{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OM2FFZGZILWW2X6X6HGHDDBMIW","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":"ac3f91f97aa47551cd932d56f12ba8ae97ab404659a0e131ebdf63fa5dc7b88d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T07:35:06Z","title_canon_sha256":"2a0fd9c0c2d65d58072d13727fa1a11b904d9ea4f1223fe94dddce80cb9a0574"},"schema_version":"1.0","source":{"id":"1507.02399","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02399","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02399v5","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02399","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"OM2FFZGZILWW","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_16","alias_value":"OM2FFZGZILWW2X6X","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_8","alias_value":"OM2FFZGZ","created_at":"2026-06-04T17:09:23Z"}],"graph_snapshots":[{"event_id":"sha256:eeecc42576a89ee6b27fab532306787a8fa27adad64b77b2eb070aecb71d3e95","target":"graph","created_at":"2026-06-04T17:09:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1507.02399/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\\le 1/2$. We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise con- stant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.","authors_text":"Jialin Hong, Yanzhao Cao, Zhihui Liu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T07:35:06Z","title":"Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02399","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:be4ec1824750201ed963687d532e163bcd880b09121f07f5910962cb852c0d9f","target":"record","created_at":"2026-06-04T17:09:23Z","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":"ac3f91f97aa47551cd932d56f12ba8ae97ab404659a0e131ebdf63fa5dc7b88d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T07:35:06Z","title_canon_sha256":"2a0fd9c0c2d65d58072d13727fa1a11b904d9ea4f1223fe94dddce80cb9a0574"},"schema_version":"1.0","source":{"id":"1507.02399","kind":"arxiv","version":5}},"canonical_sha256":"733452e4d942ed6d5fd7f1cc718c2c45b7eba7fcfa3788b61c72cc88be7d9c99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"733452e4d942ed6d5fd7f1cc718c2c45b7eba7fcfa3788b61c72cc88be7d9c99","first_computed_at":"2026-06-04T17:09:23.561630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T17:09:23.561630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E5ZnKjE0IKqCtXou+CHvAlPDS6sL5NXe5X/1tGh0hBTDXlQWnBBHlZoxvMsCoZK7YHGGNbI1prnsiPUOMhsCDQ==","signature_status":"signed_v1","signed_at":"2026-06-04T17:09:23.562126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02399","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be4ec1824750201ed963687d532e163bcd880b09121f07f5910962cb852c0d9f","sha256:eeecc42576a89ee6b27fab532306787a8fa27adad64b77b2eb070aecb71d3e95"],"state_sha256":"2464438a5cc62b968def75c77b8f4fdd33de2ca50939254f33e58bbeda088c08"}