:06:16Z","links":{"resolver":"https://pith.science/pith/NQU77WKK52Z66FUO73Y6M3JE6C","bundle":"https://pith.science/pith/NQU77WKK52Z66FUO73Y6M3JE6C/bundle.json","state":"https://pith.science/pith/NQU77WKK52Z66FUO73Y6M3JE6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQU77WKK52Z66FUO73Y6M3JE6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NQU77WKK52Z66FUO73Y6M3JE6C","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":"3234193b6f530d1d04c3bc825400125c3dfcb633663589f4de4773c6b33a3f8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-18T08:59:46Z","title_canon_sha256":"fa23bc8e22be00a6b308b35c76a19594beefee653714340083f9efd31b20cfbe"},"schema_version":"1.0","source":{"id":"1605.05481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05481","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05481v1","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05481","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"NQU77WKK52Z6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQU77WKK52Z66FUO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQU77WKK","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:0c70963ff6eb6a02edb42b120cae271faeecafe3cad0879390eebd59f14a7051","target":"graph","created_at":"2026-05-18T00:36:33Z","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":"Recently, nonlocal models attract the wide interests of scientist. They mainly come from two applied scientific fields: peridyanmics and anomalous diffusion. Even though the matrices of the algebraic equation corresponding the nonlocal models are usually Toeplitz (denote a0 as the principal diagonal element, a1 as the trailing diagonal element, etc). There are still some differences for the models in these two fields. For the model of anomalous diffusion, a0/a1 is uniformly bounded; most of the time, a0/a1 of the model for peridyanmics is unbounded as the stepsize h tends to zero. Based on the","authors_text":"Minghua Chen, Weihua Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-18T08:59:46Z","title":"Convergence proof for the multigrid method of the nonlocal model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05481","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":"sha256:5103430df8cef3eccc2b69c99df586e0a65773b1551815fc44e848cbb08fe357","target":"record","created_at":"2026-05-18T00:36:33Z","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":"3234193b6f530d1d04c3bc825400125c3dfcb633663589f4de4773c6b33a3f8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-18T08:59:46Z","title_canon_sha256":"fa23bc8e22be00a6b308b35c76a19594beefee653714340083f9efd31b20cfbe"},"schema_version":"1.0","source":{"id":"1605.05481","kind":"arxiv","version":1}},"canonical_sha256":"6c29ffd94aeeb3ef168efef1e66d24f0959ddf84079fc3a826ed683bf827f779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c29ffd94aeeb3ef168efef1e66d24f0959ddf84079fc3a826ed683bf827f779","first_computed_at":"2026-05-18T00:36:33.326732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:33.326732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yf36KlxSXftMwAWgG+wp9qX4WPxthEZaQJfQIURjnzXo1eGgQ7nXAclGiyxYvh8KJr0iBn2NEHNgeUPZJnypBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:33.327144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5103430df8cef3eccc2b69c99df586e0a65773b1551815fc44e848cbb08fe357","sha256:0c70963ff6eb6a02edb42b120cae271faeecafe3cad0879390eebd59f14a7051"],"state_sha256":"78e59ca489a57fb982f3b93766541b4a31fb2976c95a9df2234eb620a45ea6ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ip61UGXzqWjQvtxcBfG6ePw6TxCGT8vSu3g3r37RxkPQBnEr1Ua1+heFtjvfzKkBSKwvS4oVbhzjDj6m9pRXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:06:16.552627Z","bundle_sha256":"390948bc499d261b3437666ae34961b04fa947ec90d68699e7f05acc0792c137"}}