{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X7L6ESZF2FFW2OYCZAD74GE3HE","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":"efd61608c3d8e84e5a1a2de15e52023cca17f229a10c0d6d9bde4b97231c07a2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T01:36:02Z","title_canon_sha256":"23d1c017aff272814bd2ad030e0ee71812952f12b4357f2afde3427da9673b16"},"schema_version":"1.0","source":{"id":"1705.06386","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06386","created_at":"2026-07-04T23:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06386v4","created_at":"2026-07-04T23:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06386","created_at":"2026-07-04T23:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"X7L6ESZF2FFW","created_at":"2026-07-04T23:51:01Z"},{"alias_kind":"pith_short_16","alias_value":"X7L6ESZF2FFW2OYC","created_at":"2026-07-04T23:51:01Z"},{"alias_kind":"pith_short_8","alias_value":"X7L6ESZF","created_at":"2026-07-04T23:51:01Z"}],"graph_snapshots":[{"event_id":"sha256:76e2f66bb79a7b4ba3cb3ac45a5dfec03142fe14b30352fe488adc03d5761922","target":"graph","created_at":"2026-07-04T23:51:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.06386/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a sequence of real data points $X_1,\\ldots, X_n$ with underlying means $\\theta^*_1,\\dots,\\theta^*_n$. This paper starts from studying the setting that $\\theta^*_i$ is both piecewise constant and monotone as a function of the index $i$. For this, we establish the exact minimax rate of estimating such monotone functions, and thus give a non-trivial answer to an open problem in the shape-constrained analysis literature. The minimax rate involves an interesting iterated logarithmic dependence on the dimension, a phenomenon that is revealed through characterizing the interplay between the ","authors_text":"Chao Gao, Cun-Hui Zhang, Fang Han","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T01:36:02Z","title":"On Estimation of Isotonic Piecewise Constant Signals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06386","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":"sha256:3d8d27b5b94598b6acdda13927a5317858fb29dd25b681a9e10e25e8e32ea416","target":"record","created_at":"2026-07-04T23:51:01Z","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":"efd61608c3d8e84e5a1a2de15e52023cca17f229a10c0d6d9bde4b97231c07a2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T01:36:02Z","title_canon_sha256":"23d1c017aff272814bd2ad030e0ee71812952f12b4357f2afde3427da9673b16"},"schema_version":"1.0","source":{"id":"1705.06386","kind":"arxiv","version":4}},"canonical_sha256":"bfd7e24b25d14b6d3b02c807fe189b3909432cfca6cfe8161c0bdb7c2d2678d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfd7e24b25d14b6d3b02c807fe189b3909432cfca6cfe8161c0bdb7c2d2678d4","first_computed_at":"2026-07-04T23:51:01.682122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:01.682122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PseZfao6IdSqdbMR8Bu5PN/LfV77FnBPlTnheo7TXlCoxxueBDfUgBfB9uDZ+X8ovu2NSKVKSTv/nxPfVNDKBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:01.682485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06386","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8d27b5b94598b6acdda13927a5317858fb29dd25b681a9e10e25e8e32ea416","sha256:76e2f66bb79a7b4ba3cb3ac45a5dfec03142fe14b30352fe488adc03d5761922"],"state_sha256":"5188a3e75031e2e69f1b93b609531e687463903ee012deba70968f8c888cafee"}