{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IY5ZBWVC47XFC5P3K72BTBYZCK","short_pith_number":"pith:IY5ZBWVC","canonical_record":{"source":{"id":"1212.2324","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"93ec3f910538d095ce8505f50c0c30ad7739bf5794591d314c643d8e406fe6c6","abstract_canon_sha256":"8ff4d29d37a928ec82ad8426862fa59b19d6cbbf0a093f1d932b7b6682e7acc8"},"schema_version":"1.0"},"canonical_sha256":"463b90daa2e7ee5175fb57f41987191299b93a5ebb1888eda0265f3204d890e6","source":{"kind":"arxiv","id":"1212.2324","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2324","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2324v2","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2324","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"IY5ZBWVC47XF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IY5ZBWVC47XFC5P3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IY5ZBWVC","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IY5ZBWVC47XFC5P3K72BTBYZCK","target":"record","payload":{"canonical_record":{"source":{"id":"1212.2324","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"93ec3f910538d095ce8505f50c0c30ad7739bf5794591d314c643d8e406fe6c6","abstract_canon_sha256":"8ff4d29d37a928ec82ad8426862fa59b19d6cbbf0a093f1d932b7b6682e7acc8"},"schema_version":"1.0"},"canonical_sha256":"463b90daa2e7ee5175fb57f41987191299b93a5ebb1888eda0265f3204d890e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.128602Z","signature_b64":"MmSK1uD5e15CwFn8Zd8akgA8rNZEdV0BewxVXZVb4aQ3oAZMnfvDCViRfd9Ap7+eQ2upuz5v/Un6+9YD6ZRBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"463b90daa2e7ee5175fb57f41987191299b93a5ebb1888eda0265f3204d890e6","last_reissued_at":"2026-05-18T02:26:59.128246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.128246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.2324","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eh+HssP731WtsgixubCVOD1mIDsq0cT5diU7zG0Dei09IuivfQDKdaXeYdaeZJo3kUewF8uK2Ppd9MZCtRnPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T07:53:42.051644Z"},"content_sha256":"b083b97b393ff2d0879b87e0707a265ce2ea3bcf55bbdd1da1f086377a8b04d9","schema_version":"1.0","event_id":"sha256:b083b97b393ff2d0879b87e0707a265ce2ea3bcf55bbdd1da1f086377a8b04d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IY5ZBWVC47XFC5P3K72BTBYZCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic analysis for obtuse random walks","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tarek Hamdi, Uwe Franz","submitted_at":"2012-12-11T08:07:27Z","abstract_excerpt":"We present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The approach is based on the chaos representation property and discrete multiple stochastic integrals. We show that these operators satisfy similar identities as in the case of the Bernoulli randoms walks. We prove a Clark-Ocone-type predictable representation formula, obtain two covariance identities and derive a deviation inequality. We close the exposition by an application to option hedging in discrete time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2324","kind":"arxiv","version":2},"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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONh0d2IqTddrF2TlfwqHWKquTlmtkxPh8QtSZGtSpijSweIe1HyElcPsVwNjKGDkaarLnztPLDiwtHLH4gXXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T07:53:42.053914Z"},"content_sha256":"73dba25dd862b6558c76a9fe49aaa02ed6d73883ff927db92c6d1c3fe395c15e","schema_version":"1.0","event_id":"sha256:73dba25dd862b6558c76a9fe49aaa02ed6d73883ff927db92c6d1c3fe395c15e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/bundle.json","state_url":"https://pith.science/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/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":"2026-07-03T07:53:42Z","links":{"resolver":"https://pith.science/pith/IY5ZBWVC47XFC5P3K72BTBYZCK","bundle":"https://pith.science/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/bundle.json","state":"https://pith.science/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IY5ZBWVC47XFC5P3K72BTBYZCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IY5ZBWVC47XFC5P3K72BTBYZCK","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":"8ff4d29d37a928ec82ad8426862fa59b19d6cbbf0a093f1d932b7b6682e7acc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:07:27Z","title_canon_sha256":"93ec3f910538d095ce8505f50c0c30ad7739bf5794591d314c643d8e406fe6c6"},"schema_version":"1.0","source":{"id":"1212.2324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2324","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2324v2","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2324","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"IY5ZBWVC47XF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IY5ZBWVC47XFC5P3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IY5ZBWVC","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:73dba25dd862b6558c76a9fe49aaa02ed6d73883ff927db92c6d1c3fe395c15e","target":"graph","created_at":"2026-05-18T02:26:59Z","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 present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The approach is based on the chaos representation property and discrete multiple stochastic integrals. We show that these operators satisfy similar identities as in the case of the Bernoulli randoms walks. We prove a Clark-Ocone-type predictable representation formula, obtain two covariance identities and derive a deviation inequality. We close the exposition by an application to option hedging in discrete time.","authors_text":"Tarek Hamdi, Uwe Franz","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:07:27Z","title":"Stochastic analysis for obtuse random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2324","kind":"arxiv","version":2},"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:b083b97b393ff2d0879b87e0707a265ce2ea3bcf55bbdd1da1f086377a8b04d9","target":"record","created_at":"2026-05-18T02:26:59Z","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":"8ff4d29d37a928ec82ad8426862fa59b19d6cbbf0a093f1d932b7b6682e7acc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:07:27Z","title_canon_sha256":"93ec3f910538d095ce8505f50c0c30ad7739bf5794591d314c643d8e406fe6c6"},"schema_version":"1.0","source":{"id":"1212.2324","kind":"arxiv","version":2}},"canonical_sha256":"463b90daa2e7ee5175fb57f41987191299b93a5ebb1888eda0265f3204d890e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463b90daa2e7ee5175fb57f41987191299b93a5ebb1888eda0265f3204d890e6","first_computed_at":"2026-05-18T02:26:59.128246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.128246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmSK1uD5e15CwFn8Zd8akgA8rNZEdV0BewxVXZVb4aQ3oAZMnfvDCViRfd9Ap7+eQ2upuz5v/Un6+9YD6ZRBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.128602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b083b97b393ff2d0879b87e0707a265ce2ea3bcf55bbdd1da1f086377a8b04d9","sha256:73dba25dd862b6558c76a9fe49aaa02ed6d73883ff927db92c6d1c3fe395c15e"],"state_sha256":"d034fe846b8448f5701f32358f04b05e6db1b61d9d4725d8db95132b5883ff68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vV6/Dg2H1N1XZOkk77ieJ/L/NLvV+i7gYW8nHbMdbDedysOM9/p1tWo6pAz0G9YJSu47HLmLCX1jkM6rXM61AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T07:53:42.055800Z","bundle_sha256":"9a549bc8041df4c398b11d5db766cab1b8f306c29545b621eeaac3682d9cce0b"}}