{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FHSXUKP6E6PC4EPWVODR74IIMX","short_pith_number":"pith:FHSXUKP6","canonical_record":{"source":{"id":"2411.07776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2024-11-12T13:19:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cd0e3a9548c8add27c4f9b2422994f1b43ac023ade65af3d0395a02bad81ef41","abstract_canon_sha256":"9508915e88f2797fac39f5736233f2366f69577c31b9f8dfea80ff9c13be4e12"},"schema_version":"1.0"},"canonical_sha256":"29e57a29fe279e2e11f6ab871ff10865ebfa98cf500a0832665316bb3436c7fa","source":{"kind":"arxiv","id":"2411.07776","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FHSXUKP6E6PC4EPWVODR74IIMX","target":"record","payload":{"canonical_record":{"source":{"id":"2411.07776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2024-11-12T13:19:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cd0e3a9548c8add27c4f9b2422994f1b43ac023ade65af3d0395a02bad81ef41","abstract_canon_sha256":"9508915e88f2797fac39f5736233f2366f69577c31b9f8dfea80ff9c13be4e12"},"schema_version":"1.0"},"canonical_sha256":"29e57a29fe279e2e11f6ab871ff10865ebfa98cf500a0832665316bb3436c7fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:43.934389Z","signature_b64":"X3WJEtVOTwpMNuoLtXj5RdchdrtG9iozsm/oihNT5R9qMyDF9bAAIuM+2E+qi0/o5sfisVkTFZywYi/Hhe6LDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29e57a29fe279e2e11f6ab871ff10865ebfa98cf500a0832665316bb3436c7fa","last_reissued_at":"2026-07-05T11:09:43.933925Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:43.933925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.07776","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:09:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHRxNlza+AeRYlizo1sQtFsnffgJyuZscUXChBZDuwtZTSdCnS9mRUD3hv8THUiftV/WsiPK7hmZSDOcxl/7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:52:14.627403Z"},"content_sha256":"edeaaa5d2aad9fd1faf30e2d941ed34b0defa4d4249433c3e5ee18ad01a695d5","schema_version":"1.0","event_id":"sha256:edeaaa5d2aad9fd1faf30e2d941ed34b0defa4d4249433c3e5ee18ad01a695d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FHSXUKP6E6PC4EPWVODR74IIMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On theoretical guarantees and a blessing of dimensionality for nonconvex sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"stat.CO","authors_text":"Martin Chak","submitted_at":"2024-11-12T13:19:23Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07776","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.07776/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:09:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I9OGgAAWary1Rm/rEXD+/htnUGiwY92SqG5U5ak2KswFkzbFviXgv8tbCOtjLaJy3C1hsF6N1lYORK62czcHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:52:14.627984Z"},"content_sha256":"be2317fb4058b7b233e762db073232813ad5b82ede6a69afe16336fa61e4012f","schema_version":"1.0","event_id":"sha256:be2317fb4058b7b233e762db073232813ad5b82ede6a69afe16336fa61e4012f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHSXUKP6E6PC4EPWVODR74IIMX/bundle.json","state_url":"https://pith.science/pith/FHSXUKP6E6PC4EPWVODR74IIMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHSXUKP6E6PC4EPWVODR74IIMX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T23:52:14Z","links":{"resolver":"https://pith.science/pith/FHSXUKP6E6PC4EPWVODR74IIMX","bundle":"https://pith.science/pith/FHSXUKP6E6PC4EPWVODR74IIMX/bundle.json","state":"https://pith.science/pith/FHSXUKP6E6PC4EPWVODR74IIMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHSXUKP6E6PC4EPWVODR74IIMX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SHCmTe/KgHZufLA0XWJsv44c/PkC1IEaNRS+cDpJ7DiL/AGqTLMKbMORjZKI9UlwunLW0OBAA70d0XZm4zpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T23:52:14.633699Z","bundle_sha256":"dcf09d4b299e1bf8bc293b750ec72a1edc470b3629f9d1d05de7c6c2da78cdf6"}}