{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NQQDJ765OJANCDOSMBT26ES4BG","short_pith_number":"pith:NQQDJ765","canonical_record":{"source":{"id":"1905.01859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T07:46:47Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"6a7704470808febe8d336afd804fef43e2c27373f288f4496aa31e90fd4a157e","abstract_canon_sha256":"4149616833089243eced0697424ab8ac6959ea34f54f65a03681d3cb6a1d1358"},"schema_version":"1.0"},"canonical_sha256":"6c2034ffdd7240d10dd26067af125c09b5ae7150f43b79232116f8687474db94","source":{"kind":"arxiv","id":"1905.01859","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01859","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01859v2","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01859","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"NQQDJ765OJAN","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NQQDJ765OJANCDOS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NQQDJ765","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NQQDJ765OJANCDOSMBT26ES4BG","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T07:46:47Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"6a7704470808febe8d336afd804fef43e2c27373f288f4496aa31e90fd4a157e","abstract_canon_sha256":"4149616833089243eced0697424ab8ac6959ea34f54f65a03681d3cb6a1d1358"},"schema_version":"1.0"},"canonical_sha256":"6c2034ffdd7240d10dd26067af125c09b5ae7150f43b79232116f8687474db94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:45.531468Z","signature_b64":"4vXufEjIFmq3DRBOQPsXkb4z8AHmx8GrHBRbugDqb/88dmx7COZ83jCr9ZJbMULoXNuqQT+VhY83ZnQ36ef/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c2034ffdd7240d10dd26067af125c09b5ae7150f43b79232116f8687474db94","last_reissued_at":"2026-05-17T23:46:45.530977Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:45.530977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01859","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":"2026-05-17T23:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05d3opcA4MLxTscWDRGCDjCAI95loEopdCOSeMm1k9jbCKJWXivd30V5szNGLriqSmK6oMN4YNcJuvJGc8DqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:33.590986Z"},"content_sha256":"5848843354e6ac22c14fb9b8058bada97fa52afe463e78ab76c4acae52fcefeb","schema_version":"1.0","event_id":"sha256:5848843354e6ac22c14fb9b8058bada97fa52afe463e78ab76c4acae52fcefeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NQQDJ765OJANCDOSMBT26ES4BG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.MF"],"primary_cat":"math.PR","authors_text":"Martin Brown, Tomasz Zastawniak","submitted_at":"2019-05-06T07:46:47Z","abstract_excerpt":"We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values between the bid-ask spreads that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska's classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01859","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":"2026-05-17T23:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5YhWZGTQzsIydYsSFzoyt1EL+UGVtVITH7x6YHywUPvXtTjSga0VfpJg8M993qDhhIjRTknQDjNTXzo2SvjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:33.591346Z"},"content_sha256":"6ca3abe2ee4260ebc8dacd4bea7e3529be4559ddc6b1caa7395a01586a2680ff","schema_version":"1.0","event_id":"sha256:6ca3abe2ee4260ebc8dacd4bea7e3529be4559ddc6b1caa7395a01586a2680ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQQDJ765OJANCDOSMBT26ES4BG/bundle.json","state_url":"https://pith.science/pith/NQQDJ765OJANCDOSMBT26ES4BG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQQDJ765OJANCDOSMBT26ES4BG/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":"2026-06-02T23:02:33Z","links":{"resolver":"https://pith.science/pith/NQQDJ765OJANCDOSMBT26ES4BG","bundle":"https://pith.science/pith/NQQDJ765OJANCDOSMBT26ES4BG/bundle.json","state":"https://pith.science/pith/NQQDJ765OJANCDOSMBT26ES4BG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQQDJ765OJANCDOSMBT26ES4BG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NQQDJ765OJANCDOSMBT26ES4BG","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":"4149616833089243eced0697424ab8ac6959ea34f54f65a03681d3cb6a1d1358","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T07:46:47Z","title_canon_sha256":"6a7704470808febe8d336afd804fef43e2c27373f288f4496aa31e90fd4a157e"},"schema_version":"1.0","source":{"id":"1905.01859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01859","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01859v2","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01859","created_at":"2026-05-17T23:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"NQQDJ765OJAN","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NQQDJ765OJANCDOS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NQQDJ765","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:6ca3abe2ee4260ebc8dacd4bea7e3529be4559ddc6b1caa7395a01586a2680ff","target":"graph","created_at":"2026-05-17T23:46:45Z","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":"We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values between the bid-ask spreads that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska's classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.","authors_text":"Martin Brown, Tomasz Zastawniak","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T07:46:47Z","title":"Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01859","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":"sha256:5848843354e6ac22c14fb9b8058bada97fa52afe463e78ab76c4acae52fcefeb","target":"record","created_at":"2026-05-17T23:46:45Z","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":"4149616833089243eced0697424ab8ac6959ea34f54f65a03681d3cb6a1d1358","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T07:46:47Z","title_canon_sha256":"6a7704470808febe8d336afd804fef43e2c27373f288f4496aa31e90fd4a157e"},"schema_version":"1.0","source":{"id":"1905.01859","kind":"arxiv","version":2}},"canonical_sha256":"6c2034ffdd7240d10dd26067af125c09b5ae7150f43b79232116f8687474db94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c2034ffdd7240d10dd26067af125c09b5ae7150f43b79232116f8687474db94","first_computed_at":"2026-05-17T23:46:45.530977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:45.530977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vXufEjIFmq3DRBOQPsXkb4z8AHmx8GrHBRbugDqb/88dmx7COZ83jCr9ZJbMULoXNuqQT+VhY83ZnQ36ef/DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:45.531468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5848843354e6ac22c14fb9b8058bada97fa52afe463e78ab76c4acae52fcefeb","sha256:6ca3abe2ee4260ebc8dacd4bea7e3529be4559ddc6b1caa7395a01586a2680ff"],"state_sha256":"647ca58db5e5b88d816a895f42f3971e0d9a48bb008a3ecef82f3c87abcec5a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCQ/RwiGaW06P2yLoltdC86Zxjw0csgYJNytkbtkfN4eCmbBwVETJD6mV9VSEySF3OkcUn3twzbbNGBWUj6XCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:02:33.593330Z","bundle_sha256":"007886b37f3388d254b0ac53e555a5930fd7aa41cb6ff47e9ee6db21f6fb1c10"}}