{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NCX2YHC5EDTNDCTF5BJ7M3263V","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":"82896e5e8c6d1e7c1023704138c438e12effa6cae166cfca94fcc2e5d8d20c29","cross_cats_sorted":["cs.CR","cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-22T17:38:20Z","title_canon_sha256":"d6f32494e5b1c7ea7f9c503fb8a7fe661730ddd0b7dfb44e26492015f9e63428"},"schema_version":"1.0","source":{"id":"2605.23879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23879","created_at":"2026-05-25T02:02:37Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23879v1","created_at":"2026-05-25T02:02:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23879","created_at":"2026-05-25T02:02:37Z"},{"alias_kind":"pith_short_12","alias_value":"NCX2YHC5EDTN","created_at":"2026-05-25T02:02:37Z"},{"alias_kind":"pith_short_16","alias_value":"NCX2YHC5EDTNDCTF","created_at":"2026-05-25T02:02:37Z"},{"alias_kind":"pith_short_8","alias_value":"NCX2YHC5","created_at":"2026-05-25T02:02:37Z"}],"graph_snapshots":[{"event_id":"sha256:8a36236e3f735e8f28db4e020ece5d68afe0cfcc07307a7c95f5b6bcd28252f4","target":"graph","created_at":"2026-05-25T02:02:37Z","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/2605.23879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-flow sampling interprets a Gibbs distribution as the minimizer of an energy functional over probability measures and generates dynamics converging to this target. Under spherical Hellinger-Kantorovich (SHK) geometry, the flow couples transport and reaction and coincides with birth-death Langevin dynamics. In this work, we develop a perturbation theory for SHK gradient flows. For two potentials $V$ and $V^{\\prime}$, we compare the associated flows from a common initialization and quantify how potential discrepancies propagate over time. A uniform perturbation bound yields dimension-fre","authors_text":"Aratrika Mustafi, Soumya Mukherjee","cross_cats":["cs.CR","cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-22T17:38:20Z","title":"On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23879","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:ff8ef98a0e04807ab301b2001fb9001cce137f38f94bf54e6660f2ba40154e45","target":"record","created_at":"2026-05-25T02:02:37Z","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":"82896e5e8c6d1e7c1023704138c438e12effa6cae166cfca94fcc2e5d8d20c29","cross_cats_sorted":["cs.CR","cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-22T17:38:20Z","title_canon_sha256":"d6f32494e5b1c7ea7f9c503fb8a7fe661730ddd0b7dfb44e26492015f9e63428"},"schema_version":"1.0","source":{"id":"2605.23879","kind":"arxiv","version":1}},"canonical_sha256":"68afac1c5d20e6d18a65e853f66f5edd64d6b22905aad2ab73cb4db5a7590394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68afac1c5d20e6d18a65e853f66f5edd64d6b22905aad2ab73cb4db5a7590394","first_computed_at":"2026-05-25T02:02:37.310973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:37.310973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+HhiuZaBuAnp1rNUKdotLOpxnuOt8kyY/87zD0amtf6BXkLEcGiyvhtbFmei6zA70ZSm31HBTVWYH188ccsMBg==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:37.311713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff8ef98a0e04807ab301b2001fb9001cce137f38f94bf54e6660f2ba40154e45","sha256:8a36236e3f735e8f28db4e020ece5d68afe0cfcc07307a7c95f5b6bcd28252f4"],"state_sha256":"463970909f5db40b9f8c692e13fe75fdde48388004ee5cca91b882c1e8254811"}