{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M72WDL4ER37WLZ45J2PG2OLFUW","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":"0e0ce6652a70cb6b024d3b45d09c31de4ff4ccde558936b4e5e51fbf2581e4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-18T12:14:52Z","title_canon_sha256":"896063186a3f673e6ab249fd2d32d605b114c58b495e22944aac1b5c6566ddd7"},"schema_version":"1.0","source":{"id":"1309.4623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4623","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4623v2","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4623","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"M72WDL4ER37W","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M72WDL4ER37WLZ45","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M72WDL4E","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:cfbed2dda64713838f303b156bcad3cd253685f41ebeeb8fe446a8fbd34c4a6d","target":"graph","created_at":"2026-05-18T01:23:59Z","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":"Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.","authors_text":"Johannes Ruf, Nicolas Perkowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-18T12:14:52Z","title":"Supermartingales as Radon-Nikodym densities and related measure extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4623","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":"sha256:03b4a66f18acff55bd279af0909b0b9cdb113ffddb001b58d9bb8d980e3892f7","target":"record","created_at":"2026-05-18T01:23:59Z","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":"0e0ce6652a70cb6b024d3b45d09c31de4ff4ccde558936b4e5e51fbf2581e4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-18T12:14:52Z","title_canon_sha256":"896063186a3f673e6ab249fd2d32d605b114c58b495e22944aac1b5c6566ddd7"},"schema_version":"1.0","source":{"id":"1309.4623","kind":"arxiv","version":2}},"canonical_sha256":"67f561af848eff65e79d4e9e6d3965a588c953c49992ebdea7c4efd7001ccfe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67f561af848eff65e79d4e9e6d3965a588c953c49992ebdea7c4efd7001ccfe1","first_computed_at":"2026-05-18T01:23:59.052644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:59.052644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2DBzSlYHWPTJS9ezwYc8vK0fptOgGQh/2CHOxI6FkNQy9BAGsY7V8zQgAl57xOqJh14nE2QDU1hSNaSPPxetAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:59.053187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03b4a66f18acff55bd279af0909b0b9cdb113ffddb001b58d9bb8d980e3892f7","sha256:cfbed2dda64713838f303b156bcad3cd253685f41ebeeb8fe446a8fbd34c4a6d"],"state_sha256":"a812d435334cd9483d7d9c1ca13769d00be5472eccce607a2533d9dc9d716e53"}