{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E2QNCRWUQS2KWNUJ6HNKQA3KED","short_pith_number":"pith:E2QNCRWU","canonical_record":{"source":{"id":"1812.09904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-12-24T12:05:38Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"21d97eaffabc2b734f8da3cc2b0cedd825b390f08e52da179be300e805d23024","abstract_canon_sha256":"e171a2be0a09e8d607ab2ca9335d49813de7355dde672a3a39a784ecd278dc49"},"schema_version":"1.0"},"canonical_sha256":"26a0d146d484b4ab3689f1daa8036a20ea9a63dba8c7b37ec4422f97c2e76294","source":{"kind":"arxiv","id":"1812.09904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09904","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09904v1","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09904","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"E2QNCRWUQS2K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E2QNCRWUQS2KWNUJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E2QNCRWU","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E2QNCRWUQS2KWNUJ6HNKQA3KED","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-12-24T12:05:38Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"21d97eaffabc2b734f8da3cc2b0cedd825b390f08e52da179be300e805d23024","abstract_canon_sha256":"e171a2be0a09e8d607ab2ca9335d49813de7355dde672a3a39a784ecd278dc49"},"schema_version":"1.0"},"canonical_sha256":"26a0d146d484b4ab3689f1daa8036a20ea9a63dba8c7b37ec4422f97c2e76294","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:26.459210Z","signature_b64":"qZgiC9jZEO+FiSpDiQOSt8PKL58c/OAI4X7m1MxLcCIIr4aJtivnm8oz9YU/R+t1Qv18nkZnyr/N2oMrVSEYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26a0d146d484b4ab3689f1daa8036a20ea9a63dba8c7b37ec4422f97c2e76294","last_reissued_at":"2026-05-17T23:57:26.458627Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:26.458627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09904","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":"2026-05-17T23:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZcaberDOFe9klT1abnMyUiZTd3o/Z8V/xPml16m+g3nNh3aTzGNQCLhjpq7vVMMB1glANpgr7VxgTS12IxRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:45:42.573901Z"},"content_sha256":"509b597b2ae33ee63fdfcdb96692ce372eea488a6c9a2eb2392ffeafdd41bd07","schema_version":"1.0","event_id":"sha256:509b597b2ae33ee63fdfcdb96692ce372eea488a6c9a2eb2392ffeafdd41bd07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E2QNCRWUQS2KWNUJ6HNKQA3KED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A volatility-of-volatility expansion of the option prices in the SABR stochastic volatility model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"q-fin.CP","authors_text":"Olesya Grishchenko, Victor Nistor, Xiao Han","submitted_at":"2018-12-24T12:05:38Z","abstract_excerpt":"We propose a general, very fast method to quickly approximate the solution of a parabolic Partial Differential Equation (PDEs) with explicit formulas. Our method also provides equaly fast approximations of the derivatives of the solution, which is a challenge for many other methods. Our approach is based on a computable series expansion in terms of a \"small\" parameter. As an example, we treat in detail the important case of the SABR PDE for $\\beta = 1$, namely $\\partial_{\\tau}u = \\sigma^2 \\big [ \\frac{1}{2} (\\partial^2_xu - \\partial_xu) + \\nu \\rho \\partial_x\\partial_\\sigma u + \\frac{1}{2} \\nu^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09904","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":"2026-05-17T23:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/ZsjABtlv42pqTMjT0EeMZSktShRcjWV5/yBQiIB2ORbpl+0dZO3RUTfGdWVzqLCDGd5PAIz1HX+C3VmA/dBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:45:42.574514Z"},"content_sha256":"ecaf1eebaba687e58698bff5393ae345c587fb169339c5cb713de242c727c82e","schema_version":"1.0","event_id":"sha256:ecaf1eebaba687e58698bff5393ae345c587fb169339c5cb713de242c727c82e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/bundle.json","state_url":"https://pith.science/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/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":"2026-06-02T12:45:42Z","links":{"resolver":"https://pith.science/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED","bundle":"https://pith.science/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/bundle.json","state":"https://pith.science/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2QNCRWUQS2KWNUJ6HNKQA3KED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E2QNCRWUQS2KWNUJ6HNKQA3KED","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":"e171a2be0a09e8d607ab2ca9335d49813de7355dde672a3a39a784ecd278dc49","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-12-24T12:05:38Z","title_canon_sha256":"21d97eaffabc2b734f8da3cc2b0cedd825b390f08e52da179be300e805d23024"},"schema_version":"1.0","source":{"id":"1812.09904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09904","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09904v1","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09904","created_at":"2026-05-17T23:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"E2QNCRWUQS2K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E2QNCRWUQS2KWNUJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E2QNCRWU","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:ecaf1eebaba687e58698bff5393ae345c587fb169339c5cb713de242c727c82e","target":"graph","created_at":"2026-05-17T23:57:26Z","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 propose a general, very fast method to quickly approximate the solution of a parabolic Partial Differential Equation (PDEs) with explicit formulas. Our method also provides equaly fast approximations of the derivatives of the solution, which is a challenge for many other methods. Our approach is based on a computable series expansion in terms of a \"small\" parameter. As an example, we treat in detail the important case of the SABR PDE for $\\beta = 1$, namely $\\partial_{\\tau}u = \\sigma^2 \\big [ \\frac{1}{2} (\\partial^2_xu - \\partial_xu) + \\nu \\rho \\partial_x\\partial_\\sigma u + \\frac{1}{2} \\nu^","authors_text":"Olesya Grishchenko, Victor Nistor, Xiao Han","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-12-24T12:05:38Z","title":"A volatility-of-volatility expansion of the option prices in the SABR stochastic volatility model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09904","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":"sha256:509b597b2ae33ee63fdfcdb96692ce372eea488a6c9a2eb2392ffeafdd41bd07","target":"record","created_at":"2026-05-17T23:57:26Z","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":"e171a2be0a09e8d607ab2ca9335d49813de7355dde672a3a39a784ecd278dc49","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-12-24T12:05:38Z","title_canon_sha256":"21d97eaffabc2b734f8da3cc2b0cedd825b390f08e52da179be300e805d23024"},"schema_version":"1.0","source":{"id":"1812.09904","kind":"arxiv","version":1}},"canonical_sha256":"26a0d146d484b4ab3689f1daa8036a20ea9a63dba8c7b37ec4422f97c2e76294","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26a0d146d484b4ab3689f1daa8036a20ea9a63dba8c7b37ec4422f97c2e76294","first_computed_at":"2026-05-17T23:57:26.458627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:26.458627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZgiC9jZEO+FiSpDiQOSt8PKL58c/OAI4X7m1MxLcCIIr4aJtivnm8oz9YU/R+t1Qv18nkZnyr/N2oMrVSEYAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:26.459210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:509b597b2ae33ee63fdfcdb96692ce372eea488a6c9a2eb2392ffeafdd41bd07","sha256:ecaf1eebaba687e58698bff5393ae345c587fb169339c5cb713de242c727c82e"],"state_sha256":"103091990a9f01d17d705508af91e1d448e44a53a1ca8839a1b1f5238d2d8ae0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1/MWzQilLt3jeKxS2008QNEiRRxrQzIgPgHVyoFxFj0af7slzKIBAhqkmeaOxkZfRyrWb2g8mfiZ3shZWpfDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:45:42.577724Z","bundle_sha256":"b688e06366a538189e9d04eb7a03a0e53bd5750805f01ed753573e9010d9dbdd"}}