{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GCO7MXTWFKNYTB6CZBSEDTWHXR","short_pith_number":"pith:GCO7MXTW","canonical_record":{"source":{"id":"1205.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-01T09:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"1df990232dc4cdc65e388357a723008340f34aa00c658668a09e9b5dcb3f5306","abstract_canon_sha256":"851f22441a9d9fd55b9da819bdcbbefad03c6baaccc3e8ac1ade2c224b859d2f"},"schema_version":"1.0"},"canonical_sha256":"309df65e762a9b8987c2c86441cec7bc661d4eb2598e1758a7313b362998f5e4","source":{"kind":"arxiv","id":"1205.0121","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0121","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0121v2","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0121","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"GCO7MXTWFKNY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GCO7MXTWFKNYTB6C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GCO7MXTW","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GCO7MXTWFKNYTB6CZBSEDTWHXR","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-01T09:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"1df990232dc4cdc65e388357a723008340f34aa00c658668a09e9b5dcb3f5306","abstract_canon_sha256":"851f22441a9d9fd55b9da819bdcbbefad03c6baaccc3e8ac1ade2c224b859d2f"},"schema_version":"1.0"},"canonical_sha256":"309df65e762a9b8987c2c86441cec7bc661d4eb2598e1758a7313b362998f5e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:19.681193Z","signature_b64":"u1ShFqKUDOKUMlhKl3XOcvTsF1M9titpUDmQqCp1S6fcwX36+4eNLUOrASy8tqZ/foOOwJaYHqzoVg/HxAFPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"309df65e762a9b8987c2c86441cec7bc661d4eb2598e1758a7313b362998f5e4","last_reissued_at":"2026-05-18T03:53:19.680305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:19.680305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0121","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":"2026-05-18T03:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSGeqSP3yOb2w6XDhvK3eLmbEug8d4AUEBFURsqdwwwJXz3Uxizg6W23x0EubA03bWXb57mPNq91hRDh94GxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:00:09.924223Z"},"content_sha256":"1ce57e9153e053a64ec32dafe593f24c7fdcbd471052eda2193c496998de777e","schema_version":"1.0","event_id":"sha256:1ce57e9153e053a64ec32dafe593f24c7fdcbd471052eda2193c496998de777e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GCO7MXTWFKNYTB6CZBSEDTWHXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Bounds for Sparse Principal Component Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui","submitted_at":"2012-05-01T09:08:06Z","abstract_excerpt":"We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are sampled from Gaussian models with a single sparse leading component."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0121","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":""},"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":"2026-05-18T03:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzCd5ofsGLBKPSmJ1RR2UK6wjskvIJ6FPc8R74XoWG9U670SIVl8wkP72voKcSO+oqCLCxlq7IeWWPanXtkrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:00:09.925008Z"},"content_sha256":"9c75bfd94f0a3197f5b701b7208d71e988dcfc7e755f43958e513112f431abed","schema_version":"1.0","event_id":"sha256:9c75bfd94f0a3197f5b701b7208d71e988dcfc7e755f43958e513112f431abed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/bundle.json","state_url":"https://pith.science/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/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":"2026-06-11T19:00:09Z","links":{"resolver":"https://pith.science/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR","bundle":"https://pith.science/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/bundle.json","state":"https://pith.science/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCO7MXTWFKNYTB6CZBSEDTWHXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GCO7MXTWFKNYTB6CZBSEDTWHXR","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":"851f22441a9d9fd55b9da819bdcbbefad03c6baaccc3e8ac1ade2c224b859d2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-01T09:08:06Z","title_canon_sha256":"1df990232dc4cdc65e388357a723008340f34aa00c658668a09e9b5dcb3f5306"},"schema_version":"1.0","source":{"id":"1205.0121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0121","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0121v2","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0121","created_at":"2026-05-18T03:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"GCO7MXTWFKNY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GCO7MXTWFKNYTB6C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GCO7MXTW","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:9c75bfd94f0a3197f5b701b7208d71e988dcfc7e755f43958e513112f431abed","target":"graph","created_at":"2026-05-18T03:53:19Z","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 produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are sampled from Gaussian models with a single sparse leading component.","authors_text":"Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-01T09:08:06Z","title":"Approximation Bounds for Sparse Principal Component Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0121","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":"sha256:1ce57e9153e053a64ec32dafe593f24c7fdcbd471052eda2193c496998de777e","target":"record","created_at":"2026-05-18T03:53:19Z","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":"851f22441a9d9fd55b9da819bdcbbefad03c6baaccc3e8ac1ade2c224b859d2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-01T09:08:06Z","title_canon_sha256":"1df990232dc4cdc65e388357a723008340f34aa00c658668a09e9b5dcb3f5306"},"schema_version":"1.0","source":{"id":"1205.0121","kind":"arxiv","version":2}},"canonical_sha256":"309df65e762a9b8987c2c86441cec7bc661d4eb2598e1758a7313b362998f5e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"309df65e762a9b8987c2c86441cec7bc661d4eb2598e1758a7313b362998f5e4","first_computed_at":"2026-05-18T03:53:19.680305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:19.680305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u1ShFqKUDOKUMlhKl3XOcvTsF1M9titpUDmQqCp1S6fcwX36+4eNLUOrASy8tqZ/foOOwJaYHqzoVg/HxAFPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:19.681193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ce57e9153e053a64ec32dafe593f24c7fdcbd471052eda2193c496998de777e","sha256:9c75bfd94f0a3197f5b701b7208d71e988dcfc7e755f43958e513112f431abed"],"state_sha256":"2a9ebd9bde256e087a38883ac34a3ac5bb44fcd6a2e2ee1a17a6a48eaaf9656e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gO3e1hDegWr2beX5JyEoA5G5bfsRacEwbX9TWkXF5hxgaPKbKnXZ3wk+68hK64817921bbhi4I9oU7vYJT+XCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T19:00:09.929991Z","bundle_sha256":"c0b7cc7ede9e81886d07543bea688885fa567263ad13c56e8c89a7e0f62319a4"}}