{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JEMZD56AGST2ZHOGZY37B5XFBG","short_pith_number":"pith:JEMZD56A","canonical_record":{"source":{"id":"1709.01018","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-04T16:02:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6b9935cae5881551e6d45ba383ca7b49593e00a4c5fc094e6ec7ee86c1d78b83","abstract_canon_sha256":"5b6190227015e13325a756dffec7714dc4f2d989726254172a2b6b966da72a17"},"schema_version":"1.0"},"canonical_sha256":"491991f7c034a7ac9dc6ce37f0f6e5098f224bb619d390f99fd96ff12b01b02c","source":{"kind":"arxiv","id":"1709.01018","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01018","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01018v2","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01018","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"JEMZD56AGST2","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_16","alias_value":"JEMZD56AGST2ZHOG","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_8","alias_value":"JEMZD56A","created_at":"2026-06-04T19:10:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JEMZD56AGST2ZHOGZY37B5XFBG","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01018","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-04T16:02:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6b9935cae5881551e6d45ba383ca7b49593e00a4c5fc094e6ec7ee86c1d78b83","abstract_canon_sha256":"5b6190227015e13325a756dffec7714dc4f2d989726254172a2b6b966da72a17"},"schema_version":"1.0"},"canonical_sha256":"491991f7c034a7ac9dc6ce37f0f6e5098f224bb619d390f99fd96ff12b01b02c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:10:56.560732Z","signature_b64":"8wD3ced8KT4XZz64nXoucDsDh8YJdoEAtuCRd1fQYChjBm0zJ6yl8phX2dmZrAD3obRMztJKU3tmHKjC73OWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"491991f7c034a7ac9dc6ce37f0f6e5098f224bb619d390f99fd96ff12b01b02c","last_reissued_at":"2026-06-04T19:10:56.560118Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:10:56.560118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01018","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+waDgxW/9jRqNdBTtYn8UVaAoeUBnvJIdeb4m32+0cI3SScRtAmixr/p3134ENVMVDyDndYAcAtaSa7tQ88ECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:14:24.439266Z"},"content_sha256":"d27cd1f4fe29aff10a9a7d96bd797e3d91fc14af31f094b7d31bc454535c5131","schema_version":"1.0","event_id":"sha256:d27cd1f4fe29aff10a9a7d96bd797e3d91fc14af31f094b7d31bc454535c5131"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JEMZD56AGST2ZHOGZY37B5XFBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Mih\\'aly Kov\\'acs, Monika Eisenmann, Raphael Kruse, Stig Larsson","submitted_at":"2017-09-04T16:02:56Z","abstract_excerpt":"In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we consider Carath\\'eodory type functions satisfying a one-sided Lipschitz condition. After investigating the well-posedness and the stability properties of the randomized scheme, we prove the convergence to the exact solution with a rate of $0.5$ in the root-mean-square norm assuming only that the coefficient function is square integrable with respect to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01018","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1709.01018/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T19:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tfhzB3QflfClMOp5i3O8X3yr6Paocxbc/F+vj6AyX6tBeDWsOSAo1cxEXAM/xm5xlHIQaknWfxRW7PH4Uc9jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:14:24.440095Z"},"content_sha256":"9c9e382bdfc0555edbc7fe4452f26eadacf83aee29d82fb95423f3e3639ff838","schema_version":"1.0","event_id":"sha256:9c9e382bdfc0555edbc7fe4452f26eadacf83aee29d82fb95423f3e3639ff838"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEMZD56AGST2ZHOGZY37B5XFBG/bundle.json","state_url":"https://pith.science/pith/JEMZD56AGST2ZHOGZY37B5XFBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEMZD56AGST2ZHOGZY37B5XFBG/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":"2026-06-08T04:14:24Z","links":{"resolver":"https://pith.science/pith/JEMZD56AGST2ZHOGZY37B5XFBG","bundle":"https://pith.science/pith/JEMZD56AGST2ZHOGZY37B5XFBG/bundle.json","state":"https://pith.science/pith/JEMZD56AGST2ZHOGZY37B5XFBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEMZD56AGST2ZHOGZY37B5XFBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JEMZD56AGST2ZHOGZY37B5XFBG","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":"5b6190227015e13325a756dffec7714dc4f2d989726254172a2b6b966da72a17","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-04T16:02:56Z","title_canon_sha256":"6b9935cae5881551e6d45ba383ca7b49593e00a4c5fc094e6ec7ee86c1d78b83"},"schema_version":"1.0","source":{"id":"1709.01018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01018","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01018v2","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01018","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"JEMZD56AGST2","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_16","alias_value":"JEMZD56AGST2ZHOG","created_at":"2026-06-04T19:10:56Z"},{"alias_kind":"pith_short_8","alias_value":"JEMZD56A","created_at":"2026-06-04T19:10:56Z"}],"graph_snapshots":[{"event_id":"sha256:9c9e382bdfc0555edbc7fe4452f26eadacf83aee29d82fb95423f3e3639ff838","target":"graph","created_at":"2026-06-04T19:10:56Z","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/1709.01018/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we consider Carath\\'eodory type functions satisfying a one-sided Lipschitz condition. After investigating the well-posedness and the stability properties of the randomized scheme, we prove the convergence to the exact solution with a rate of $0.5$ in the root-mean-square norm assuming only that the coefficient function is square integrable with respect to the ","authors_text":"Mih\\'aly Kov\\'acs, Monika Eisenmann, Raphael Kruse, Stig Larsson","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-04T16:02:56Z","title":"On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01018","kind":"arxiv","version":2},"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:d27cd1f4fe29aff10a9a7d96bd797e3d91fc14af31f094b7d31bc454535c5131","target":"record","created_at":"2026-06-04T19:10:56Z","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":"5b6190227015e13325a756dffec7714dc4f2d989726254172a2b6b966da72a17","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-04T16:02:56Z","title_canon_sha256":"6b9935cae5881551e6d45ba383ca7b49593e00a4c5fc094e6ec7ee86c1d78b83"},"schema_version":"1.0","source":{"id":"1709.01018","kind":"arxiv","version":2}},"canonical_sha256":"491991f7c034a7ac9dc6ce37f0f6e5098f224bb619d390f99fd96ff12b01b02c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"491991f7c034a7ac9dc6ce37f0f6e5098f224bb619d390f99fd96ff12b01b02c","first_computed_at":"2026-06-04T19:10:56.560118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:10:56.560118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8wD3ced8KT4XZz64nXoucDsDh8YJdoEAtuCRd1fQYChjBm0zJ6yl8phX2dmZrAD3obRMztJKU3tmHKjC73OWAw==","signature_status":"signed_v1","signed_at":"2026-06-04T19:10:56.560732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d27cd1f4fe29aff10a9a7d96bd797e3d91fc14af31f094b7d31bc454535c5131","sha256:9c9e382bdfc0555edbc7fe4452f26eadacf83aee29d82fb95423f3e3639ff838"],"state_sha256":"9478b48a26eb7b9088deb68039aa8786440c172ff800535f43a3da18e9f6db23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5i/pco0K4baPdtD8NVPIPq4VHNh0z0qV2/3se9gNa13SDlhAsoMQ18eejhPshpgmPjoPIA2hHjQMMx5WzlUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:14:24.444676Z","bundle_sha256":"083e91f43e15be721ec7054b0129fb89d2bd5e4a07657dfde20e240ae130a5b9"}}