{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FHLDHUFABZIE7OR4GBLPKCTIBA","short_pith_number":"pith:FHLDHUFA","canonical_record":{"source":{"id":"1405.4537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-18T18:49:32Z","cross_cats_sorted":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"title_canon_sha256":"0811f847cf7c67cdd6d35a75fb98f7230c0f71b9bdce7ac031f31f5dd56d5744","abstract_canon_sha256":"4ef8fdcc73d5da0500f3db72eb2756eb620c83b8d3ba125a796c922c0b189079"},"schema_version":"1.0"},"canonical_sha256":"29d633d0a00e504fba3c3056f50a680805309a462c0ad49ab135d6107b318abe","source":{"kind":"arxiv","id":"1405.4537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4537","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4537v1","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4537","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"FHLDHUFABZIE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHLDHUFABZIE7OR4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHLDHUFA","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FHLDHUFABZIE7OR4GBLPKCTIBA","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-18T18:49:32Z","cross_cats_sorted":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"title_canon_sha256":"0811f847cf7c67cdd6d35a75fb98f7230c0f71b9bdce7ac031f31f5dd56d5744","abstract_canon_sha256":"4ef8fdcc73d5da0500f3db72eb2756eb620c83b8d3ba125a796c922c0b189079"},"schema_version":"1.0"},"canonical_sha256":"29d633d0a00e504fba3c3056f50a680805309a462c0ad49ab135d6107b318abe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:35.227183Z","signature_b64":"RYyY6mNnEMo4rMcF7m2XzWPPj8CIbPTfBQNFBAF01Ok0nfRLZYrA17BR+F32hPrpEbwmfdID5FoA4+5UcKXeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29d633d0a00e504fba3c3056f50a680805309a462c0ad49ab135d6107b318abe","last_reissued_at":"2026-05-18T02:51:35.226740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:35.226740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4537","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":"2026-05-18T02:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOhWVUZXQ3XH88+4QB6ekc+p3K6N4xHSfOxuIAuyOkifCWfQcd0fA23B237vAiDQI6W60o0u1PLxSMgAThvGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T16:36:41.534231Z"},"content_sha256":"a2087bda5fa3f4587d9574bf161f5b4a25be995723ed8785aa35082760135628","schema_version":"1.0","event_id":"sha256:a2087bda5fa3f4587d9574bf161f5b4a25be995723ed8785aa35082760135628"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FHLDHUFABZIE7OR4GBLPKCTIBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rough paths, Signatures and the modelling of functions on streams","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"primary_cat":"math.PR","authors_text":"Terry Lyons","submitted_at":"2014-05-18T18:49:32Z","abstract_excerpt":"Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform estimates, have widespread application and have simplified proofs of basic questions from the large deviation theory and extended Ito's theory of SDEs; the recent applications contribute to (Graham) automated recognition of Chinese handwriting and (Hairer) formulation of appropriate SPDEs to model randomly evolving interfaces. At the heart of the mathematics is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4537","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":"2026-05-18T02:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U4GXn4XEp+krhA47Fnx/NZhVXkjNjlXQoscnB7e+1ZRYP02OP9N6ESgx0m7tenfQ00H8NT0catbguRaW91qdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T16:36:41.534924Z"},"content_sha256":"ebcced4697dbab32bd45bd452173f0df1d8e9152529c091076dadaaf1722a4e4","schema_version":"1.0","event_id":"sha256:ebcced4697dbab32bd45bd452173f0df1d8e9152529c091076dadaaf1722a4e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/bundle.json","state_url":"https://pith.science/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/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":"2026-05-18T16:36:41Z","links":{"resolver":"https://pith.science/pith/FHLDHUFABZIE7OR4GBLPKCTIBA","bundle":"https://pith.science/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/bundle.json","state":"https://pith.science/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHLDHUFABZIE7OR4GBLPKCTIBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FHLDHUFABZIE7OR4GBLPKCTIBA","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":"4ef8fdcc73d5da0500f3db72eb2756eb620c83b8d3ba125a796c922c0b189079","cross_cats_sorted":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-18T18:49:32Z","title_canon_sha256":"0811f847cf7c67cdd6d35a75fb98f7230c0f71b9bdce7ac031f31f5dd56d5744"},"schema_version":"1.0","source":{"id":"1405.4537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4537","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4537v1","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4537","created_at":"2026-05-18T02:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"FHLDHUFABZIE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHLDHUFABZIE7OR4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHLDHUFA","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:ebcced4697dbab32bd45bd452173f0df1d8e9152529c091076dadaaf1722a4e4","target":"graph","created_at":"2026-05-18T02:51:35Z","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":"Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform estimates, have widespread application and have simplified proofs of basic questions from the large deviation theory and extended Ito's theory of SDEs; the recent applications contribute to (Graham) automated recognition of Chinese handwriting and (Hairer) formulation of appropriate SPDEs to model randomly evolving interfaces. At the heart of the mathematics is the","authors_text":"Terry Lyons","cross_cats":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-18T18:49:32Z","title":"Rough paths, Signatures and the modelling of functions on streams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4537","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:a2087bda5fa3f4587d9574bf161f5b4a25be995723ed8785aa35082760135628","target":"record","created_at":"2026-05-18T02:51:35Z","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":"4ef8fdcc73d5da0500f3db72eb2756eb620c83b8d3ba125a796c922c0b189079","cross_cats_sorted":["math.CA","math.RA","math.ST","q-fin.MF","stat.TH"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-18T18:49:32Z","title_canon_sha256":"0811f847cf7c67cdd6d35a75fb98f7230c0f71b9bdce7ac031f31f5dd56d5744"},"schema_version":"1.0","source":{"id":"1405.4537","kind":"arxiv","version":1}},"canonical_sha256":"29d633d0a00e504fba3c3056f50a680805309a462c0ad49ab135d6107b318abe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29d633d0a00e504fba3c3056f50a680805309a462c0ad49ab135d6107b318abe","first_computed_at":"2026-05-18T02:51:35.226740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:35.226740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RYyY6mNnEMo4rMcF7m2XzWPPj8CIbPTfBQNFBAF01Ok0nfRLZYrA17BR+F32hPrpEbwmfdID5FoA4+5UcKXeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:35.227183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2087bda5fa3f4587d9574bf161f5b4a25be995723ed8785aa35082760135628","sha256:ebcced4697dbab32bd45bd452173f0df1d8e9152529c091076dadaaf1722a4e4"],"state_sha256":"9434bc7a35363abf73244bf501d548082788268ba4b1137bcaa9a82188eee2d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dxROJWJ36mAIROj1m5CQg/aAKx7zuvHro0cKlt5L0wD0dv8f8JNlTzufQdV1o9VnV5hBkqJfuktsplj7Mmo3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T16:36:41.536942Z","bundle_sha256":"ac18081e5717a3dac04401cd8645afd42979b71408df8a3b02cbc435610b9f02"}}