{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FBMC4U746RDYEGNCNQENZPF6GV","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":"227b334aaa0764a126c5fc62a2c4e310562df1659d4fffb8b2409052d9cecfb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T01:15:31Z","title_canon_sha256":"b8762683d2fb73e8901b502535db9dc0bc87dcd75a0c56a4cb24e6aa6c81ea2d"},"schema_version":"1.0","source":{"id":"1701.02818","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02818","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02818v5","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02818","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"FBMC4U746RDY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBMC4U746RDYEGNC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBMC4U74","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:70dcba3dcf1a298113e3ee273c8b0a9df3529baccb355c15d91fc46fee8be4a8","target":"graph","created_at":"2026-05-18T00:12:00Z","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 work, we calculate the convergence rate of the finite difference approximation for a class of nonlocal fracture models. We consider two point force interactions characterized by a double well potential. We show the existence of a evolving displacement field in H\\\"{o}lder space with H\\\"{o}lder exponent $\\gamma \\in (0,1]$. The rate of convergence of the finite difference approximation depends on the factor $C_s h^\\gamma/\\epsilon^2$ where $\\epsilon$ gives the length scale of nonlocal interaction, $h$ is the discretization length and $C_s$ is the maximum of H\\\"older norm of the solution an","authors_text":"Prashant K. Jha, Robert Lipton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T01:15:31Z","title":"Numerical analysis of nonlocal fracture models in H\\\"older space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02818","kind":"arxiv","version":5},"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":"sha256:8bd82610b1147b70b515c984f98dbc9f14dc417df561f4fea62704e2786af3cd","target":"record","created_at":"2026-05-18T00:12:00Z","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":"227b334aaa0764a126c5fc62a2c4e310562df1659d4fffb8b2409052d9cecfb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T01:15:31Z","title_canon_sha256":"b8762683d2fb73e8901b502535db9dc0bc87dcd75a0c56a4cb24e6aa6c81ea2d"},"schema_version":"1.0","source":{"id":"1701.02818","kind":"arxiv","version":5}},"canonical_sha256":"28582e53fcf4478219a26c08dcbcbe354b11fc5f494882ce07a5162a4b3a97c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28582e53fcf4478219a26c08dcbcbe354b11fc5f494882ce07a5162a4b3a97c8","first_computed_at":"2026-05-18T00:12:00.694149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:00.694149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J563/FMeshdiaWeoY5A3HF+jSfcfpJu05lhZH8FVWsGDauOzhKVPMtsijPMhSVvZUGOKXJR6BcW6dpeqTxjeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:00.694863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02818","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd82610b1147b70b515c984f98dbc9f14dc417df561f4fea62704e2786af3cd","sha256:70dcba3dcf1a298113e3ee273c8b0a9df3529baccb355c15d91fc46fee8be4a8"],"state_sha256":"546777fe42c7b3d68cbd2807c55e355a66ecee8e767a350ea15ce26ae9e646be"}