{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XI2GEIHSLHUUAMYQAZ2ZWMPRGY","short_pith_number":"pith:XI2GEIHS","canonical_record":{"source":{"id":"1710.11592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"084db9c7d8d7f8f69eefe0a871d18c26709cc64153af2dc6f1312e1c1cc9905f","abstract_canon_sha256":"796214ce164fa9d846883735a4fa25c5f0d223e7a26c7e74beb221c327d8c4c9"},"schema_version":"1.0"},"canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","source":{"kind":"arxiv","id":"1710.11592","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11592","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11592v1","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11592","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"XI2GEIHSLHUU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XI2GEIHSLHUUAMYQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XI2GEIHS","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XI2GEIHSLHUUAMYQAZ2ZWMPRGY","target":"record","payload":{"canonical_record":{"source":{"id":"1710.11592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"084db9c7d8d7f8f69eefe0a871d18c26709cc64153af2dc6f1312e1c1cc9905f","abstract_canon_sha256":"796214ce164fa9d846883735a4fa25c5f0d223e7a26c7e74beb221c327d8c4c9"},"schema_version":"1.0"},"canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:36.882346Z","signature_b64":"4H1/YCs5hwU+osjx8hY0pdDY6NMptX7+5JnXuQDpXPGbb6icYo5PPtbSMUXcXe/mFUSpOUWMwt+/zAFzvZXbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","last_reissued_at":"2026-05-18T00:31:36.881823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:36.881823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.11592","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOBOT5OxqHE2FInRIVKqSSjsp8CQdJunuKKHu+QW0I72JsQyc6aVrfs4RCjkDB7op+cK+ltfulB1LZxDFkcpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:04:24.970355Z"},"content_sha256":"6defe903007e82e48b0c9ffd00780cee31d1eebc6d55257970dd86f01b5f81c5","schema_version":"1.0","event_id":"sha256:6defe903007e82e48b0c9ffd00780cee31d1eebc6d55257970dd86f01b5f81c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XI2GEIHSLHUUAMYQAZ2ZWMPRGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Learning Mixtures of Well-Separated Gaussians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Aravindan Vijayaraghavan, Oded Regev","submitted_at":"2017-10-31T17:10:21Z","abstract_excerpt":"We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\\delta$ using $poly(k,d, 1/\\delta)$ samples.\n  In this work, we study the following question: what is the minimum separation needed between the means for solving this task? The best known algorithm due to Vempala and Wang [JCSS 2004] requires a separation of roughly $\\mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11592","kind":"arxiv","version":1},"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":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVLx/2sSVGT2cIrWh5XWXoRep9tbCLzePliZTPbys+lc5opbqqTYdnIbmjc8+/UWFROKxatwWDB0PgmT1vruCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:04:24.970996Z"},"content_sha256":"800694e58e2604ea3651223a8b8b142294f19be53ccf3f8d478f3b27e723770f","schema_version":"1.0","event_id":"sha256:800694e58e2604ea3651223a8b8b142294f19be53ccf3f8d478f3b27e723770f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/bundle.json","state_url":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/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":"2026-06-09T06:04:24Z","links":{"resolver":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY","bundle":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/bundle.json","state":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XI2GEIHSLHUUAMYQAZ2ZWMPRGY","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":"796214ce164fa9d846883735a4fa25c5f0d223e7a26c7e74beb221c327d8c4c9","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","title_canon_sha256":"084db9c7d8d7f8f69eefe0a871d18c26709cc64153af2dc6f1312e1c1cc9905f"},"schema_version":"1.0","source":{"id":"1710.11592","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11592","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11592v1","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11592","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"XI2GEIHSLHUU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XI2GEIHSLHUUAMYQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XI2GEIHS","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:800694e58e2604ea3651223a8b8b142294f19be53ccf3f8d478f3b27e723770f","target":"graph","created_at":"2026-05-18T00:31:36Z","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 consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\\delta$ using $poly(k,d, 1/\\delta)$ samples.\n  In this work, we study the following question: what is the minimum separation needed between the means for solving this task? The best known algorithm due to Vempala and Wang [JCSS 2004] requires a separation of roughly $\\mi","authors_text":"Aravindan Vijayaraghavan, Oded Regev","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","title":"On Learning Mixtures of Well-Separated Gaussians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11592","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":"sha256:6defe903007e82e48b0c9ffd00780cee31d1eebc6d55257970dd86f01b5f81c5","target":"record","created_at":"2026-05-18T00:31:36Z","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":"796214ce164fa9d846883735a4fa25c5f0d223e7a26c7e74beb221c327d8c4c9","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","title_canon_sha256":"084db9c7d8d7f8f69eefe0a871d18c26709cc64153af2dc6f1312e1c1cc9905f"},"schema_version":"1.0","source":{"id":"1710.11592","kind":"arxiv","version":1}},"canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","first_computed_at":"2026-05-18T00:31:36.881823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:36.881823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4H1/YCs5hwU+osjx8hY0pdDY6NMptX7+5JnXuQDpXPGbb6icYo5PPtbSMUXcXe/mFUSpOUWMwt+/zAFzvZXbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:36.882346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11592","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6defe903007e82e48b0c9ffd00780cee31d1eebc6d55257970dd86f01b5f81c5","sha256:800694e58e2604ea3651223a8b8b142294f19be53ccf3f8d478f3b27e723770f"],"state_sha256":"78c893697378fa1baa60bb71cca3e92abd25bc0cfc08bd72c8765cffc9d6bb03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWNGFRglEs6Wu9EkNU0i9Q56V15Z328h3SL5/zrN1vM0fNf5LWL69nyrf0jcGOyTCcLYPP4+uQXqwtXUUntvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:04:24.975176Z","bundle_sha256":"c24d7d0a67f6a2ec81ddce06ede166011da3c48b1ffc100984c05f4a20a6fd3e"}}