{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KNL37FTXOTXJKMSNBYUKO54YL6","short_pith_number":"pith:KNL37FTX","canonical_record":{"source":{"id":"1610.04384","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"1053484457b1f1a6d836e29ee34e8b2f74d631769fdc5771171cd1067a5c2274","abstract_canon_sha256":"1ea2a271b3c7570838c906107c2b1876525f88573b4975890eea19f5b7989b20"},"schema_version":"1.0"},"canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","source":{"kind":"arxiv","id":"1610.04384","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04384","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04384v4","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04384","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"KNL37FTXOTXJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KNL37FTXOTXJKMSN","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KNL37FTX","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KNL37FTXOTXJKMSNBYUKO54YL6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04384","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"1053484457b1f1a6d836e29ee34e8b2f74d631769fdc5771171cd1067a5c2274","abstract_canon_sha256":"1ea2a271b3c7570838c906107c2b1876525f88573b4975890eea19f5b7989b20"},"schema_version":"1.0"},"canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:41.966417Z","signature_b64":"8UNj897k3mJn6p4IgV4hUsrrUl/nhGrUnY/e+QhSH7C2HmT8l3eH4g6AJFFfTXXWvV92NS2EbWcCFcovNFWnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","last_reissued_at":"2026-05-18T00:04:41.965775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:41.965775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04384","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQJ5PwglgGuuthG0AgiE2JP7J2F5KDBeBpWJGLUl0foYara+i3HAfKtNY9YXEWO2VpIGKQpR1vK9qz1Qbu2+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:04:09.018206Z"},"content_sha256":"bd3eaeea4c19b8d8eb6056f707c5c15d9e450c816003a0ec05c738687170b0bb","schema_version":"1.0","event_id":"sha256:bd3eaeea4c19b8d8eb6056f707c5c15d9e450c816003a0ec05c738687170b0bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KNL37FTXOTXJKMSNBYUKO54YL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erika Hausenblas, Hakima Bessaih, Paul A. Razafimandimby, Tsiry Randrianasolo","submitted_at":"2016-10-14T09:50:48Z","abstract_excerpt":"The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and { a class of nonlinear heat equations.} The space-time numerical scheme is defined in terms of a Galerkin approximation in space and a { semi-implicit Euler--Maruyama scheme in time}. {We prove the convergence in probability of our scheme by means of an estimate of the error on a localized set of arbitrary large probability.} Our error estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04384","kind":"arxiv","version":4},"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":"2026-05-18T00:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QzB2tnZVtX1sq2sNFD2QL0iCHlki7XnmoWnoVWg0/pZqUHob4+F7//XANxBLdKLJViLviWgvjHXhGEGQ8sEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:04:09.018623Z"},"content_sha256":"bff6b9a5dc8565da4095292320d22c106daebc5d4752744915cd674e1560b771","schema_version":"1.0","event_id":"sha256:bff6b9a5dc8565da4095292320d22c106daebc5d4752744915cd674e1560b771"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/bundle.json","state_url":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNL37FTXOTXJKMSNBYUKO54YL6/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":"2026-05-28T23:04:09Z","links":{"resolver":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6","bundle":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/bundle.json","state":"https://pith.science/pith/KNL37FTXOTXJKMSNBYUKO54YL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNL37FTXOTXJKMSNBYUKO54YL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KNL37FTXOTXJKMSNBYUKO54YL6","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":"1ea2a271b3c7570838c906107c2b1876525f88573b4975890eea19f5b7989b20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","title_canon_sha256":"1053484457b1f1a6d836e29ee34e8b2f74d631769fdc5771171cd1067a5c2274"},"schema_version":"1.0","source":{"id":"1610.04384","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04384","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04384v4","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04384","created_at":"2026-05-18T00:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"KNL37FTXOTXJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KNL37FTXOTXJKMSN","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KNL37FTX","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:bff6b9a5dc8565da4095292320d22c106daebc5d4752744915cd674e1560b771","target":"graph","created_at":"2026-05-18T00:04:41Z","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":"The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and { a class of nonlinear heat equations.} The space-time numerical scheme is defined in terms of a Galerkin approximation in space and a { semi-implicit Euler--Maruyama scheme in time}. {We prove the convergence in probability of our scheme by means of an estimate of the error on a localized set of arbitrary large probability.} Our error estimat","authors_text":"Erika Hausenblas, Hakima Bessaih, Paul A. Razafimandimby, Tsiry Randrianasolo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","title":"Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04384","kind":"arxiv","version":4},"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:bd3eaeea4c19b8d8eb6056f707c5c15d9e450c816003a0ec05c738687170b0bb","target":"record","created_at":"2026-05-18T00:04:41Z","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":"1ea2a271b3c7570838c906107c2b1876525f88573b4975890eea19f5b7989b20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-14T09:50:48Z","title_canon_sha256":"1053484457b1f1a6d836e29ee34e8b2f74d631769fdc5771171cd1067a5c2274"},"schema_version":"1.0","source":{"id":"1610.04384","kind":"arxiv","version":4}},"canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5357bf967774ee95324d0e28a777985fafd9a4afa707e7231501bd1daf13a252","first_computed_at":"2026-05-18T00:04:41.965775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:41.965775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8UNj897k3mJn6p4IgV4hUsrrUl/nhGrUnY/e+QhSH7C2HmT8l3eH4g6AJFFfTXXWvV92NS2EbWcCFcovNFWnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:41.966417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04384","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd3eaeea4c19b8d8eb6056f707c5c15d9e450c816003a0ec05c738687170b0bb","sha256:bff6b9a5dc8565da4095292320d22c106daebc5d4752744915cd674e1560b771"],"state_sha256":"ea712ffd3f61b79d0a4ab77f34b7f8b929542699c8ed6449946176a09dbd4470"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w73e6wGVKePV/0D1OniLrbwKb0kKZnTZFcU3/ILJtLfCf4v+oxKIDsq8lOn1pk9KRdb8M20DLRJQ7lBFkvG1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:04:09.021622Z","bundle_sha256":"f85e99f733bcff50d27e199f78e7e19b0de5b45146efaf9076afe96429d46f09"}}