{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GAUF2E2NKKYD5S3BMPSNCNBLPW","short_pith_number":"pith:GAUF2E2N","canonical_record":{"source":{"id":"1512.07392","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-23T08:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"c58abda7298822d3c482a453fbc8df2b11b1601d5844ab1051aaec038ba4674b","abstract_canon_sha256":"a100ccdc8d22b0be91ea90898af018061183186635cf61aa6f7202ffe419834f"},"schema_version":"1.0"},"canonical_sha256":"30285d134d52b03ecb6163e4d1342b7dba2198a6a52461de5cf1a744ae06192a","source":{"kind":"arxiv","id":"1512.07392","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07392","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07392v6","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07392","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"pith_short_12","alias_value":"GAUF2E2NKKYD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAUF2E2NKKYD5S3B","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAUF2E2N","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GAUF2E2NKKYD5S3BMPSNCNBLPW","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07392","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-23T08:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"c58abda7298822d3c482a453fbc8df2b11b1601d5844ab1051aaec038ba4674b","abstract_canon_sha256":"a100ccdc8d22b0be91ea90898af018061183186635cf61aa6f7202ffe419834f"},"schema_version":"1.0"},"canonical_sha256":"30285d134d52b03ecb6163e4d1342b7dba2198a6a52461de5cf1a744ae06192a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:04.781566Z","signature_b64":"t6k8gx+KcwMifa/3IWuO8f7wIgw2VKddziXHZ6yzcWGeiVSdfH+SHDdKcXlIdWdB0rbInHvMBOoxJOqx8lnxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30285d134d52b03ecb6163e4d1342b7dba2198a6a52461de5cf1a744ae06192a","last_reissued_at":"2026-05-18T00:57:04.780972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:04.780972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07392","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTKK7ST8rivY3RoTHkhy3v5NF7aMAAh3XWpUnKCR2NcEyFKweggsdA0Q7FUR/0lQph0EaIPwT/uzKKrwABvEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:49:58.040374Z"},"content_sha256":"06671c4f376c0db6d8ba9b4c48290c05e671a64a7bdd109f308c790d23e528dc","schema_version":"1.0","event_id":"sha256:06671c4f376c0db6d8ba9b4c48290c05e671a64a7bdd109f308c790d23e528dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GAUF2E2NKKYD5S3BMPSNCNBLPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Stein Factors for a Class of Strongly Log-concave Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jackson Gorham, Lester Mackey","submitted_at":"2015-12-23T08:58:10Z","abstract_excerpt":"We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These \"Stein factor\" bounds deliver control over Wasserstein and related smooth function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07392","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:57:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hERifIq2KVMK57zkyDPhoHcdmE3ucFZZjPSHMQ5X09q62vzdISurS9EMOObCPst6v7PL+pEJE8KaUSC+XE7qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:49:58.040750Z"},"content_sha256":"40fa37f5dae082612f453e6737f9f89407fe8e189824ff291cdd2efdaf25e1e0","schema_version":"1.0","event_id":"sha256:40fa37f5dae082612f453e6737f9f89407fe8e189824ff291cdd2efdaf25e1e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/bundle.json","state_url":"https://pith.science/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/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":"2026-06-11T22:49:58Z","links":{"resolver":"https://pith.science/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW","bundle":"https://pith.science/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/bundle.json","state":"https://pith.science/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAUF2E2NKKYD5S3BMPSNCNBLPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GAUF2E2NKKYD5S3BMPSNCNBLPW","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":"a100ccdc8d22b0be91ea90898af018061183186635cf61aa6f7202ffe419834f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-23T08:58:10Z","title_canon_sha256":"c58abda7298822d3c482a453fbc8df2b11b1601d5844ab1051aaec038ba4674b"},"schema_version":"1.0","source":{"id":"1512.07392","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07392","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07392v6","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07392","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"pith_short_12","alias_value":"GAUF2E2NKKYD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAUF2E2NKKYD5S3B","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAUF2E2N","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:40fa37f5dae082612f453e6737f9f89407fe8e189824ff291cdd2efdaf25e1e0","target":"graph","created_at":"2026-05-18T00:57:04Z","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"},"paper":{"abstract_excerpt":"We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These \"Stein factor\" bounds deliver control over Wasserstein and related smooth function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.","authors_text":"Jackson Gorham, Lester Mackey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-23T08:58:10Z","title":"Multivariate Stein Factors for a Class of Strongly Log-concave Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07392","kind":"arxiv","version":6},"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":"sha256:06671c4f376c0db6d8ba9b4c48290c05e671a64a7bdd109f308c790d23e528dc","target":"record","created_at":"2026-05-18T00:57:04Z","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":"a100ccdc8d22b0be91ea90898af018061183186635cf61aa6f7202ffe419834f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-23T08:58:10Z","title_canon_sha256":"c58abda7298822d3c482a453fbc8df2b11b1601d5844ab1051aaec038ba4674b"},"schema_version":"1.0","source":{"id":"1512.07392","kind":"arxiv","version":6}},"canonical_sha256":"30285d134d52b03ecb6163e4d1342b7dba2198a6a52461de5cf1a744ae06192a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30285d134d52b03ecb6163e4d1342b7dba2198a6a52461de5cf1a744ae06192a","first_computed_at":"2026-05-18T00:57:04.780972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:04.780972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6k8gx+KcwMifa/3IWuO8f7wIgw2VKddziXHZ6yzcWGeiVSdfH+SHDdKcXlIdWdB0rbInHvMBOoxJOqx8lnxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:04.781566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07392","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06671c4f376c0db6d8ba9b4c48290c05e671a64a7bdd109f308c790d23e528dc","sha256:40fa37f5dae082612f453e6737f9f89407fe8e189824ff291cdd2efdaf25e1e0"],"state_sha256":"8caa6a2690f2e68c7fb18c73b9a8bc62338d3e14bdbbb401f73ef73e7a6a78d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IA3pLTNDcG2aADCaa2e361oA7woiHEivjovVHuYik9Xpx/U441I1XGMV780rB5Zgr4ALS7GXO5OBaoTzb9FDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:49:58.043245Z","bundle_sha256":"e7ddc9c20058c54b2ac88ca028b7acc8a0c702425e284ea95dccbdfb302503e9"}}