{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VPTZREY3CKPEMPO4PQ3HIELJIZ","short_pith_number":"pith:VPTZREY3","canonical_record":{"source":{"id":"1612.06067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T07:58:00Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"abc0d7101b9fa799205da65d8b454dceb5fe7271970cc7ad0a974f5eacfc8e9a","abstract_canon_sha256":"3b241e41e0f0e8659ee032d0084c351f536a68e46dc8eafb5b89ddb964c43e42"},"schema_version":"1.0"},"canonical_sha256":"abe798931b129e463ddc7c36741169465cf275419b2796e97af8ab0123401cdb","source":{"kind":"arxiv","id":"1612.06067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06067","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06067v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06067","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"VPTZREY3CKPE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VPTZREY3CKPEMPO4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VPTZREY3","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VPTZREY3CKPEMPO4PQ3HIELJIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T07:58:00Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"abc0d7101b9fa799205da65d8b454dceb5fe7271970cc7ad0a974f5eacfc8e9a","abstract_canon_sha256":"3b241e41e0f0e8659ee032d0084c351f536a68e46dc8eafb5b89ddb964c43e42"},"schema_version":"1.0"},"canonical_sha256":"abe798931b129e463ddc7c36741169465cf275419b2796e97af8ab0123401cdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.760818Z","signature_b64":"HvYdGbOVsYFjcgmpGy73wkytY4NQ2MK2E3G1TIj1RzVjffP2WS4KF6UPbLug9xnXU7+9dnEvdqMe1zttqjUnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe798931b129e463ddc7c36741169465cf275419b2796e97af8ab0123401cdb","last_reissued_at":"2026-05-17T23:56:48.760375Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.760375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06067","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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HfQb6X/gZ+gOdI98WaqxbAJQnASPY+yhH0QWouo4QLdQXpyMSRyxqaonSfRUVjkZHZxlBj0A3Y2pdV2m0hE1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:32:55.718089Z"},"content_sha256":"0a9a1a7e2b654f73a64f22ebd6ef9fc4c48b8554d8ae0bb5a8172bad20a762af","schema_version":"1.0","event_id":"sha256:0a9a1a7e2b654f73a64f22ebd6ef9fc4c48b8554d8ae0bb5a8172bad20a762af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VPTZREY3CKPEMPO4PQ3HIELJIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Convex Program for Mixed Linear Regression with a Recovery Guarantee for Well-Separated Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Babhru Joshi, Paul Hand","submitted_at":"2016-12-19T07:58:00Z","abstract_excerpt":"We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06067","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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKDMsT+6SNiCd2KKgUrtcflPOKpng9DUEIAm/D7imCjvxBjhkHW79uzHjUzHQIwJp2Z173EBwTpBZv2kYTuCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:32:55.718460Z"},"content_sha256":"099ca75ea8560562f77b5ee1f58127a9a95b65235069cb84069c5bcda665765a","schema_version":"1.0","event_id":"sha256:099ca75ea8560562f77b5ee1f58127a9a95b65235069cb84069c5bcda665765a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/bundle.json","state_url":"https://pith.science/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/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":"2026-06-01T04:32:55Z","links":{"resolver":"https://pith.science/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ","bundle":"https://pith.science/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/bundle.json","state":"https://pith.science/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPTZREY3CKPEMPO4PQ3HIELJIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VPTZREY3CKPEMPO4PQ3HIELJIZ","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":"3b241e41e0f0e8659ee032d0084c351f536a68e46dc8eafb5b89ddb964c43e42","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T07:58:00Z","title_canon_sha256":"abc0d7101b9fa799205da65d8b454dceb5fe7271970cc7ad0a974f5eacfc8e9a"},"schema_version":"1.0","source":{"id":"1612.06067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06067","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06067v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06067","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"VPTZREY3CKPE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VPTZREY3CKPEMPO4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VPTZREY3","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:099ca75ea8560562f77b5ee1f58127a9a95b65235069cb84069c5bcda665765a","target":"graph","created_at":"2026-05-17T23:56:48Z","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 introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each cla","authors_text":"Babhru Joshi, Paul Hand","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T07:58:00Z","title":"A Convex Program for Mixed Linear Regression with a Recovery Guarantee for Well-Separated Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06067","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":"sha256:0a9a1a7e2b654f73a64f22ebd6ef9fc4c48b8554d8ae0bb5a8172bad20a762af","target":"record","created_at":"2026-05-17T23:56:48Z","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":"3b241e41e0f0e8659ee032d0084c351f536a68e46dc8eafb5b89ddb964c43e42","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T07:58:00Z","title_canon_sha256":"abc0d7101b9fa799205da65d8b454dceb5fe7271970cc7ad0a974f5eacfc8e9a"},"schema_version":"1.0","source":{"id":"1612.06067","kind":"arxiv","version":2}},"canonical_sha256":"abe798931b129e463ddc7c36741169465cf275419b2796e97af8ab0123401cdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe798931b129e463ddc7c36741169465cf275419b2796e97af8ab0123401cdb","first_computed_at":"2026-05-17T23:56:48.760375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:48.760375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvYdGbOVsYFjcgmpGy73wkytY4NQ2MK2E3G1TIj1RzVjffP2WS4KF6UPbLug9xnXU7+9dnEvdqMe1zttqjUnAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:48.760818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a9a1a7e2b654f73a64f22ebd6ef9fc4c48b8554d8ae0bb5a8172bad20a762af","sha256:099ca75ea8560562f77b5ee1f58127a9a95b65235069cb84069c5bcda665765a"],"state_sha256":"4a957f600ff361659a4ea432a10a526aa61cfef050f971acae874273616c94eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mdSVngf7Acsoqe4KI4Pg3LiSv+qWaSAfkVup7IgroMPnJaZDTInH+zGWgyh4USCic0f3Lfb5VNOCFexf97qlAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:32:55.720696Z","bundle_sha256":"342f42337062dccccd2ca2ddd16c4a0e9f4b3cf649dfe84269f72e83f099b56b"}}