{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AYOLXPJZXIOCH2WIGWUPYHSFT6","short_pith_number":"pith:AYOLXPJZ","canonical_record":{"source":{"id":"1306.1062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-05T11:26:28Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"9a37260d38cd11d9034f0e8ff5031c0ba8ebc6e5bb825d07cff2270e3287d373","abstract_canon_sha256":"5ee5037146360c2e1a87afb5f74e993f9b3d476211a88d3539073bcc73eda430"},"schema_version":"1.0"},"canonical_sha256":"061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26","source":{"kind":"arxiv","id":"1306.1062","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1062","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1062v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1062","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"AYOLXPJZXIOC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AYOLXPJZXIOCH2WI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AYOLXPJZ","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AYOLXPJZXIOCH2WIGWUPYHSFT6","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-05T11:26:28Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"9a37260d38cd11d9034f0e8ff5031c0ba8ebc6e5bb825d07cff2270e3287d373","abstract_canon_sha256":"5ee5037146360c2e1a87afb5f74e993f9b3d476211a88d3539073bcc73eda430"},"schema_version":"1.0"},"canonical_sha256":"061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:44.482139Z","signature_b64":"QklG/DLh/7P7eYLrJlIwTZC6+XE60epn3PUkayN5Um/0bWa8fXmoOp083S1+oejuDlRRA6G61m8Sh5KCDgKJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26","last_reissued_at":"2026-05-18T03:21:44.481343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:44.481343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1062","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFr080WqrB7o+PbaAuBOMlm1/K9NgpdG9bnUDOqFgI9zp3jeoi3NEH/5b9qUQ1/TPbUlK/qja+QIbHPMZnh2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:31:35.328201Z"},"content_sha256":"ebb232751f980cc02b5e78c93e899a3420f40c0f9d17ac2ab86f15661d73ba2c","schema_version":"1.0","event_id":"sha256:ebb232751f980cc02b5e78c93e899a3420f40c0f9d17ac2ab86f15661d73ba2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AYOLXPJZXIOCH2WIGWUPYHSFT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An alternative proof of a result of Takaoka","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"math.PR","authors_text":"Shiqi Song","submitted_at":"2013-06-05T11:26:28Z","abstract_excerpt":"In Karatzas and Kardaras's paper on semimartingale financial models, it is proved that the NUPBR condition is a property of the local characteristic of the asset process alone. In Takaoka's paper on NUPBR, it is proved that the NUPBR condition is equivalent to the existence of a simga-martingale deflator. However, Takaoka's paper founds its proof on Delbaen and Schachermayer's fundamental asset pricing theorem, i.e. the NFLVR condition, which is not a pure property of the local characteristic of the asset process. In this paper we give an alternative proof of the result of Takaoka, which makes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1062","kind":"arxiv","version":1},"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":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AFr9+4VBzrKX7mcIe/RUUiWv03qzYt/2aEqHVkAv60ulFqELK2mUP1rYO7b02FPkpNmI+IgPKoga+B7KWioKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:31:35.328819Z"},"content_sha256":"26faf2eca7a5111e4f834b44442ac05bf5da3607c932c11fcd7ad5b973cf7fd5","schema_version":"1.0","event_id":"sha256:26faf2eca7a5111e4f834b44442ac05bf5da3607c932c11fcd7ad5b973cf7fd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/bundle.json","state_url":"https://pith.science/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/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":"2026-06-30T02:31:35Z","links":{"resolver":"https://pith.science/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6","bundle":"https://pith.science/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/bundle.json","state":"https://pith.science/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYOLXPJZXIOCH2WIGWUPYHSFT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AYOLXPJZXIOCH2WIGWUPYHSFT6","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":"5ee5037146360c2e1a87afb5f74e993f9b3d476211a88d3539073bcc73eda430","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-05T11:26:28Z","title_canon_sha256":"9a37260d38cd11d9034f0e8ff5031c0ba8ebc6e5bb825d07cff2270e3287d373"},"schema_version":"1.0","source":{"id":"1306.1062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1062","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1062v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1062","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"AYOLXPJZXIOC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AYOLXPJZXIOCH2WI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AYOLXPJZ","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:26faf2eca7a5111e4f834b44442ac05bf5da3607c932c11fcd7ad5b973cf7fd5","target":"graph","created_at":"2026-05-18T03:21:44Z","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":"In Karatzas and Kardaras's paper on semimartingale financial models, it is proved that the NUPBR condition is a property of the local characteristic of the asset process alone. In Takaoka's paper on NUPBR, it is proved that the NUPBR condition is equivalent to the existence of a simga-martingale deflator. However, Takaoka's paper founds its proof on Delbaen and Schachermayer's fundamental asset pricing theorem, i.e. the NFLVR condition, which is not a pure property of the local characteristic of the asset process. In this paper we give an alternative proof of the result of Takaoka, which makes","authors_text":"Shiqi Song","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-05T11:26:28Z","title":"An alternative proof of a result of Takaoka"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1062","kind":"arxiv","version":1},"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:ebb232751f980cc02b5e78c93e899a3420f40c0f9d17ac2ab86f15661d73ba2c","target":"record","created_at":"2026-05-18T03:21:44Z","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":"5ee5037146360c2e1a87afb5f74e993f9b3d476211a88d3539073bcc73eda430","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-05T11:26:28Z","title_canon_sha256":"9a37260d38cd11d9034f0e8ff5031c0ba8ebc6e5bb825d07cff2270e3287d373"},"schema_version":"1.0","source":{"id":"1306.1062","kind":"arxiv","version":1}},"canonical_sha256":"061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26","first_computed_at":"2026-05-18T03:21:44.481343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:44.481343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QklG/DLh/7P7eYLrJlIwTZC6+XE60epn3PUkayN5Um/0bWa8fXmoOp083S1+oejuDlRRA6G61m8Sh5KCDgKJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:44.482139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebb232751f980cc02b5e78c93e899a3420f40c0f9d17ac2ab86f15661d73ba2c","sha256:26faf2eca7a5111e4f834b44442ac05bf5da3607c932c11fcd7ad5b973cf7fd5"],"state_sha256":"a46bba7c7a997c35a570cc171243231c9c1567fa78ecb45f1ab7ac27c114e536"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gE8vzOorapXKaF9iAk+5BODkdSNIgGlveJ9mNTQIutIDNCUnlkHyM6GQwZHaaQVa7cM22uj8UkUYJZ/mspRLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T02:31:35.331957Z","bundle_sha256":"ffe7cb42ef509b973be2720a90fc9204deb8dcffa88570d9c84686019b0099ef"}}