{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VWXCLNCY3OPNSK7RMXUSSP22S6","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":"588277e8d02921fba6e12745e0ad70a37eb5e92fb74a56bc7ce44a3395cd265b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-13T08:15:22Z","title_canon_sha256":"44112554b2744cfa132bc894e5e02d72a247bcd08c37029927ad6959967b7c80"},"schema_version":"1.0","source":{"id":"1402.3056","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3056","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3056v3","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3056","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"VWXCLNCY3OPN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWXCLNCY3OPNSK7R","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWXCLNCY","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:9d5569956d70befff353971fcf7b4b0ee2fee54b5c776090e4d3d7adafcbaf58","target":"graph","created_at":"2026-05-18T00:52:08Z","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 consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with respect to the pointwise convergence of non-decreasing sequences of real-valued functions $f_n$, $n\\in\\mathbb{N}_0$, where each $f_n$ is $n$-measurable. For the Ville-Vovk-Shafer natural extension, a similar result is shown to hold for non-increasing sequences, provided that they converge to a bounded function.","authors_text":"Gert de Cooman, Jasper De Bock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-13T08:15:22Z","title":"Continuity of imprecise stochastic processes with respect to the pointwise convergence of monotone sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3056","kind":"arxiv","version":3},"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:eabee2cdd13a2871043f1818ef42b40feaa7bca875c38d81cfc88442434a8b8c","target":"record","created_at":"2026-05-18T00:52:08Z","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":"588277e8d02921fba6e12745e0ad70a37eb5e92fb74a56bc7ce44a3395cd265b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-13T08:15:22Z","title_canon_sha256":"44112554b2744cfa132bc894e5e02d72a247bcd08c37029927ad6959967b7c80"},"schema_version":"1.0","source":{"id":"1402.3056","kind":"arxiv","version":3}},"canonical_sha256":"adae25b458db9ed92bf165e9293f5a97b099f715ad06604a69be06336d2d732a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adae25b458db9ed92bf165e9293f5a97b099f715ad06604a69be06336d2d732a","first_computed_at":"2026-05-18T00:52:08.703157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:08.703157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bit+SdXd8eP6OVZH32PecHVywR7nNQ0DXWaYTKCTxrJdGjmWoA/YNjFvE2afQDkDwmqW8ugxMr1G23NhuYk8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:08.703781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3056","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eabee2cdd13a2871043f1818ef42b40feaa7bca875c38d81cfc88442434a8b8c","sha256:9d5569956d70befff353971fcf7b4b0ee2fee54b5c776090e4d3d7adafcbaf58"],"state_sha256":"2129603851539aafa546e23ce56a21f28622a1521965aa303183eac91f715fd1"}