{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IOIYBDUQAMWSBDW3LSYZASYRF6","short_pith_number":"pith:IOIYBDUQ","canonical_record":{"source":{"id":"1005.1760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2010-05-11T08:51:57Z","cross_cats_sorted":["math.PR","q-fin.GN","q-fin.PR"],"title_canon_sha256":"d287288c866614714e75a7b9af1e906675cd1f520df19708753e3f668c5015f7","abstract_canon_sha256":"c9f31e194ebe2d3680db1a03bc850b3c98e17d322c8b6edf3b487473c1869d36"},"schema_version":"1.0"},"canonical_sha256":"4391808e90032d208edb5cb1904b112f8006ca33870fe5dd04747976cc3ac8e3","source":{"kind":"arxiv","id":"1005.1760","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1760","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1760v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1760","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"IOIYBDUQAMWS","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOIYBDUQAMWSBDW3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOIYBDUQ","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IOIYBDUQAMWSBDW3LSYZASYRF6","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2010-05-11T08:51:57Z","cross_cats_sorted":["math.PR","q-fin.GN","q-fin.PR"],"title_canon_sha256":"d287288c866614714e75a7b9af1e906675cd1f520df19708753e3f668c5015f7","abstract_canon_sha256":"c9f31e194ebe2d3680db1a03bc850b3c98e17d322c8b6edf3b487473c1869d36"},"schema_version":"1.0"},"canonical_sha256":"4391808e90032d208edb5cb1904b112f8006ca33870fe5dd04747976cc3ac8e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:10.882495Z","signature_b64":"K3Pnqjxuexh7GX8E2Gmxi8zOL8LkRHBnccuCjSADX0pWk/eNlltkHXwj/0+qpZFCRkXZ7ub0YJBrRgptoie/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4391808e90032d208edb5cb1904b112f8006ca33870fe5dd04747976cc3ac8e3","last_reissued_at":"2026-05-18T04:21:10.881907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:10.881907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1760","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wgrW9hKermdAhKwWxzspP2M08tKlzOeRF/3v3m+Mo/KJBbBrar3JZZCMfTDWufVirH1RLQZ3XsqA56JHPKPxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:27:45.471557Z"},"content_sha256":"4f7e7eaa2c65471cdeea47a3d0e645b927a653cc2482cc6ba611c2ba4d3fb1d2","schema_version":"1.0","event_id":"sha256:4f7e7eaa2c65471cdeea47a3d0e645b927a653cc2482cc6ba611c2ba4d3fb1d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IOIYBDUQAMWSBDW3LSYZASYRF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two stock options at the races: Black-Scholes forecasts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.GN","q-fin.PR"],"primary_cat":"q-fin.ST","authors_text":"Gleb Oshanin, Gregory Schehr","submitted_at":"2010-05-11T08:51:57Z","abstract_excerpt":"Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within the classical Black and Scholes (BS) model, focusing on the evolution of the probability density function P(w) of a random variable w = a_T^{(1)}/(a_T^{(1)} + a_T^{(2)}) where a_T^{(1)} and a_T^{(2)} are the values of two (either European- or the Asian-style) options produced by two absolutely identical BS stochastic equations. We show that within the realm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1760","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZt1mxtEQlyJUMwpARe2TOZYD2GlgcjbISu4ZXJzxmrJb9RzLvY23WMCYKRmqbPu8aG3pVEFzNRdN7sgtdybBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:27:45.472161Z"},"content_sha256":"9a8e1307c7453ed7ccf34049598bc994b4cd4b27c2ff92b75a3338e94bd9ac12","schema_version":"1.0","event_id":"sha256:9a8e1307c7453ed7ccf34049598bc994b4cd4b27c2ff92b75a3338e94bd9ac12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/bundle.json","state_url":"https://pith.science/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/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":"2026-05-27T02:27:45Z","links":{"resolver":"https://pith.science/pith/IOIYBDUQAMWSBDW3LSYZASYRF6","bundle":"https://pith.science/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/bundle.json","state":"https://pith.science/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOIYBDUQAMWSBDW3LSYZASYRF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IOIYBDUQAMWSBDW3LSYZASYRF6","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":"c9f31e194ebe2d3680db1a03bc850b3c98e17d322c8b6edf3b487473c1869d36","cross_cats_sorted":["math.PR","q-fin.GN","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2010-05-11T08:51:57Z","title_canon_sha256":"d287288c866614714e75a7b9af1e906675cd1f520df19708753e3f668c5015f7"},"schema_version":"1.0","source":{"id":"1005.1760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1760","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1760v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1760","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"IOIYBDUQAMWS","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOIYBDUQAMWSBDW3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOIYBDUQ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9a8e1307c7453ed7ccf34049598bc994b4cd4b27c2ff92b75a3338e94bd9ac12","target":"graph","created_at":"2026-05-18T04:21:10Z","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":"Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within the classical Black and Scholes (BS) model, focusing on the evolution of the probability density function P(w) of a random variable w = a_T^{(1)}/(a_T^{(1)} + a_T^{(2)}) where a_T^{(1)} and a_T^{(2)} are the values of two (either European- or the Asian-style) options produced by two absolutely identical BS stochastic equations. We show that within the realm","authors_text":"Gleb Oshanin, Gregory Schehr","cross_cats":["math.PR","q-fin.GN","q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2010-05-11T08:51:57Z","title":"Two stock options at the races: Black-Scholes forecasts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1760","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":"sha256:4f7e7eaa2c65471cdeea47a3d0e645b927a653cc2482cc6ba611c2ba4d3fb1d2","target":"record","created_at":"2026-05-18T04:21:10Z","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":"c9f31e194ebe2d3680db1a03bc850b3c98e17d322c8b6edf3b487473c1869d36","cross_cats_sorted":["math.PR","q-fin.GN","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2010-05-11T08:51:57Z","title_canon_sha256":"d287288c866614714e75a7b9af1e906675cd1f520df19708753e3f668c5015f7"},"schema_version":"1.0","source":{"id":"1005.1760","kind":"arxiv","version":2}},"canonical_sha256":"4391808e90032d208edb5cb1904b112f8006ca33870fe5dd04747976cc3ac8e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4391808e90032d208edb5cb1904b112f8006ca33870fe5dd04747976cc3ac8e3","first_computed_at":"2026-05-18T04:21:10.881907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:10.881907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3Pnqjxuexh7GX8E2Gmxi8zOL8LkRHBnccuCjSADX0pWk/eNlltkHXwj/0+qpZFCRkXZ7ub0YJBrRgptoie/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:10.882495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f7e7eaa2c65471cdeea47a3d0e645b927a653cc2482cc6ba611c2ba4d3fb1d2","sha256:9a8e1307c7453ed7ccf34049598bc994b4cd4b27c2ff92b75a3338e94bd9ac12"],"state_sha256":"aa3c660f382b51b2526984862dd0caee4e6a807f6267901e7c1f57dd46ef8ef1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UvHBezWfumauS2S1DALoefhyW0vzEDMW7W6azsqqgnpvvDenottOuocrYG8zHu3YRon5LNtzmqngZMQjggHUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:27:45.475332Z","bundle_sha256":"f3fdd4e0800eaf5a26fa1cc0d0b3ee0100f9261f0fb83cf91d226ddd2294f15c"}}