{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ADZZUETWZAHVN3VI4DYN5J5HB4","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":"47e9e1d3f09efd0e02de0fa7c7d8d35ae163e3a7fa5c549ae77af1fff53656ce","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-09T17:29:39Z","title_canon_sha256":"88edc2de3ddc89490eb2df1ec667f0cf46932273d0bef29b14862b903ecd08ce"},"schema_version":"1.0","source":{"id":"2602.08927","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.08927","created_at":"2026-05-25T02:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"2602.08927v3","created_at":"2026-05-25T02:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.08927","created_at":"2026-05-25T02:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"ADZZUETWZAHV","created_at":"2026-05-25T02:01:14Z"},{"alias_kind":"pith_short_16","alias_value":"ADZZUETWZAHVN3VI","created_at":"2026-05-25T02:01:14Z"},{"alias_kind":"pith_short_8","alias_value":"ADZZUETW","created_at":"2026-05-25T02:01:14Z"}],"graph_snapshots":[{"event_id":"sha256:da0a6700a290a74bb77ccd84367c707de171ed98f97c2e126dd198d8e427caf5","target":"graph","created_at":"2026-05-25T02:01:14Z","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/2602.08927/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of online monotone density estimation, where density estimators must be constructed in a predictable manner from sequentially observed data. We propose two online estimators: an online analogue of the classical Grenander estimator, and an expert aggregation estimator inspired by exponential weighting methods from the online learning literature. In the well-specified stochastic setting, where the underlying density is monotone, we show that the expected cumulative log-likelihood gap between the online estimators and the true density admits an $O(n^{1/3})$ bound. We further ","authors_text":"Aaditya Ramdas, Rohan Hore, Ruodu Wang","cross_cats":["cs.LG","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-09T17:29:39Z","title":"Online monotone density estimation and log-optimal calibration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.08927","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":"sha256:10dd5fa0e1e3e7a4c8dc752d2b5c0e992a1a680bd150f092cb84d3ae5c0ec646","target":"record","created_at":"2026-05-25T02:01:14Z","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":"47e9e1d3f09efd0e02de0fa7c7d8d35ae163e3a7fa5c549ae77af1fff53656ce","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-02-09T17:29:39Z","title_canon_sha256":"88edc2de3ddc89490eb2df1ec667f0cf46932273d0bef29b14862b903ecd08ce"},"schema_version":"1.0","source":{"id":"2602.08927","kind":"arxiv","version":3}},"canonical_sha256":"00f39a1276c80f56eea8e0f0dea7a70f02145c767e539fd941c7ae53aaaa9b96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f39a1276c80f56eea8e0f0dea7a70f02145c767e539fd941c7ae53aaaa9b96","first_computed_at":"2026-05-25T02:01:14.873076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:14.873076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+RACt9iARewYTfmKqS5sFdJeT6AHu8DV3RYOE+8i+WLNVgSfoNK7QsT6rQvXD5mXs/6eNwSRaduZV69je3gCg==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:14.873880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.08927","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10dd5fa0e1e3e7a4c8dc752d2b5c0e992a1a680bd150f092cb84d3ae5c0ec646","sha256:da0a6700a290a74bb77ccd84367c707de171ed98f97c2e126dd198d8e427caf5"],"state_sha256":"38b5e6ed05fe376b01ccd458c60bc0f1f6778fe5223617106ec602939b4baa48"}