{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PAVHDPLOE2VZINKSSDEUFA4J3U","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":"960097065f46ca34c7d48f0ea69ca5e59ac96f85c50399e2b4176eaa650633ea","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T11:44:56Z","title_canon_sha256":"598f269617d81db288495e31cc8776505952fb957c17ca5f218b8061ee13ef98"},"schema_version":"1.0","source":{"id":"1306.2793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2793","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2793v2","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2793","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"PAVHDPLOE2VZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PAVHDPLOE2VZINKS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PAVHDPLO","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e24107fa64196703d6457e5d6afa799d0efa0e3e3f2015a594121acb62be5f8c","target":"graph","created_at":"2026-05-18T01:17:47Z","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":"The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short time and small volatility expansions, respectively. The method works for general multi-factor models with correlations and leads to the analysis of a system of ordinary (Hamiltonian) differential equations. Surprisingly perhaps, even in two asset Black-Scholes situation (with its","authors_text":"Christian Bayer, Peter Friz, Peter Laurence","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T11:44:56Z","title":"On the probability density function of baskets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2793","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":"sha256:09d231b1d816f3f3ef007b594115853ed1a857c2ebf1d3fd59e2e5df4792a316","target":"record","created_at":"2026-05-18T01:17:47Z","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":"960097065f46ca34c7d48f0ea69ca5e59ac96f85c50399e2b4176eaa650633ea","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T11:44:56Z","title_canon_sha256":"598f269617d81db288495e31cc8776505952fb957c17ca5f218b8061ee13ef98"},"schema_version":"1.0","source":{"id":"1306.2793","kind":"arxiv","version":2}},"canonical_sha256":"782a71bd6e26ab94355290c9428389dd3cc757ccc8d9563b51461f2a9a14a42e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"782a71bd6e26ab94355290c9428389dd3cc757ccc8d9563b51461f2a9a14a42e","first_computed_at":"2026-05-18T01:17:47.362208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:47.362208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZeaSzlm2YbnHjbTyhrwgaBSMpW9t0jc5V2N+mD3w9vgOs89nZR1BPmiEvepsQqweLFqLeFToSSZ4tg5ITK/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:47.362877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09d231b1d816f3f3ef007b594115853ed1a857c2ebf1d3fd59e2e5df4792a316","sha256:e24107fa64196703d6457e5d6afa799d0efa0e3e3f2015a594121acb62be5f8c"],"state_sha256":"f44656fdecb6b541bfa575b6027c08e234a92d328921822a7d54c596ba9a05e7"}