{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FHSXUKP6E6PC4EPWVODR74IIMX","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":"9508915e88f2797fac39f5736233f2366f69577c31b9f8dfea80ff9c13be4e12","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2024-11-12T13:19:23Z","title_canon_sha256":"cd0e3a9548c8add27c4f9b2422994f1b43ac023ade65af3d0395a02bad81ef41"},"schema_version":"1.0","source":{"id":"2411.07776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07776","created_at":"2026-07-05T11:09:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07776v2","created_at":"2026-07-05T11:09:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07776","created_at":"2026-07-05T11:09:43Z"},{"alias_kind":"pith_short_12","alias_value":"FHSXUKP6E6PC","created_at":"2026-07-05T11:09:43Z"},{"alias_kind":"pith_short_16","alias_value":"FHSXUKP6E6PC4EPW","created_at":"2026-07-05T11:09:43Z"},{"alias_kind":"pith_short_8","alias_value":"FHSXUKP6","created_at":"2026-07-05T11:09:43Z"}],"graph_snapshots":[{"event_id":"sha256:be2317fb4058b7b233e762db073232813ad5b82ede6a69afe16336fa61e4012f","target":"graph","created_at":"2026-07-05T11:09:43Z","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/2411.07776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Existing guarantees for algorithms sampling from nonlogconcave measures on $\\mathbb{R}^d$ are generally inexplicit or unscalable. Even for the class of measures with logdensities that have bounded Hessians and are strongly concave outside a Euclidean ball of radius $R$, no available theory is comprehensively satisfactory with respect to both $R$ and $d$. In this paper, it is shown that complete polynomial complexity can in fact be achieved if $R\\leq c\\sqrt{d}$, whilst an exponential number of point evaluations is generally necessary for any algorithm as soon as $R\\geq C\\sqrt{d}$ for constants ","authors_text":"Martin Chak","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2024-11-12T13:19:23Z","title":"On theoretical guarantees and a blessing of dimensionality for nonconvex sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07776","kind":"arxiv","version":2},"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:edeaaa5d2aad9fd1faf30e2d941ed34b0defa4d4249433c3e5ee18ad01a695d5","target":"record","created_at":"2026-07-05T11:09:43Z","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":"9508915e88f2797fac39f5736233f2366f69577c31b9f8dfea80ff9c13be4e12","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2024-11-12T13:19:23Z","title_canon_sha256":"cd0e3a9548c8add27c4f9b2422994f1b43ac023ade65af3d0395a02bad81ef41"},"schema_version":"1.0","source":{"id":"2411.07776","kind":"arxiv","version":2}},"canonical_sha256":"29e57a29fe279e2e11f6ab871ff10865ebfa98cf500a0832665316bb3436c7fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29e57a29fe279e2e11f6ab871ff10865ebfa98cf500a0832665316bb3436c7fa","first_computed_at":"2026-07-05T11:09:43.933925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:43.933925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X3WJEtVOTwpMNuoLtXj5RdchdrtG9iozsm/oihNT5R9qMyDF9bAAIuM+2E+qi0/o5sfisVkTFZywYi/Hhe6LDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:43.934389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.07776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edeaaa5d2aad9fd1faf30e2d941ed34b0defa4d4249433c3e5ee18ad01a695d5","sha256:be2317fb4058b7b233e762db073232813ad5b82ede6a69afe16336fa61e4012f"],"state_sha256":"c0e35a7ae0d7cf3a62b7a89543716cb1ab6828bf474c0f79a2690c4da3e2ce25"}