{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ODFJTIMKLPFIL7VIR6UYRERWWA","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":"f33bf92d1761a39b525eca9dbd4015eb45bf740bc1bf894db33214bc359dc99a","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-26T22:52:54Z","title_canon_sha256":"1fd180c1b30061084456a2d2dc2553188f3d06a11782ac8eef9f416f51cf775d"},"schema_version":"1.0","source":{"id":"2606.28641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28641","created_at":"2026-06-30T00:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28641v1","created_at":"2026-06-30T00:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28641","created_at":"2026-06-30T00:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"ODFJTIMKLPFI","created_at":"2026-06-30T00:15:21Z"},{"alias_kind":"pith_short_16","alias_value":"ODFJTIMKLPFIL7VI","created_at":"2026-06-30T00:15:21Z"},{"alias_kind":"pith_short_8","alias_value":"ODFJTIMK","created_at":"2026-06-30T00:15:21Z"}],"graph_snapshots":[{"event_id":"sha256:fdfc305ae102e28291d245af6ede3efcb1bfa76020727f0cd8b1825adf5d2bee","target":"graph","created_at":"2026-06-30T00:15:21Z","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/2606.28641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Considering pointwise and sup-norm estimation, we analyze the non-asymptotic behavior of local averaging estimators for Lipschitz regression functions. Building on a general deviation bound for estimators based on a VC family of localizing sets, we introduce the notion of shape-regular local maps, where averaging is performed over sets with an almost isotropic geometry. Our main message is a characterization: shape regularity is both necessary and sufficient to attain optimal rates, up to logarithmic factors. Necessity is established non-asymptotically through an explicit anisotropic example, ","authors_text":"Adrien Saumard, Fran\\c{c}ois Portier, J\\'er\\'emy Bettinger","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-26T22:52:54Z","title":"Revisiting local regression: shape regularity, uniform rates, and the limits of random splits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28641","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:e6005a2b1ab87e99a1de454ce49cb3341ff3d7e55f94c8299d859197e333ab67","target":"record","created_at":"2026-06-30T00:15:21Z","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":"f33bf92d1761a39b525eca9dbd4015eb45bf740bc1bf894db33214bc359dc99a","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-26T22:52:54Z","title_canon_sha256":"1fd180c1b30061084456a2d2dc2553188f3d06a11782ac8eef9f416f51cf775d"},"schema_version":"1.0","source":{"id":"2606.28641","kind":"arxiv","version":1}},"canonical_sha256":"70ca99a18a5bca85fea88fa9889236b01c261593d9dcd165da7917436f3c1003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70ca99a18a5bca85fea88fa9889236b01c261593d9dcd165da7917436f3c1003","first_computed_at":"2026-06-30T00:15:21.483972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T00:15:21.483972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xG6fCv/vAiq0KaXkqAea+fbFDiGJqoVOwcLlMRE6wMGgzZeE3kCpGUknKcicbGqY8CQ9DC/JWYYujvHvDnHPCw==","signature_status":"signed_v1","signed_at":"2026-06-30T00:15:21.484303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6005a2b1ab87e99a1de454ce49cb3341ff3d7e55f94c8299d859197e333ab67","sha256:fdfc305ae102e28291d245af6ede3efcb1bfa76020727f0cd8b1825adf5d2bee"],"state_sha256":"623612211512dc76a803a8227950cdf78f7cd1af8d39b46da384b39ebe969586"}