{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LPTQ2DKBT6BZQY47WLXHBM3LXR","short_pith_number":"pith:LPTQ2DKB","canonical_record":{"source":{"id":"1804.03355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-10T06:25:51Z","cross_cats_sorted":[],"title_canon_sha256":"ba0e43eb4d38304d30217a20459cab6c3ce0ad198256b8c5cfa3f9f542c13516","abstract_canon_sha256":"b59b50e37a01f097ab610dd0e83ab7ca894bb602d2561d1b289e8ed8d0085e7b"},"schema_version":"1.0"},"canonical_sha256":"5be70d0d419f8398639fb2ee70b36bbc7bb1fd68b53bb2337e1ee2818191a77e","source":{"kind":"arxiv","id":"1804.03355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03355","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03355v1","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03355","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"LPTQ2DKBT6BZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LPTQ2DKBT6BZQY47","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LPTQ2DKB","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LPTQ2DKBT6BZQY47WLXHBM3LXR","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-10T06:25:51Z","cross_cats_sorted":[],"title_canon_sha256":"ba0e43eb4d38304d30217a20459cab6c3ce0ad198256b8c5cfa3f9f542c13516","abstract_canon_sha256":"b59b50e37a01f097ab610dd0e83ab7ca894bb602d2561d1b289e8ed8d0085e7b"},"schema_version":"1.0"},"canonical_sha256":"5be70d0d419f8398639fb2ee70b36bbc7bb1fd68b53bb2337e1ee2818191a77e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:56.317920Z","signature_b64":"EePc+wdPUNpdaeXmPWtidnHijxiiAnuLsT/KQrJJrvYMqd2iHHdSr8f2z8fDVXLf0R8C4ejRm3fRGpkD+trZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5be70d0d419f8398639fb2ee70b36bbc7bb1fd68b53bb2337e1ee2818191a77e","last_reissued_at":"2026-05-18T00:18:56.317477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:56.317477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03355","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":"2026-05-18T00:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6zYrnWKtRXQLgbDaQzblE5aGTnAWGwyB3DWlv/Jcuj7hWABPfQmVrEOktwai/Xq9NBsOmV0KlQ5Bry24oi+YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:51:21.001759Z"},"content_sha256":"08da5284758cc5a55ee50248e7dc1e33f924e87984e3c3ff4055c17cb42941b0","schema_version":"1.0","event_id":"sha256:08da5284758cc5a55ee50248e7dc1e33f924e87984e3c3ff4055c17cb42941b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LPTQ2DKBT6BZQY47WLXHBM3LXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yoshihito Kazashi","submitted_at":"2018-04-10T06:25:51Z","abstract_excerpt":"An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A discrete analogue of maximal $L^2$-regularity of the scheme and the discretised stochastic convolution is established, which has the same form as their continuous counterpart."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03355","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":"2026-05-18T00:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGh0WJI+o1SbkRsCuOsRLT2sqeqBqdKJeFqGcjKDXwr+zTxyC2O5IT4KROjeIAl9GbNPJv/tz666VNA64haFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:51:21.002098Z"},"content_sha256":"19be2ebd3646c9432ad451c309348d0e6c96d7a3dee1ebac8226f63037f587e6","schema_version":"1.0","event_id":"sha256:19be2ebd3646c9432ad451c309348d0e6c96d7a3dee1ebac8226f63037f587e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/bundle.json","state_url":"https://pith.science/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/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":"2026-06-20T07:51:21Z","links":{"resolver":"https://pith.science/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR","bundle":"https://pith.science/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/bundle.json","state":"https://pith.science/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPTQ2DKBT6BZQY47WLXHBM3LXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LPTQ2DKBT6BZQY47WLXHBM3LXR","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":"b59b50e37a01f097ab610dd0e83ab7ca894bb602d2561d1b289e8ed8d0085e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-10T06:25:51Z","title_canon_sha256":"ba0e43eb4d38304d30217a20459cab6c3ce0ad198256b8c5cfa3f9f542c13516"},"schema_version":"1.0","source":{"id":"1804.03355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03355","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03355v1","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03355","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"LPTQ2DKBT6BZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LPTQ2DKBT6BZQY47","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LPTQ2DKB","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:19be2ebd3646c9432ad451c309348d0e6c96d7a3dee1ebac8226f63037f587e6","target":"graph","created_at":"2026-05-18T00:18:56Z","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"},"paper":{"abstract_excerpt":"An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A discrete analogue of maximal $L^2$-regularity of the scheme and the discretised stochastic convolution is established, which has the same form as their continuous counterpart.","authors_text":"Yoshihito Kazashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-10T06:25:51Z","title":"Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03355","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":"sha256:08da5284758cc5a55ee50248e7dc1e33f924e87984e3c3ff4055c17cb42941b0","target":"record","created_at":"2026-05-18T00:18:56Z","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":"b59b50e37a01f097ab610dd0e83ab7ca894bb602d2561d1b289e8ed8d0085e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-10T06:25:51Z","title_canon_sha256":"ba0e43eb4d38304d30217a20459cab6c3ce0ad198256b8c5cfa3f9f542c13516"},"schema_version":"1.0","source":{"id":"1804.03355","kind":"arxiv","version":1}},"canonical_sha256":"5be70d0d419f8398639fb2ee70b36bbc7bb1fd68b53bb2337e1ee2818191a77e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5be70d0d419f8398639fb2ee70b36bbc7bb1fd68b53bb2337e1ee2818191a77e","first_computed_at":"2026-05-18T00:18:56.317477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:56.317477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EePc+wdPUNpdaeXmPWtidnHijxiiAnuLsT/KQrJJrvYMqd2iHHdSr8f2z8fDVXLf0R8C4ejRm3fRGpkD+trZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:56.317920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08da5284758cc5a55ee50248e7dc1e33f924e87984e3c3ff4055c17cb42941b0","sha256:19be2ebd3646c9432ad451c309348d0e6c96d7a3dee1ebac8226f63037f587e6"],"state_sha256":"35b9558120aefc8ce87c907218d0025d0302d5168f9a40c6530bfd2a18903b8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sl34PYgwW+291eClCeBiJYtkS22EIAqXVMFXxqypwPkEzyWaoA3Z9ajYztuk307m1Yhqd1MIVUZUg0eCBhA4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:51:21.004022Z","bundle_sha256":"155d1398785cff4efc85719d36e0aee5201d74996f9d39fa20ab454388e5d260"}}