{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IFGXYZ3TQQBQJXQGRP4N62GZBR","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":"6b909b85392fe45ef27fbb59ae919c69b7218d858178a472822d52c9a5be46ef","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-14T18:20:52Z","title_canon_sha256":"9c4189cabb896b87d8fc5beb5bf93db2c47317b324b0b41ce8755c7a1267f21b"},"schema_version":"1.0","source":{"id":"2607.13170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13170","created_at":"2026-07-16T00:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13170v1","created_at":"2026-07-16T00:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13170","created_at":"2026-07-16T00:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"IFGXYZ3TQQBQ","created_at":"2026-07-16T00:22:01Z"},{"alias_kind":"pith_short_16","alias_value":"IFGXYZ3TQQBQJXQG","created_at":"2026-07-16T00:22:01Z"},{"alias_kind":"pith_short_8","alias_value":"IFGXYZ3T","created_at":"2026-07-16T00:22:01Z"}],"graph_snapshots":[{"event_id":"sha256:4d1fe31ac25e662d87b59a9391fe44c2b060587886a5136350f0c80f32f2a0d6","target":"graph","created_at":"2026-07-16T00:22:01Z","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/2607.13170/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a negative answer to a problem posed by James Robins on estimating a constant conditional variance in nonparametric regression under random design. For every $s>1$ and integer $d>4s$, when the regression function is $s$-H\\\"older, the unknown design density is bounded above and away from zero, and the conditional error laws may depend on the design but have mean zero, a common variance, and uniformly bounded fourth moments, we show that the minimax root-mean-square risk is bounded below by $n^{-\\beta}$ with $\\beta=\\frac{d(3s+1)+8s}{(d+2s)(d+4)}$. Hence the conjectured rate $n^{-4s/(d+4s","authors_text":"Patrick Lopatto, P. M. Aronow","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-14T18:20:52Z","title":"On Rates Attainable under Random Design: A Negative Answer to a Problem of Robins"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13170","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:a8253b0b0ebe4690a06e02057419e28379d872ef0ede8b0496b32fba1192aad9","target":"record","created_at":"2026-07-16T00:22:01Z","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":"6b909b85392fe45ef27fbb59ae919c69b7218d858178a472822d52c9a5be46ef","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-14T18:20:52Z","title_canon_sha256":"9c4189cabb896b87d8fc5beb5bf93db2c47317b324b0b41ce8755c7a1267f21b"},"schema_version":"1.0","source":{"id":"2607.13170","kind":"arxiv","version":1}},"canonical_sha256":"414d7c6773840304de068bf8df68d90c5c9caed99f93d53c1687c2fc5139015d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"414d7c6773840304de068bf8df68d90c5c9caed99f93d53c1687c2fc5139015d","first_computed_at":"2026-07-16T00:22:01.004769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T00:22:01.004769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DT4oXdMIKwNS5rJd4184kGEL+wrIw325KRIJ0PI61AiL2veNIGiKlZYYJO53S/dAFUficbpmil5DsdOTOzEiCg==","signature_status":"signed_v1","signed_at":"2026-07-16T00:22:01.005641Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8253b0b0ebe4690a06e02057419e28379d872ef0ede8b0496b32fba1192aad9","sha256:4d1fe31ac25e662d87b59a9391fe44c2b060587886a5136350f0c80f32f2a0d6"],"state_sha256":"6d37fd00950e99c9a688798d9cadfc39bd3aacaa6f9472796602441edef1f90d"}