{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MEKCT37MTL6R3KEVNXLGYGDGZF","short_pith_number":"pith:MEKCT37M","canonical_record":{"source":{"id":"1307.3578","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T20:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"d00c15200fb1493ea55f5b1f676676b21d68c02c878ebdb1d1c841941622cef2","abstract_canon_sha256":"66c8017eec629dd41e202419173d11f0576daddf08f23f9df8c4cff103ec457d"},"schema_version":"1.0"},"canonical_sha256":"611429efec9afd1da8956dd66c1866c96499d088a805685678038514deea22b7","source":{"kind":"arxiv","id":"1307.3578","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3578","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3578v5","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3578","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"MEKCT37MTL6R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MEKCT37MTL6R3KEV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MEKCT37M","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MEKCT37MTL6R3KEVNXLGYGDGZF","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3578","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T20:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"d00c15200fb1493ea55f5b1f676676b21d68c02c878ebdb1d1c841941622cef2","abstract_canon_sha256":"66c8017eec629dd41e202419173d11f0576daddf08f23f9df8c4cff103ec457d"},"schema_version":"1.0"},"canonical_sha256":"611429efec9afd1da8956dd66c1866c96499d088a805685678038514deea22b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:12.299649Z","signature_b64":"0bI6JYs6GBW24IiCDir57zPhJaVwSJkQgYFk4su/3DCRnMreXE6CAUwhE8N+tGvAJaClN9YKYIetHDqXwDTXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"611429efec9afd1da8956dd66c1866c96499d088a805685678038514deea22b7","last_reissued_at":"2026-05-18T02:32:12.299218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:12.299218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3578","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lee+sTz6JLjOmwUbXZIm6xWO4w/ziHLZXAaAF13T3yKWlyAOm5tHDGb/kzTNtvgajpTY2dcnPg22TeMufpVKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:15:26.534718Z"},"content_sha256":"a74e172630b9057dc9074870bd0dfe897306b905f7ea3c0e9d21358e2ad03dd8","schema_version":"1.0","event_id":"sha256:a74e172630b9057dc9074870bd0dfe897306b905f7ea3c0e9d21358e2ad03dd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MEKCT37MTL6R3KEVNXLGYGDGZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pathwise integrals and Ito-Tanaka Formula for Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lauri Viitasaari, Tommi Sottinen","submitted_at":"2013-07-12T20:59:02Z","abstract_excerpt":"We prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by F\\\"ollmer and as pathwise generalized Lebesgue-Stieltjes integrals introduced by Z\\\"ahle. As an application, we illustrate the importance of Ito-Tanaka formula for pricing and hedging of financial derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3578","kind":"arxiv","version":5},"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":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIPuodFiPB4JyMQ0U8VZ1md/jTNwzzuHE25oGxAzCKI7KRdl+9O2GU5OrL91w9Mt4KAdJPXjg7pBDdsDTeuZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:15:26.535062Z"},"content_sha256":"dde78233ada3ef8b70aeb90c283aca426734e2eb35f26f893644c87e72436ada","schema_version":"1.0","event_id":"sha256:dde78233ada3ef8b70aeb90c283aca426734e2eb35f26f893644c87e72436ada"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/bundle.json","state_url":"https://pith.science/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/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":"2026-06-25T13:15:26Z","links":{"resolver":"https://pith.science/pith/MEKCT37MTL6R3KEVNXLGYGDGZF","bundle":"https://pith.science/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/bundle.json","state":"https://pith.science/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEKCT37MTL6R3KEVNXLGYGDGZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MEKCT37MTL6R3KEVNXLGYGDGZF","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":"66c8017eec629dd41e202419173d11f0576daddf08f23f9df8c4cff103ec457d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T20:59:02Z","title_canon_sha256":"d00c15200fb1493ea55f5b1f676676b21d68c02c878ebdb1d1c841941622cef2"},"schema_version":"1.0","source":{"id":"1307.3578","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3578","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3578v5","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3578","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"MEKCT37MTL6R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MEKCT37MTL6R3KEV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MEKCT37M","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:dde78233ada3ef8b70aeb90c283aca426734e2eb35f26f893644c87e72436ada","target":"graph","created_at":"2026-05-18T02:32:12Z","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 prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by F\\\"ollmer and as pathwise generalized Lebesgue-Stieltjes integrals introduced by Z\\\"ahle. As an application, we illustrate the importance of Ito-Tanaka formula for pricing and hedging of financial derivatives.","authors_text":"Lauri Viitasaari, Tommi Sottinen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T20:59:02Z","title":"Pathwise integrals and Ito-Tanaka Formula for Gaussian processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3578","kind":"arxiv","version":5},"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:a74e172630b9057dc9074870bd0dfe897306b905f7ea3c0e9d21358e2ad03dd8","target":"record","created_at":"2026-05-18T02:32:12Z","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":"66c8017eec629dd41e202419173d11f0576daddf08f23f9df8c4cff103ec457d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T20:59:02Z","title_canon_sha256":"d00c15200fb1493ea55f5b1f676676b21d68c02c878ebdb1d1c841941622cef2"},"schema_version":"1.0","source":{"id":"1307.3578","kind":"arxiv","version":5}},"canonical_sha256":"611429efec9afd1da8956dd66c1866c96499d088a805685678038514deea22b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"611429efec9afd1da8956dd66c1866c96499d088a805685678038514deea22b7","first_computed_at":"2026-05-18T02:32:12.299218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:12.299218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0bI6JYs6GBW24IiCDir57zPhJaVwSJkQgYFk4su/3DCRnMreXE6CAUwhE8N+tGvAJaClN9YKYIetHDqXwDTXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:12.299649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3578","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a74e172630b9057dc9074870bd0dfe897306b905f7ea3c0e9d21358e2ad03dd8","sha256:dde78233ada3ef8b70aeb90c283aca426734e2eb35f26f893644c87e72436ada"],"state_sha256":"02808d8ab084882f1db3e5eeedb3bd258a8367d52b6b40a0970a9b893f86074d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6egHF5sm+OUwB3ueWUpu9hiionIwZpvQo88YI8buASvxartnawsgqdwYogLY+8XPV637HQVI5C5gRBUCJfFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:15:26.537074Z","bundle_sha256":"1efa363aa0e91b737dc70bae05401d3bc64306d27dc80788bd62d0c755fb6ae2"}}