{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KBFCMEZCGTMQ5Z3DZT4CYGHCBV","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":"4f7b2a04ad574375e072f116f7ec88433544c2eba919d2b25eb3b80f379ef055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-23T19:00:58Z","title_canon_sha256":"18e4d501c6760b722054ce852de972394a0a91611e4086690bd2cf1da41c0f90"},"schema_version":"1.0","source":{"id":"1111.5583","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5583","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5583v4","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5583","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"KBFCMEZCGTMQ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KBFCMEZCGTMQ5Z3D","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KBFCMEZC","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:82a51823accab4fa5420ba6a1ddb05fbee165340f6e2f6990a07f90950ba074b","target":"graph","created_at":"2026-05-18T03:37:53Z","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":"This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov's condition and Kazamaki's criterion follow directly from the existence of F\\\"ollmer's measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales.","authors_text":"Johannes Ruf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-23T19:00:58Z","title":"A new proof for the conditions of Novikov and Kazamaki"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5583","kind":"arxiv","version":4},"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":"sha256:2e86b9fb3f6ab116cbb8dd8157f678b4928673716ddd73748aedbf25aec3bf32","target":"record","created_at":"2026-05-18T03:37:53Z","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":"4f7b2a04ad574375e072f116f7ec88433544c2eba919d2b25eb3b80f379ef055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-23T19:00:58Z","title_canon_sha256":"18e4d501c6760b722054ce852de972394a0a91611e4086690bd2cf1da41c0f90"},"schema_version":"1.0","source":{"id":"1111.5583","kind":"arxiv","version":4}},"canonical_sha256":"504a26132234d90ee763ccf82c18e20d75b0c2409e3067db32e6cb76fea54516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"504a26132234d90ee763ccf82c18e20d75b0c2409e3067db32e6cb76fea54516","first_computed_at":"2026-05-18T03:37:53.213426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:53.213426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pOePhzeCaDBq/1oZUWfXY+deBu7lGp+vaLh9+ka+MiueDHSiJlYaJjtA25jPQcYvvPpEkLezjtHLL794shsEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:53.214010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5583","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e86b9fb3f6ab116cbb8dd8157f678b4928673716ddd73748aedbf25aec3bf32","sha256:82a51823accab4fa5420ba6a1ddb05fbee165340f6e2f6990a07f90950ba074b"],"state_sha256":"8a2f5d1f826c24cb172367b2896ddc8fac838383695406473c7e1e9420e9cddd"}