{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BSKAJJSTZKP7QKH6RUSFMWPEC5","short_pith_number":"pith:BSKAJJST","canonical_record":{"source":{"id":"1006.3224","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","cross_cats_sorted":["math.AP","math.OC","math.PR","q-fin.PM"],"title_canon_sha256":"ab2eb038d06274a7e8b39d6d162ccc51cb126231bfc6dd4fff01ba6b49184ea0","abstract_canon_sha256":"208c3b19310aa8e5b6f1daad8d8a6a70382621b8e3b9baaa765aa3efcbc23970"},"schema_version":"1.0"},"canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","source":{"kind":"arxiv","id":"1006.3224","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3224","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3224v6","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3224","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"BSKAJJSTZKP7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BSKAJJSTZKP7QKH6","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BSKAJJST","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BSKAJJSTZKP7QKH6RUSFMWPEC5","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3224","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","cross_cats_sorted":["math.AP","math.OC","math.PR","q-fin.PM"],"title_canon_sha256":"ab2eb038d06274a7e8b39d6d162ccc51cb126231bfc6dd4fff01ba6b49184ea0","abstract_canon_sha256":"208c3b19310aa8e5b6f1daad8d8a6a70382621b8e3b9baaa765aa3efcbc23970"},"schema_version":"1.0"},"canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:24.514515Z","signature_b64":"Ic/wBrXwsFNkMI3/J7frfXPC/m7aG1//vB9jgOivz0QCgESaieWiIWZEGiWSXD5XQpJ/dh4o11MdYyxVJeHUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","last_reissued_at":"2026-05-18T03:48:24.513811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:24.513811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3224","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIx/5SLPlAT0Le1cn5odpDhE2Y/BOU62anlxnuv7E3fffebdvTbLSnyzXzV/EXuIcUftTtTI0Wh5WKEZRJznBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T14:39:31.619555Z"},"content_sha256":"7cdb81bca66467f2fa8009df20a294c3c58818c328bb131d12e4ede87fc789a0","schema_version":"1.0","event_id":"sha256:7cdb81bca66467f2fa8009df20a294c3c58818c328bb131d12e4ede87fc789a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BSKAJJSTZKP7QKH6RUSFMWPEC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outperforming the market portfolio with a given probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC","math.PR","q-fin.PM"],"primary_cat":"q-fin.CP","authors_text":"Erhan Bayraktar, Qingshuo Song, Yu-Jui Huang","submitted_at":"2010-06-13T12:57:30Z","abstract_excerpt":"Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3224","kind":"arxiv","version":6},"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":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G3RprE5tc1RVHXohEGMYjmjf+cvdGoh5NNFwE+P6ZlGsChyBSPHK8Aey3bFzbabe+UjcprjqldWx4LVmAgVSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T14:39:31.619900Z"},"content_sha256":"9973b2d862c20d5bafebf95114b37d56e41665dc20e79c04d99ab77fc67e8903","schema_version":"1.0","event_id":"sha256:9973b2d862c20d5bafebf95114b37d56e41665dc20e79c04d99ab77fc67e8903"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/bundle.json","state_url":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/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":"2026-05-20T14:39:31Z","links":{"resolver":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5","bundle":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/bundle.json","state":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BSKAJJSTZKP7QKH6RUSFMWPEC5","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":"208c3b19310aa8e5b6f1daad8d8a6a70382621b8e3b9baaa765aa3efcbc23970","cross_cats_sorted":["math.AP","math.OC","math.PR","q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","title_canon_sha256":"ab2eb038d06274a7e8b39d6d162ccc51cb126231bfc6dd4fff01ba6b49184ea0"},"schema_version":"1.0","source":{"id":"1006.3224","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3224","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3224v6","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3224","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"BSKAJJSTZKP7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BSKAJJSTZKP7QKH6","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BSKAJJST","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:9973b2d862c20d5bafebf95114b37d56e41665dc20e79c04d99ab77fc67e8903","target":"graph","created_at":"2026-05-18T03:48:24Z","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":"Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local","authors_text":"Erhan Bayraktar, Qingshuo Song, Yu-Jui Huang","cross_cats":["math.AP","math.OC","math.PR","q-fin.PM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","title":"Outperforming the market portfolio with a given probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3224","kind":"arxiv","version":6},"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":"sha256:7cdb81bca66467f2fa8009df20a294c3c58818c328bb131d12e4ede87fc789a0","target":"record","created_at":"2026-05-18T03:48:24Z","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":"208c3b19310aa8e5b6f1daad8d8a6a70382621b8e3b9baaa765aa3efcbc23970","cross_cats_sorted":["math.AP","math.OC","math.PR","q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","title_canon_sha256":"ab2eb038d06274a7e8b39d6d162ccc51cb126231bfc6dd4fff01ba6b49184ea0"},"schema_version":"1.0","source":{"id":"1006.3224","kind":"arxiv","version":6}},"canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","first_computed_at":"2026-05-18T03:48:24.513811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:24.513811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ic/wBrXwsFNkMI3/J7frfXPC/m7aG1//vB9jgOivz0QCgESaieWiIWZEGiWSXD5XQpJ/dh4o11MdYyxVJeHUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:24.514515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3224","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cdb81bca66467f2fa8009df20a294c3c58818c328bb131d12e4ede87fc789a0","sha256:9973b2d862c20d5bafebf95114b37d56e41665dc20e79c04d99ab77fc67e8903"],"state_sha256":"2ec701960acca0aaa0e94d539856269e2ae3967b9c05b47de682520f471bcf2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASQiSDDMZ2lUcY0GbBGA+KB4tRB7yObdp6uVwBLh2tCDGJ8SKwlp8pbBOZt731/esdWLLMeFwedmp6LGHx3+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T14:39:31.621805Z","bundle_sha256":"0afec3adfb759ee2a15073fd044307607bd9bfab36ef943f219e1660435b1d57"}}