{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MB7KDFVCSBHAQMIJA4ZUAZCOM7","short_pith_number":"pith:MB7KDFVC","canonical_record":{"source":{"id":"1605.08996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-29T12:06:12Z","cross_cats_sorted":[],"title_canon_sha256":"9fd8f3da0c1afded6e8e8893a60baf590b8a5f22eb4a41d12249c85056d23a6e","abstract_canon_sha256":"ffe82793aecb95a3cd88791edea1fc86526fe97461c2415b4c49cd2840874920"},"schema_version":"1.0"},"canonical_sha256":"607ea196a2904e083109073340644e67d96995145fec1ccecf98271ecd4d0c31","source":{"kind":"arxiv","id":"1605.08996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08996","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08996v1","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08996","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"MB7KDFVCSBHA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MB7KDFVCSBHAQMIJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MB7KDFVC","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MB7KDFVCSBHAQMIJA4ZUAZCOM7","target":"record","payload":{"canonical_record":{"source":{"id":"1605.08996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-29T12:06:12Z","cross_cats_sorted":[],"title_canon_sha256":"9fd8f3da0c1afded6e8e8893a60baf590b8a5f22eb4a41d12249c85056d23a6e","abstract_canon_sha256":"ffe82793aecb95a3cd88791edea1fc86526fe97461c2415b4c49cd2840874920"},"schema_version":"1.0"},"canonical_sha256":"607ea196a2904e083109073340644e67d96995145fec1ccecf98271ecd4d0c31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:22.384271Z","signature_b64":"otYOlHw+jSetaFUN1L5yKLAwVR4dp7bHvNN4GsRhdfBTce3445V2wq8exyNZSN/o9/T6gz9BN3vj9N8ZGUa/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"607ea196a2904e083109073340644e67d96995145fec1ccecf98271ecd4d0c31","last_reissued_at":"2026-05-18T01:13:22.383747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:22.383747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.08996","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":"2026-05-18T01:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBEKHRJTFxDNa5x/BNucN+htFSFLDldNuc9hDQG8LhPPdCzwaosuEXrEOxsGxRLltT1P2gi42EMlDk1ey9yhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:15:47.439464Z"},"content_sha256":"92a76b4184f2af1f72dd3d0f6a85f919843e893d48a890cffbcbe169635f15bc","schema_version":"1.0","event_id":"sha256:92a76b4184f2af1f72dd3d0f6a85f919843e893d48a890cffbcbe169635f15bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MB7KDFVCSBHAQMIJA4ZUAZCOM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wasserstein approximations of the L\\'evy area random walk via polynomial perturbations of Gaussian distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guy Flint","submitted_at":"2016-05-29T12:06:12Z","abstract_excerpt":"We construct a coupling between the random walk composed of L\\'evy area increments from a $d$-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used to produce a new pathwise approximation scheme for stochastic differential equations in the preprint [Flint-Lyons-2015]. The coupling arguments of the present paper are based extensively on the recent coupling results of Davie concerning a multidimensional variant of the Koml\\'os-Major-Tusn\\'ady theorem and Wasserstein estimates for polynomial perturbations o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08996","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":"2026-05-18T01:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQ9Nj86VGCgWLBFjQaE5rJOdxUH/0dda2CUt0h7z1YTJ4i216C64rg5bH51EZXJ4EiicOTOgDCwS81Qg6yRGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:15:47.439820Z"},"content_sha256":"739906cdf1c60f2c984d7dcd1baba9ad79bed2e1fec967a73907320047e7c9b4","schema_version":"1.0","event_id":"sha256:739906cdf1c60f2c984d7dcd1baba9ad79bed2e1fec967a73907320047e7c9b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/bundle.json","state_url":"https://pith.science/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/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":"2026-06-12T05:15:47Z","links":{"resolver":"https://pith.science/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7","bundle":"https://pith.science/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/bundle.json","state":"https://pith.science/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MB7KDFVCSBHAQMIJA4ZUAZCOM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MB7KDFVCSBHAQMIJA4ZUAZCOM7","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":"ffe82793aecb95a3cd88791edea1fc86526fe97461c2415b4c49cd2840874920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-29T12:06:12Z","title_canon_sha256":"9fd8f3da0c1afded6e8e8893a60baf590b8a5f22eb4a41d12249c85056d23a6e"},"schema_version":"1.0","source":{"id":"1605.08996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08996","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08996v1","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08996","created_at":"2026-05-18T01:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"MB7KDFVCSBHA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MB7KDFVCSBHAQMIJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MB7KDFVC","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:739906cdf1c60f2c984d7dcd1baba9ad79bed2e1fec967a73907320047e7c9b4","target":"graph","created_at":"2026-05-18T01:13:22Z","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":"We construct a coupling between the random walk composed of L\\'evy area increments from a $d$-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used to produce a new pathwise approximation scheme for stochastic differential equations in the preprint [Flint-Lyons-2015]. The coupling arguments of the present paper are based extensively on the recent coupling results of Davie concerning a multidimensional variant of the Koml\\'os-Major-Tusn\\'ady theorem and Wasserstein estimates for polynomial perturbations o","authors_text":"Guy Flint","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-29T12:06:12Z","title":"Wasserstein approximations of the L\\'evy area random walk via polynomial perturbations of Gaussian distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08996","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":"sha256:92a76b4184f2af1f72dd3d0f6a85f919843e893d48a890cffbcbe169635f15bc","target":"record","created_at":"2026-05-18T01:13:22Z","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":"ffe82793aecb95a3cd88791edea1fc86526fe97461c2415b4c49cd2840874920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-29T12:06:12Z","title_canon_sha256":"9fd8f3da0c1afded6e8e8893a60baf590b8a5f22eb4a41d12249c85056d23a6e"},"schema_version":"1.0","source":{"id":"1605.08996","kind":"arxiv","version":1}},"canonical_sha256":"607ea196a2904e083109073340644e67d96995145fec1ccecf98271ecd4d0c31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607ea196a2904e083109073340644e67d96995145fec1ccecf98271ecd4d0c31","first_computed_at":"2026-05-18T01:13:22.383747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:22.383747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"otYOlHw+jSetaFUN1L5yKLAwVR4dp7bHvNN4GsRhdfBTce3445V2wq8exyNZSN/o9/T6gz9BN3vj9N8ZGUa/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:22.384271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a76b4184f2af1f72dd3d0f6a85f919843e893d48a890cffbcbe169635f15bc","sha256:739906cdf1c60f2c984d7dcd1baba9ad79bed2e1fec967a73907320047e7c9b4"],"state_sha256":"afe354932b63fb13c142b374d24f966a329842d7325c0cbe92ce4b7f2a9d64c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/7tSTGIT5PAzKbgGtR0ZUT4R/N5lthrvZL8+/rP/dQHG0VUrFZHL2lp63UIKgvic7+AgRlrGsvi06w4cd7d+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:15:47.442105Z","bundle_sha256":"2156739fefc8fcab0a368f16763208f18a3205aa07409d952473e2488c52add5"}}