{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UQIUVKFXAKRTIZMU4ANXMLRYG4","short_pith_number":"pith:UQIUVKFX","canonical_record":{"source":{"id":"1508.04296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T12:32:41Z","cross_cats_sorted":[],"title_canon_sha256":"5fde527fa7b03a3da8967c8702c8081b1f4d49261f57d7bf994b2e97e3656c48","abstract_canon_sha256":"5a592784d418c3c2b948d24963847e1909472bf8ed8c8e1cfd84083cd48a4178"},"schema_version":"1.0"},"canonical_sha256":"a4114aa8b702a3346594e01b762e383723f8f23640d84d4eabc99c5100cae936","source":{"kind":"arxiv","id":"1508.04296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04296","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04296v1","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04296","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"UQIUVKFXAKRT","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UQIUVKFXAKRTIZMU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UQIUVKFX","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UQIUVKFXAKRTIZMU4ANXMLRYG4","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T12:32:41Z","cross_cats_sorted":[],"title_canon_sha256":"5fde527fa7b03a3da8967c8702c8081b1f4d49261f57d7bf994b2e97e3656c48","abstract_canon_sha256":"5a592784d418c3c2b948d24963847e1909472bf8ed8c8e1cfd84083cd48a4178"},"schema_version":"1.0"},"canonical_sha256":"a4114aa8b702a3346594e01b762e383723f8f23640d84d4eabc99c5100cae936","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.705276Z","signature_b64":"KIJ7H5BiPrs3RR7O+TlnvMw6ScfnkZHPyobI30NP+Q+un5zcM8LRMwlcp1YX6f7Z8OjO1GP4dPfnM4kR9ZTgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4114aa8b702a3346594e01b762e383723f8f23640d84d4eabc99c5100cae936","last_reissued_at":"2026-05-18T01:35:05.704664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.704664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04296","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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GUvMw5GsbVdENAF00apE+ZD4zlflbZPa1lxfmDAyT2lvOqfawhT5YcN2pmyhwHkrBxor6uIHgeNAdD976DtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:55:44.250856Z"},"content_sha256":"4561e4779d8bac438048d366fd3a2bfaf54a1baa41c14f0492e1fb6ef4748a4d","schema_version":"1.0","event_id":"sha256:4561e4779d8bac438048d366fd3a2bfaf54a1baa41c14f0492e1fb6ef4748a4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UQIUVKFXAKRTIZMU4ANXMLRYG4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence analysis of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with nonsmooth initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Maarten Wyns","submitted_at":"2015-08-18T12:32:41Z","abstract_excerpt":"In this paper we consider the Modified Craig-Sneyd (MCS) scheme which forms a prominent time stepping method of the Alternating Direction Implicit type for multidimensional time-dependent convection-diffusion equations with mixed spatial derivative terms. When the initial function is nonsmooth, which is often the case for example in financial mathematics, application of the MCS scheme can lead to spurious erratic behaviour of the numerical approximations. We prove that this undesirable feature can be resolved by replacing the very first MCS timesteps by several (sub)steps of the implicit Euler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04296","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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nmRejEZYSPjvBxBzKjiJBxDJeBv0lMvZ8MGPrirYnh8em8vb4wrwookG2IJHPR8+THf4LBgCxkkFuj8JPiMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:55:44.251198Z"},"content_sha256":"68e1efcf595da1533d1acf1b03649729dde73ab095f3f06534b86927db4bd399","schema_version":"1.0","event_id":"sha256:68e1efcf595da1533d1acf1b03649729dde73ab095f3f06534b86927db4bd399"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/bundle.json","state_url":"https://pith.science/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/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":"2026-06-24T18:55:44Z","links":{"resolver":"https://pith.science/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4","bundle":"https://pith.science/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/bundle.json","state":"https://pith.science/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQIUVKFXAKRTIZMU4ANXMLRYG4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UQIUVKFXAKRTIZMU4ANXMLRYG4","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":"5a592784d418c3c2b948d24963847e1909472bf8ed8c8e1cfd84083cd48a4178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T12:32:41Z","title_canon_sha256":"5fde527fa7b03a3da8967c8702c8081b1f4d49261f57d7bf994b2e97e3656c48"},"schema_version":"1.0","source":{"id":"1508.04296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04296","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04296v1","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04296","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"UQIUVKFXAKRT","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UQIUVKFXAKRTIZMU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UQIUVKFX","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:68e1efcf595da1533d1acf1b03649729dde73ab095f3f06534b86927db4bd399","target":"graph","created_at":"2026-05-18T01:35:05Z","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 paper we consider the Modified Craig-Sneyd (MCS) scheme which forms a prominent time stepping method of the Alternating Direction Implicit type for multidimensional time-dependent convection-diffusion equations with mixed spatial derivative terms. When the initial function is nonsmooth, which is often the case for example in financial mathematics, application of the MCS scheme can lead to spurious erratic behaviour of the numerical approximations. We prove that this undesirable feature can be resolved by replacing the very first MCS timesteps by several (sub)steps of the implicit Euler","authors_text":"Maarten Wyns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T12:32:41Z","title":"Convergence analysis of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with nonsmooth initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04296","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":"sha256:4561e4779d8bac438048d366fd3a2bfaf54a1baa41c14f0492e1fb6ef4748a4d","target":"record","created_at":"2026-05-18T01:35:05Z","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":"5a592784d418c3c2b948d24963847e1909472bf8ed8c8e1cfd84083cd48a4178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T12:32:41Z","title_canon_sha256":"5fde527fa7b03a3da8967c8702c8081b1f4d49261f57d7bf994b2e97e3656c48"},"schema_version":"1.0","source":{"id":"1508.04296","kind":"arxiv","version":1}},"canonical_sha256":"a4114aa8b702a3346594e01b762e383723f8f23640d84d4eabc99c5100cae936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4114aa8b702a3346594e01b762e383723f8f23640d84d4eabc99c5100cae936","first_computed_at":"2026-05-18T01:35:05.704664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:05.704664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KIJ7H5BiPrs3RR7O+TlnvMw6ScfnkZHPyobI30NP+Q+un5zcM8LRMwlcp1YX6f7Z8OjO1GP4dPfnM4kR9ZTgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:05.705276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4561e4779d8bac438048d366fd3a2bfaf54a1baa41c14f0492e1fb6ef4748a4d","sha256:68e1efcf595da1533d1acf1b03649729dde73ab095f3f06534b86927db4bd399"],"state_sha256":"9275d12ee16a8b1f3499531560c1c6b15c4939e046d80cfdb562417dba2d7ee2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywA67PhxuCBced2xLYAh23y9NHBtl1rBTDQbwoHtmVTfste23RB4xOB4oOywx+qcG11z9tXBTd5Z304Y8XkBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:55:44.253091Z","bundle_sha256":"df1f1008cd508ecd4df869b4645eb1fb3710508e476f647fbde34ec51bb52405"}}