{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KYFO7I5KPKGRNG6J2WCSJRIV7I","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":"ec34d6e5dfaf84045f263d94f8103318d8a639c52ec17b5afc67b48cca555017","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-16T18:45:48Z","title_canon_sha256":"921e5b5419285b1085e0b3cb5b651ab25b24def6ad761976a9017b85746d24c9"},"schema_version":"1.0","source":{"id":"1706.05404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05404","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05404v1","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05404","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"pith_short_12","alias_value":"KYFO7I5KPKGR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KYFO7I5KPKGRNG6J","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KYFO7I5K","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:bf4fe172e8c74e9f6badbbe84a0418e375769a8c4fc5c09699322fa65cc47d5c","target":"graph","created_at":"2026-05-18T00:42:11Z","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 discusses the possibility to find and construct \\textit{piecewise constant martingales}, that is, martingales with piecewise constant sample paths evolving in a connected subset of $\\mathbb{R}$. After a brief review of standard possible techniques, we propose a construction based on the sampling of latent martingales $\\tilde{Z}$ with \\textit{lazy clocks} $\\theta$. These $\\theta$ are time-change processes staying in arrears of the true time but that can synchronize at random times to the real clock. This specific choice makes the resulting time-changed process $Z_t=\\tilde{Z}_{\\theta_","authors_text":"Christophe Profeta, Fr\\'ed\\'eric Vrins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-16T18:45:48Z","title":"Piecewise Constant Martingales and Lazy Clocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05404","kind":"arxiv","version":1},"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:ea702f112fc40b79dbea66eeff80b172e4edfc9b2ebb80dee4c322308268cf76","target":"record","created_at":"2026-05-18T00:42:11Z","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":"ec34d6e5dfaf84045f263d94f8103318d8a639c52ec17b5afc67b48cca555017","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-16T18:45:48Z","title_canon_sha256":"921e5b5419285b1085e0b3cb5b651ab25b24def6ad761976a9017b85746d24c9"},"schema_version":"1.0","source":{"id":"1706.05404","kind":"arxiv","version":1}},"canonical_sha256":"560aefa3aa7a8d169bc9d58524c515fa1f61ae7f69dd0d51f785b9e3522befbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"560aefa3aa7a8d169bc9d58524c515fa1f61ae7f69dd0d51f785b9e3522befbe","first_computed_at":"2026-05-18T00:42:11.754475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:11.754475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6b3hAzNC6wbKv8mQ3QDqzmmGNzlw0g+FD9oRW3kX2VOI5ogObIiPf0a7UrItV78bbY3Z5CQ6TgSo6PhKmeRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:11.755032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea702f112fc40b79dbea66eeff80b172e4edfc9b2ebb80dee4c322308268cf76","sha256:bf4fe172e8c74e9f6badbbe84a0418e375769a8c4fc5c09699322fa65cc47d5c"],"state_sha256":"91bc3b67633f245e1ad735c8609cd1bc744df1d53db506291d8c21e7144d0d56"}