{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XTDQVZ5MFQE2IP7EO4QF63AY7E","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":"69b236fee59b08c38c6e071e17e587cd0bd992245c70e76bb107752b94860c49","cross_cats_sorted":["cs.LG","stat.ME","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-31T17:55:02Z","title_canon_sha256":"15468db132227b80180c8c3d97339cd99ed2506d5bf2e5f4e807a43fc20a4b37"},"schema_version":"1.0","source":{"id":"2607.29675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29675","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29675v1","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29675","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"XTDQVZ5MFQE2","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_16","alias_value":"XTDQVZ5MFQE2IP7E","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_8","alias_value":"XTDQVZ5M","created_at":"2026-08-03T01:41:43Z"}],"graph_snapshots":[{"event_id":"sha256:995bebba880b7b34a73d2355d2af5aa9830aad46ed93593b18d5624db28776d6","target":"graph","created_at":"2026-08-03T01:41:43Z","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/2607.29675/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Density modes provide a localized and interpretable summary of multimodal distributions, but their estimation under rigorous differential privacy constraints remains largely unexplored. We study differentially private recovery of density modes for multivariate distributions under local smoothness, curvature, and separation conditions. We propose DP-GRAMS, a mean-shift inspired method that performs noisy ascent on a differentially private score estimator. Assuming the density belongs locally to a H\\\"older class with smoothness parameter $\\beta > 2$, our score estimator uses bias-reducing higher","authors_text":"Arkajyoti Bhattacharjee, Arnab Auddy","cross_cats":["cs.LG","stat.ME","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-31T17:55:02Z","title":"Differentially Private Nonparametric Modal Learning with Applications to Regression and Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29675","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":"sha256:0da66b4093351c7f95531b476992c20722e56d7926c495aa14a71f3727445cf1","target":"record","created_at":"2026-08-03T01:41:43Z","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":"69b236fee59b08c38c6e071e17e587cd0bd992245c70e76bb107752b94860c49","cross_cats_sorted":["cs.LG","stat.ME","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-31T17:55:02Z","title_canon_sha256":"15468db132227b80180c8c3d97339cd99ed2506d5bf2e5f4e807a43fc20a4b37"},"schema_version":"1.0","source":{"id":"2607.29675","kind":"arxiv","version":1}},"canonical_sha256":"bcc70ae7ac2c09a43fe477205f6c18f930f5e44dd9374c0a63ada579d9e9015f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcc70ae7ac2c09a43fe477205f6c18f930f5e44dd9374c0a63ada579d9e9015f","first_computed_at":"2026-08-03T01:41:43.295285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:41:43.295285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ls2x3B4Tt2UXY9RjtNrbrHIrCPDeBaX1IUUDTUUvn8AELWvgz4dP9A4GdHg4sK73AMhscKCancBwuxqtM/NyAA==","signature_status":"signed_v1","signed_at":"2026-08-03T01:41:43.296743Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0da66b4093351c7f95531b476992c20722e56d7926c495aa14a71f3727445cf1","sha256:995bebba880b7b34a73d2355d2af5aa9830aad46ed93593b18d5624db28776d6"],"state_sha256":"6f3317b9f2f11a6b90f505bc7cd5a844f3c056117234a5c3f03570cb3ade8d4c"}