{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LJCGXXBQKPPIX5MUJKGD6D3D4U","short_pith_number":"pith:LJCGXXBQ","canonical_record":{"source":{"id":"2411.12438","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-19T11:58:51Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"125665ae6221985cb3e8274c4aefa78e236080d6e818bb715242bfb19f5d2391","abstract_canon_sha256":"708879892ecdb31506b6d8bf78a297df2d3179b5c8e6163d91d5c27ae0f83210"},"schema_version":"1.0"},"canonical_sha256":"5a446bdc3053de8bf5944a8c3f0f63e520fa28e201ce03153992a0e301b8f558","source":{"kind":"arxiv","id":"2411.12438","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12438","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12438v2","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12438","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"LJCGXXBQKPPI","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"LJCGXXBQKPPIX5MU","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"LJCGXXBQ","created_at":"2026-06-02T02:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LJCGXXBQKPPIX5MUJKGD6D3D4U","target":"record","payload":{"canonical_record":{"source":{"id":"2411.12438","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-19T11:58:51Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"125665ae6221985cb3e8274c4aefa78e236080d6e818bb715242bfb19f5d2391","abstract_canon_sha256":"708879892ecdb31506b6d8bf78a297df2d3179b5c8e6163d91d5c27ae0f83210"},"schema_version":"1.0"},"canonical_sha256":"5a446bdc3053de8bf5944a8c3f0f63e520fa28e201ce03153992a0e301b8f558","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:45.379603Z","signature_b64":"N7KKPdQcyE6NnzZ8NJ3X/R48/QQTqNcfU6uLj3qI+CqAmouHH6gnqXg76p6x01kztXsXVH2fajU2Lf+pN91yBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a446bdc3053de8bf5944a8c3f0f63e520fa28e201ce03153992a0e301b8f558","last_reissued_at":"2026-06-02T02:04:45.379074Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:45.379074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.12438","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":"2026-06-02T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcEG9OyE8HNbkbLPWZqd+kIhpThHIThUsShJ23URKpWTVC8UGbXmSiqOge4shMYXYcBGfPrI76Z1197aT+zzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:15:35.661726Z"},"content_sha256":"13435cfdb373216a05a5817d32ecfd40e6a119adaaf2815c0e59e0aa72f83aa5","schema_version":"1.0","event_id":"sha256:13435cfdb373216a05a5817d32ecfd40e6a119adaaf2815c0e59e0aa72f83aa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LJCGXXBQKPPIX5MUJKGD6D3D4U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David Steurer, Mitali Bafna, Prashanti Anderson, Pravesh K. Kothari, Rares-Darius Buhai","submitted_at":"2024-11-19T11:58:51Z","abstract_excerpt":"We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the celebrated spherical clustering algorithm of Vempala and Wang [VW04].\n  As applications, we obtain an algorithm to (1) cluster an arbitrary total-variation sepa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12438","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/2411.12438/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":"2026-06-02T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qn6BkFYFd6FzEwJGxn5q2gkgzi83mNUViXHTBphqtsXsQV13pQHtjDjEeRHYU5uMwMjhFSDJd75KEYehMLyGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:15:35.662418Z"},"content_sha256":"431a0e26fa434e6b350ec27d96d847a51723c3ea10e48c0b3d4de41a341161dc","schema_version":"1.0","event_id":"sha256:431a0e26fa434e6b350ec27d96d847a51723c3ea10e48c0b3d4de41a341161dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/bundle.json","state_url":"https://pith.science/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/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":"2026-06-05T23:15:35Z","links":{"resolver":"https://pith.science/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U","bundle":"https://pith.science/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/bundle.json","state":"https://pith.science/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJCGXXBQKPPIX5MUJKGD6D3D4U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LJCGXXBQKPPIX5MUJKGD6D3D4U","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":"708879892ecdb31506b6d8bf78a297df2d3179b5c8e6163d91d5c27ae0f83210","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-19T11:58:51Z","title_canon_sha256":"125665ae6221985cb3e8274c4aefa78e236080d6e818bb715242bfb19f5d2391"},"schema_version":"1.0","source":{"id":"2411.12438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12438","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12438v2","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12438","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"LJCGXXBQKPPI","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"LJCGXXBQKPPIX5MU","created_at":"2026-06-02T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"LJCGXXBQ","created_at":"2026-06-02T02:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:431a0e26fa434e6b350ec27d96d847a51723c3ea10e48c0b3d4de41a341161dc","target":"graph","created_at":"2026-06-02T02:04:45Z","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/2411.12438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the celebrated spherical clustering algorithm of Vempala and Wang [VW04].\n  As applications, we obtain an algorithm to (1) cluster an arbitrary total-variation sepa","authors_text":"David Steurer, Mitali Bafna, Prashanti Anderson, Pravesh K. Kothari, Rares-Darius Buhai","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-19T11:58:51Z","title":"Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12438","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":"sha256:13435cfdb373216a05a5817d32ecfd40e6a119adaaf2815c0e59e0aa72f83aa5","target":"record","created_at":"2026-06-02T02:04:45Z","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":"708879892ecdb31506b6d8bf78a297df2d3179b5c8e6163d91d5c27ae0f83210","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-19T11:58:51Z","title_canon_sha256":"125665ae6221985cb3e8274c4aefa78e236080d6e818bb715242bfb19f5d2391"},"schema_version":"1.0","source":{"id":"2411.12438","kind":"arxiv","version":2}},"canonical_sha256":"5a446bdc3053de8bf5944a8c3f0f63e520fa28e201ce03153992a0e301b8f558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a446bdc3053de8bf5944a8c3f0f63e520fa28e201ce03153992a0e301b8f558","first_computed_at":"2026-06-02T02:04:45.379074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:45.379074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N7KKPdQcyE6NnzZ8NJ3X/R48/QQTqNcfU6uLj3qI+CqAmouHH6gnqXg76p6x01kztXsXVH2fajU2Lf+pN91yBg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:45.379603Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.12438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13435cfdb373216a05a5817d32ecfd40e6a119adaaf2815c0e59e0aa72f83aa5","sha256:431a0e26fa434e6b350ec27d96d847a51723c3ea10e48c0b3d4de41a341161dc"],"state_sha256":"ba88672b2a7e38190301218a351e5abb8cc982b7d96bde2bc658ecd34b376fbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6v/c54ML+5rxdMl+7tPjid8KGrq8oggmh9M3QEmz7ORnjiEro4aT/Fsab8wHBmoWjignQvQWgIHQqxKDX1oVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T23:15:35.667272Z","bundle_sha256":"8e403f2146a9ac287fcdc8e9da1ca9bcfae8d3292168e27c83faa2291ec267e5"}}