{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VRJETIDF5BXT6MNNMKWINQHOH2","short_pith_number":"pith:VRJETIDF","canonical_record":{"source":{"id":"1004.4153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-04-23T14:58:56Z","cross_cats_sorted":["math.PR","q-fin.CP"],"title_canon_sha256":"78d74b7a96c856ec9cde0f99dcbf2041d4b6d830947d6b336a7655a7baa39654","abstract_canon_sha256":"3d811b649a6ea06cd464d0ad417d0e01b6ff3fe50c406c96ea5cc27b0d68acdf"},"schema_version":"1.0"},"canonical_sha256":"ac5249a065e86f3f31ad62ac86c0ee3eb7b09f526bb4f75e471bb0a1b26a8a8b","source":{"kind":"arxiv","id":"1004.4153","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4153","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4153v2","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4153","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRJETIDF5BXT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VRJETIDF5BXT6MNN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VRJETIDF","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VRJETIDF5BXT6MNNMKWINQHOH2","target":"record","payload":{"canonical_record":{"source":{"id":"1004.4153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-04-23T14:58:56Z","cross_cats_sorted":["math.PR","q-fin.CP"],"title_canon_sha256":"78d74b7a96c856ec9cde0f99dcbf2041d4b6d830947d6b336a7655a7baa39654","abstract_canon_sha256":"3d811b649a6ea06cd464d0ad417d0e01b6ff3fe50c406c96ea5cc27b0d68acdf"},"schema_version":"1.0"},"canonical_sha256":"ac5249a065e86f3f31ad62ac86c0ee3eb7b09f526bb4f75e471bb0a1b26a8a8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:50.345662Z","signature_b64":"fdlo5rMW12CBJunmni+KSZzvjYHzkXbq/Rc56giHZ5mqEMgaq2nTlKG4ZOBL2nOppPq7NURIEmSQ8Me5gRU2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac5249a065e86f3f31ad62ac86c0ee3eb7b09f526bb4f75e471bb0a1b26a8a8b","last_reissued_at":"2026-05-18T04:25:50.344947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:50.344947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.4153","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":"2026-05-18T04:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Yp/i8XXzkpS0KfH77zgRHdpEFXBI65iEh7UWo2ZsSjuQU3GmQr7oiXuknANs4Dw+cveK0P6WfivAlr16j+6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:34:30.514564Z"},"content_sha256":"7c3e70c2b1827d2190ee11a18bde4aa344cc60c203fe692a8a0f2b57b0e159a7","schema_version":"1.0","event_id":"sha256:7c3e70c2b1827d2190ee11a18bde4aa344cc60c203fe692a8a0f2b57b0e159a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VRJETIDF5BXT6MNNMKWINQHOH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Frechet bounds and model-free pricing of multi-asset options","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.CP"],"primary_cat":"q-fin.PR","authors_text":"Ecole Polytechnique), Peter Tankov (CMAP","submitted_at":"2010-04-23T14:58:56Z","abstract_excerpt":"Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of $[0,1]^2$, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4153","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":"2026-05-18T04:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dwmnMktOWeCsQcWnAFaYZjJVBmrrOG0s+JMrnmHPLo5s9CMxn1yNTo2wxN2jtFmigTmR9XkMxwrMzQr5K4wNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:34:30.514909Z"},"content_sha256":"a5c35c936a743a35f7a9d576a1313e9f518dee23239d561e4fcfc09be2214ece","schema_version":"1.0","event_id":"sha256:a5c35c936a743a35f7a9d576a1313e9f518dee23239d561e4fcfc09be2214ece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRJETIDF5BXT6MNNMKWINQHOH2/bundle.json","state_url":"https://pith.science/pith/VRJETIDF5BXT6MNNMKWINQHOH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRJETIDF5BXT6MNNMKWINQHOH2/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":"2026-06-04T06:34:30Z","links":{"resolver":"https://pith.science/pith/VRJETIDF5BXT6MNNMKWINQHOH2","bundle":"https://pith.science/pith/VRJETIDF5BXT6MNNMKWINQHOH2/bundle.json","state":"https://pith.science/pith/VRJETIDF5BXT6MNNMKWINQHOH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRJETIDF5BXT6MNNMKWINQHOH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VRJETIDF5BXT6MNNMKWINQHOH2","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":"3d811b649a6ea06cd464d0ad417d0e01b6ff3fe50c406c96ea5cc27b0d68acdf","cross_cats_sorted":["math.PR","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-04-23T14:58:56Z","title_canon_sha256":"78d74b7a96c856ec9cde0f99dcbf2041d4b6d830947d6b336a7655a7baa39654"},"schema_version":"1.0","source":{"id":"1004.4153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4153","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4153v2","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4153","created_at":"2026-05-18T04:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRJETIDF5BXT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VRJETIDF5BXT6MNN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VRJETIDF","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a5c35c936a743a35f7a9d576a1313e9f518dee23239d561e4fcfc09be2214ece","target":"graph","created_at":"2026-05-18T04:25:50Z","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":"Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of $[0,1]^2$, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.","authors_text":"Ecole Polytechnique), Peter Tankov (CMAP","cross_cats":["math.PR","q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-04-23T14:58:56Z","title":"Improved Frechet bounds and model-free pricing of multi-asset options"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4153","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":"sha256:7c3e70c2b1827d2190ee11a18bde4aa344cc60c203fe692a8a0f2b57b0e159a7","target":"record","created_at":"2026-05-18T04:25:50Z","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":"3d811b649a6ea06cd464d0ad417d0e01b6ff3fe50c406c96ea5cc27b0d68acdf","cross_cats_sorted":["math.PR","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2010-04-23T14:58:56Z","title_canon_sha256":"78d74b7a96c856ec9cde0f99dcbf2041d4b6d830947d6b336a7655a7baa39654"},"schema_version":"1.0","source":{"id":"1004.4153","kind":"arxiv","version":2}},"canonical_sha256":"ac5249a065e86f3f31ad62ac86c0ee3eb7b09f526bb4f75e471bb0a1b26a8a8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac5249a065e86f3f31ad62ac86c0ee3eb7b09f526bb4f75e471bb0a1b26a8a8b","first_computed_at":"2026-05-18T04:25:50.344947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:50.344947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fdlo5rMW12CBJunmni+KSZzvjYHzkXbq/Rc56giHZ5mqEMgaq2nTlKG4ZOBL2nOppPq7NURIEmSQ8Me5gRU2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:50.345662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c3e70c2b1827d2190ee11a18bde4aa344cc60c203fe692a8a0f2b57b0e159a7","sha256:a5c35c936a743a35f7a9d576a1313e9f518dee23239d561e4fcfc09be2214ece"],"state_sha256":"3ac1c95474d37d8823411b6af7a7ae2250b9858c276936787bca5e4d2c0d2776"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIGDXkh/XJf4z9sIj45rvZfVb2TWcO0cOZSTgt/p6mALMgKRuz2gmuXUbKVBHv6dbkjUkE/SpZiQJmNfbUXbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:34:30.517159Z","bundle_sha256":"c6631610a4de4f743e1a6a0ec9cbc0749d892cea0c477546d238ee67fcd8b3d5"}}