{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RIC45PAIAOMRZWBYZAG3HMMN7P","short_pith_number":"pith:RIC45PAI","canonical_record":{"source":{"id":"1003.4397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-03-23T12:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"ae1c6bb2584963c24e8f3a292216ebc74d6caefbeba465257645619ba547d843","abstract_canon_sha256":"ff21e98a793b3c6d4b26a400300a1fbe06208268beae064fa71a6e363b5b6bc2"},"schema_version":"1.0"},"canonical_sha256":"8a05cebc0803991cd838c80db3b18dfbcd39533fe94dc1add9905e7e203eb671","source":{"kind":"arxiv","id":"1003.4397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4397","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4397v2","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4397","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"pith_short_12","alias_value":"RIC45PAIAOMR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RIC45PAIAOMRZWBY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RIC45PAI","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RIC45PAIAOMRZWBYZAG3HMMN7P","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-03-23T12:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"ae1c6bb2584963c24e8f3a292216ebc74d6caefbeba465257645619ba547d843","abstract_canon_sha256":"ff21e98a793b3c6d4b26a400300a1fbe06208268beae064fa71a6e363b5b6bc2"},"schema_version":"1.0"},"canonical_sha256":"8a05cebc0803991cd838c80db3b18dfbcd39533fe94dc1add9905e7e203eb671","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:59.765577Z","signature_b64":"s+rAePHURHTkZmbgDUSxO/PY9/OVuO1aWInWjT0iFGvQ2jSBe++iRMOyHLLbMyAfu/0q+wIXVVlzNLHZhIpwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a05cebc0803991cd838c80db3b18dfbcd39533fe94dc1add9905e7e203eb671","last_reissued_at":"2026-05-18T04:30:59.764675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:59.764675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4397","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":"2026-05-18T04:30:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AoaAgJ8ErwODnTSPnwNkb/dyvZZ0inFeAlaB/4BhhV89qM7dH2XdD7S9FB8Q0ywtjNYDFBlXzZj3ZwkJeErlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:43:39.196868Z"},"content_sha256":"22590ccdd9a6ad403dda12f9c4141450d2f7e034d200f4ccc18ac1aa1f24ebf3","schema_version":"1.0","event_id":"sha256:22590ccdd9a6ad403dda12f9c4141450d2f7e034d200f4ccc18ac1aa1f24ebf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RIC45PAIAOMRZWBYZAG3HMMN7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Composition of stochastic B-series with applications to implicit Taylor methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anne Kv{\\ae}rn{\\o}, Kristian Debrabant","submitted_at":"2010-03-23T12:50:48Z","abstract_excerpt":"In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in a simple manner a family of strong order 1.5 Taylor methods applicable to It\\^o SDEs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4397","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":""},"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":"2026-05-18T04:30:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g7b/8JDXXRXTCzchRzhuXU9kiN6jVvrNs4UTwEJylopaTiCoG8Awgj/KjzM6InIljH5vMAhY38BBkWaAtGy6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:43:39.197422Z"},"content_sha256":"26d01f86dfec6b53a6ee93ac317256df218a4469e024f57bf6c3807f568eb982","schema_version":"1.0","event_id":"sha256:26d01f86dfec6b53a6ee93ac317256df218a4469e024f57bf6c3807f568eb982"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/bundle.json","state_url":"https://pith.science/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/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":"2026-07-01T07:43:39Z","links":{"resolver":"https://pith.science/pith/RIC45PAIAOMRZWBYZAG3HMMN7P","bundle":"https://pith.science/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/bundle.json","state":"https://pith.science/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIC45PAIAOMRZWBYZAG3HMMN7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RIC45PAIAOMRZWBYZAG3HMMN7P","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":"ff21e98a793b3c6d4b26a400300a1fbe06208268beae064fa71a6e363b5b6bc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-03-23T12:50:48Z","title_canon_sha256":"ae1c6bb2584963c24e8f3a292216ebc74d6caefbeba465257645619ba547d843"},"schema_version":"1.0","source":{"id":"1003.4397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4397","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4397v2","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4397","created_at":"2026-05-18T04:30:59Z"},{"alias_kind":"pith_short_12","alias_value":"RIC45PAIAOMR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RIC45PAIAOMRZWBY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RIC45PAI","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:26d01f86dfec6b53a6ee93ac317256df218a4469e024f57bf6c3807f568eb982","target":"graph","created_at":"2026-05-18T04:30:59Z","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 article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in a simple manner a family of strong order 1.5 Taylor methods applicable to It\\^o SDEs.","authors_text":"Anne Kv{\\ae}rn{\\o}, Kristian Debrabant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-03-23T12:50:48Z","title":"Composition of stochastic B-series with applications to implicit Taylor methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4397","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":"sha256:22590ccdd9a6ad403dda12f9c4141450d2f7e034d200f4ccc18ac1aa1f24ebf3","target":"record","created_at":"2026-05-18T04:30:59Z","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":"ff21e98a793b3c6d4b26a400300a1fbe06208268beae064fa71a6e363b5b6bc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-03-23T12:50:48Z","title_canon_sha256":"ae1c6bb2584963c24e8f3a292216ebc74d6caefbeba465257645619ba547d843"},"schema_version":"1.0","source":{"id":"1003.4397","kind":"arxiv","version":2}},"canonical_sha256":"8a05cebc0803991cd838c80db3b18dfbcd39533fe94dc1add9905e7e203eb671","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a05cebc0803991cd838c80db3b18dfbcd39533fe94dc1add9905e7e203eb671","first_computed_at":"2026-05-18T04:30:59.764675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:59.764675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s+rAePHURHTkZmbgDUSxO/PY9/OVuO1aWInWjT0iFGvQ2jSBe++iRMOyHLLbMyAfu/0q+wIXVVlzNLHZhIpwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:59.765577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22590ccdd9a6ad403dda12f9c4141450d2f7e034d200f4ccc18ac1aa1f24ebf3","sha256:26d01f86dfec6b53a6ee93ac317256df218a4469e024f57bf6c3807f568eb982"],"state_sha256":"b5d6337eabb88601a90798316ed7a77758312e614410a46dc85987444db8d519"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIJxv36fMnmQl9PQ8eHifzGXxjs4kIHs7K3coPVSNK7zqKNgzkbldUdbNkXIkQJgrhAyzr+Paf3uf6PSk/xfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:43:39.199971Z","bundle_sha256":"40d14b1f4d97c9b8fdd785a5a24c4242628c7eae8213e76bf4c7f84c76202adb"}}