{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2H4S36ONYJ4TPQRR6UBTV7MLXH","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":"61b2a44be86fb8857b672bebfe5eb50aed7f5d30203da066e1ffdde2e19e9840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-15T10:38:33Z","title_canon_sha256":"e0b30a9688f5cd0e5dc17b2fc34fe6433690d44262acb345d3a7416fb00a1ed3"},"schema_version":"1.0","source":{"id":"1701.04025","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04025","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04025v2","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04025","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"pith_short_12","alias_value":"2H4S36ONYJ4T","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2H4S36ONYJ4TPQRR","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2H4S36ON","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:f499743ff577ec168efae03cd11cd83044943ea48ead1f976af855dc9af774d3","target":"graph","created_at":"2026-05-18T00:16:56Z","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":"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 $\\frac{dQ}{dP} \\leq 1+\\varepsilon$.","authors_text":"Johannes Ruf, Vilmos Prokaj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-15T10:38:33Z","title":"Local martingales in discrete time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04025","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:f7b7169490638419953b18a17bd21fb6f305170118337f2d4e423a52b4a5ffc0","target":"record","created_at":"2026-05-18T00:16:56Z","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":"61b2a44be86fb8857b672bebfe5eb50aed7f5d30203da066e1ffdde2e19e9840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-15T10:38:33Z","title_canon_sha256":"e0b30a9688f5cd0e5dc17b2fc34fe6433690d44262acb345d3a7416fb00a1ed3"},"schema_version":"1.0","source":{"id":"1701.04025","kind":"arxiv","version":2}},"canonical_sha256":"d1f92df9cdc27937c231f5033afd8bb9ed9416e6b8ecd3331e2a58e8aac9a78a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1f92df9cdc27937c231f5033afd8bb9ed9416e6b8ecd3331e2a58e8aac9a78a","first_computed_at":"2026-05-18T00:16:56.627649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:56.627649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWnvwAzVcpYFc4Yt++tkA3TdCDJcJhauQ5/ZxA1sPCUv5NkP80EijOyi8KBa0SunKqiZMHxmvv7dyuTrIi1JDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:56.628261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04025","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7b7169490638419953b18a17bd21fb6f305170118337f2d4e423a52b4a5ffc0","sha256:f499743ff577ec168efae03cd11cd83044943ea48ead1f976af855dc9af774d3"],"state_sha256":"948408fc6f6c353b79a3cdf170507702da220f84ce0fd76510a2caefb685e58f"}