{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LP2BEJBBGW3EMY2BGNKIN4QVS2","short_pith_number":"pith:LP2BEJBB","canonical_record":{"source":{"id":"1304.4623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T21:09:50Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"b17afe9d8785fda63a95d3513365b57ac9f029663d9d7f334d011ad65fe57038","abstract_canon_sha256":"12a7e871ff8c24a7a38d861c3d48516d550d5fe45ca5fef2fadc9e2e3019eaaf"},"schema_version":"1.0"},"canonical_sha256":"5bf412242135b6466341335486f21596b329711a23b758c4a5eabc28790dfa7b","source":{"kind":"arxiv","id":"1304.4623","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4623","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4623v1","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4623","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"LP2BEJBBGW3E","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LP2BEJBBGW3EMY2B","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LP2BEJBB","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LP2BEJBBGW3EMY2BGNKIN4QVS2","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T21:09:50Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"b17afe9d8785fda63a95d3513365b57ac9f029663d9d7f334d011ad65fe57038","abstract_canon_sha256":"12a7e871ff8c24a7a38d861c3d48516d550d5fe45ca5fef2fadc9e2e3019eaaf"},"schema_version":"1.0"},"canonical_sha256":"5bf412242135b6466341335486f21596b329711a23b758c4a5eabc28790dfa7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:44.170087Z","signature_b64":"uOqzfD1mC63ygSWdLVBY1zm1tdJRONk0w1jchjR2k6mMZTajNvD4FdUQSPfY8vQQSXyWsX4/eqD7pNt+l3qwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bf412242135b6466341335486f21596b329711a23b758c4a5eabc28790dfa7b","last_reissued_at":"2026-05-18T03:27:44.169445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:44.169445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4623","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eeC+4QFbJpQkCeAnG7MznUmU1PhOMHkOapxlEQR5FLihm6QXWJFbcXm+abcBSEKUFHFUM9pjdpA2QSz1sR9UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:19:12.927990Z"},"content_sha256":"fd2ca18e7b5f44d10dcfbf7f0062465266235a60c5c3c0a015deb4144ae17bcb","schema_version":"1.0","event_id":"sha256:fd2ca18e7b5f44d10dcfbf7f0062465266235a60c5c3c0a015deb4144ae17bcb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LP2BEJBBGW3EMY2BGNKIN4QVS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubature on Wiener space: pathwise convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.PR","authors_text":"Christian Bayer, Peter K. Friz","submitted_at":"2013-04-16T21:09:50Z","abstract_excerpt":"Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models.\n  We give a random walk interpretation of cubature and similar (e.g. the Ninomiya--Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4623","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dm0jbqNMI0wKCzrY7v5C5jW8oNnqYzeDGEFKaY75GlYeIa1VtJJzFfT3NiwVuEbU8mTOogbFNZED5u6qkhnMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:19:12.928347Z"},"content_sha256":"38475a40705f9fc06f834a40f7b9c5d60c329a71a05dc643c1097c6294ffb566","schema_version":"1.0","event_id":"sha256:38475a40705f9fc06f834a40f7b9c5d60c329a71a05dc643c1097c6294ffb566"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/bundle.json","state_url":"https://pith.science/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/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":"2026-05-30T13:19:12Z","links":{"resolver":"https://pith.science/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2","bundle":"https://pith.science/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/bundle.json","state":"https://pith.science/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LP2BEJBBGW3EMY2BGNKIN4QVS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LP2BEJBBGW3EMY2BGNKIN4QVS2","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":"12a7e871ff8c24a7a38d861c3d48516d550d5fe45ca5fef2fadc9e2e3019eaaf","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T21:09:50Z","title_canon_sha256":"b17afe9d8785fda63a95d3513365b57ac9f029663d9d7f334d011ad65fe57038"},"schema_version":"1.0","source":{"id":"1304.4623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4623","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4623v1","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4623","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"LP2BEJBBGW3E","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LP2BEJBBGW3EMY2B","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LP2BEJBB","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:38475a40705f9fc06f834a40f7b9c5d60c329a71a05dc643c1097c6294ffb566","target":"graph","created_at":"2026-05-18T03:27:44Z","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":"Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models.\n  We give a random walk interpretation of cubature and similar (e.g. the Ninomiya--Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dep","authors_text":"Christian Bayer, Peter K. Friz","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T21:09:50Z","title":"Cubature on Wiener space: pathwise convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4623","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:fd2ca18e7b5f44d10dcfbf7f0062465266235a60c5c3c0a015deb4144ae17bcb","target":"record","created_at":"2026-05-18T03:27:44Z","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":"12a7e871ff8c24a7a38d861c3d48516d550d5fe45ca5fef2fadc9e2e3019eaaf","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T21:09:50Z","title_canon_sha256":"b17afe9d8785fda63a95d3513365b57ac9f029663d9d7f334d011ad65fe57038"},"schema_version":"1.0","source":{"id":"1304.4623","kind":"arxiv","version":1}},"canonical_sha256":"5bf412242135b6466341335486f21596b329711a23b758c4a5eabc28790dfa7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bf412242135b6466341335486f21596b329711a23b758c4a5eabc28790dfa7b","first_computed_at":"2026-05-18T03:27:44.169445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:44.169445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uOqzfD1mC63ygSWdLVBY1zm1tdJRONk0w1jchjR2k6mMZTajNvD4FdUQSPfY8vQQSXyWsX4/eqD7pNt+l3qwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:44.170087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd2ca18e7b5f44d10dcfbf7f0062465266235a60c5c3c0a015deb4144ae17bcb","sha256:38475a40705f9fc06f834a40f7b9c5d60c329a71a05dc643c1097c6294ffb566"],"state_sha256":"819706ec361065cb19164f85eaa897fb9812132627360e24b93961b1e4e83ee3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYlfQywSjAJJeM3t8l4J1zD3E08uGgVQVJ1yP+pxYvQNwtZGFiyhYm0gjAQbVIL4YVbo+gMB9hpgWFH4e5BZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:19:12.930336Z","bundle_sha256":"0be514890687fc232bcb9fd16fd640d040960d1f131c9ebd3e526f2ca8b8f4ca"}}