{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2H4S36ONYJ4TPQRR6UBTV7MLXH","short_pith_number":"pith:2H4S36ON","schema_version":"1.0","canonical_sha256":"d1f92df9cdc27937c231f5033afd8bb9ed9416e6b8ecd3331e2a58e8aac9a78a","source":{"kind":"arxiv","id":"1701.04025","version":2},"attestation_state":"computed","paper":{"title":"Local martingales in discrete time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes Ruf, Vilmos Prokaj","submitted_at":"2017-01-15T10:38:33Z","abstract_excerpt":"For any discrete-time $P$--local martingale $S$ there exists a probability measure $Q \\sim P$ such that $S$ is a $Q$--martingale. A new proof for this result is provided. The core idea relies on an appropriate modification of an argument by Chris Rogers, used to prove a version of the fundamental theorem of asset pricing in discrete time. This proof also yields that, for any $\\varepsilon>0$, the measure $Q$ can be chosen so that $\\frac{dQ}{dP} \\leq 1+\\varepsilon$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.04025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-15T10:38:33Z","cross_cats_sorted":[],"title_canon_sha256":"e0b30a9688f5cd0e5dc17b2fc34fe6433690d44262acb345d3a7416fb00a1ed3","abstract_canon_sha256":"61b2a44be86fb8857b672bebfe5eb50aed7f5d30203da066e1ffdde2e19e9840"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:56.628261Z","signature_b64":"oWnvwAzVcpYFc4Yt++tkA3TdCDJcJhauQ5/ZxA1sPCUv5NkP80EijOyi8KBa0SunKqiZMHxmvv7dyuTrIi1JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1f92df9cdc27937c231f5033afd8bb9ed9416e6b8ecd3331e2a58e8aac9a78a","last_reissued_at":"2026-05-18T00:16:56.627649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:56.627649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local martingales in discrete time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes Ruf, Vilmos Prokaj","submitted_at":"2017-01-15T10:38:33Z","abstract_excerpt":"For any discrete-time $P$--local martingale $S$ there exists a probability measure $Q \\sim P$ such that $S$ is a $Q$--martingale. A new proof for this result is provided. The core idea relies on an appropriate modification of an argument by Chris Rogers, used to prove a version of the fundamental theorem of asset pricing in discrete time. This proof also yields that, for any $\\varepsilon>0$, the measure $Q$ can be chosen so that $\\frac{dQ}{dP} \\leq 1+\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04025","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.04025","created_at":"2026-05-18T00:16:56.627741+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04025v2","created_at":"2026-05-18T00:16:56.627741+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04025","created_at":"2026-05-18T00:16:56.627741+00:00"},{"alias_kind":"pith_short_12","alias_value":"2H4S36ONYJ4T","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2H4S36ONYJ4TPQRR","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2H4S36ON","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH","json":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH.json","graph_json":"https://pith.science/api/pith-number/2H4S36ONYJ4TPQRR6UBTV7MLXH/graph.json","events_json":"https://pith.science/api/pith-number/2H4S36ONYJ4TPQRR6UBTV7MLXH/events.json","paper":"https://pith.science/paper/2H4S36ON"},"agent_actions":{"view_html":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH","download_json":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH.json","view_paper":"https://pith.science/paper/2H4S36ON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04025&json=true","fetch_graph":"https://pith.science/api/pith-number/2H4S36ONYJ4TPQRR6UBTV7MLXH/graph.json","fetch_events":"https://pith.science/api/pith-number/2H4S36ONYJ4TPQRR6UBTV7MLXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH/action/storage_attestation","attest_author":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH/action/author_attestation","sign_citation":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH/action/citation_signature","submit_replication":"https://pith.science/pith/2H4S36ONYJ4TPQRR6UBTV7MLXH/action/replication_record"}},"created_at":"2026-05-18T00:16:56.627741+00:00","updated_at":"2026-05-18T00:16:56.627741+00:00"}