{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:743ML57WFMS34VSQQVB7WVPS25","short_pith_number":"pith:743ML57W","canonical_record":{"source":{"id":"1606.02404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-08T05:28:14Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bc6514e7be263bf21db4a270196fcf7404ce95990b659f48f62ff316416b601d","abstract_canon_sha256":"bd86e7f760c5d8ade47b5667cb32ecb29eaabd30448b73ff7ed0aa95c87bfbd6"},"schema_version":"1.0"},"canonical_sha256":"ff36c5f7f62b25be56508543fb55f2d758d9924bf3dccf998eed6c3f7347499d","source":{"kind":"arxiv","id":"1606.02404","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02404","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02404v2","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02404","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"pith_short_12","alias_value":"743ML57WFMS3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"743ML57WFMS34VSQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"743ML57W","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:743ML57WFMS34VSQQVB7WVPS25","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-08T05:28:14Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bc6514e7be263bf21db4a270196fcf7404ce95990b659f48f62ff316416b601d","abstract_canon_sha256":"bd86e7f760c5d8ade47b5667cb32ecb29eaabd30448b73ff7ed0aa95c87bfbd6"},"schema_version":"1.0"},"canonical_sha256":"ff36c5f7f62b25be56508543fb55f2d758d9924bf3dccf998eed6c3f7347499d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:30.741099Z","signature_b64":"uD9E/2RPRaGW7Nd+U5ziqLBqy56qZAWNUJSphH4t8U1+zYcRbwlJMDe2J2Niux0/XP0B9CQdYR9a+z8cXsSwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff36c5f7f62b25be56508543fb55f2d758d9924bf3dccf998eed6c3f7347499d","last_reissued_at":"2026-05-18T00:57:30.740611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:30.740611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02404","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":"2026-05-18T00:57:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QjbF7PftExFeSLm2tqhRhrRf4poLseltPE+1xoWF03g3942HqGc5cJUabYxb15NgI37NnUzo1BCwM+HvhpzNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:39:50.894636Z"},"content_sha256":"44c78440c6876f020c549bca76f5b957c4d08a9ea06b8bb610b210be065dbeac","schema_version":"1.0","event_id":"sha256:44c78440c6876f020c549bca76f5b957c4d08a9ea06b8bb610b210be065dbeac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:743ML57WFMS34VSQQVB7WVPS25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clustering with Same-Cluster Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Hassan Ashtiani, Shai Ben-David, Shrinu Kushagra","submitted_at":"2016-06-08T05:28:14Z","abstract_excerpt":"We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where the expert conforms to a center-based clustering with a notion of margin. We show that there is a trade off between computational complexity and query complexity; We prove that for the case of $k$-means clustering (i.e., when the expert conforms to a solution of $k$-means), havi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02404","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":"2026-05-18T00:57:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uHvzfXkU7v0x7ILupDi0s8mTHtqjemhGOLSCEfux1rbCOGSSE0GR0YMyn8BgGZg59zOfWlbh6lg37dYWrib0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:39:50.894984Z"},"content_sha256":"9059ae2447954a904252eea50b976f4f846743a319f4c8b93296498c8c25bc2b","schema_version":"1.0","event_id":"sha256:9059ae2447954a904252eea50b976f4f846743a319f4c8b93296498c8c25bc2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/743ML57WFMS34VSQQVB7WVPS25/bundle.json","state_url":"https://pith.science/pith/743ML57WFMS34VSQQVB7WVPS25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/743ML57WFMS34VSQQVB7WVPS25/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":"2026-07-09T03:39:50Z","links":{"resolver":"https://pith.science/pith/743ML57WFMS34VSQQVB7WVPS25","bundle":"https://pith.science/pith/743ML57WFMS34VSQQVB7WVPS25/bundle.json","state":"https://pith.science/pith/743ML57WFMS34VSQQVB7WVPS25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/743ML57WFMS34VSQQVB7WVPS25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:743ML57WFMS34VSQQVB7WVPS25","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":"bd86e7f760c5d8ade47b5667cb32ecb29eaabd30448b73ff7ed0aa95c87bfbd6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-08T05:28:14Z","title_canon_sha256":"bc6514e7be263bf21db4a270196fcf7404ce95990b659f48f62ff316416b601d"},"schema_version":"1.0","source":{"id":"1606.02404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02404","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02404v2","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02404","created_at":"2026-05-18T00:57:30Z"},{"alias_kind":"pith_short_12","alias_value":"743ML57WFMS3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"743ML57WFMS34VSQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"743ML57W","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:9059ae2447954a904252eea50b976f4f846743a319f4c8b93296498c8c25bc2b","target":"graph","created_at":"2026-05-18T00:57:30Z","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 propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where the expert conforms to a center-based clustering with a notion of margin. We show that there is a trade off between computational complexity and query complexity; We prove that for the case of $k$-means clustering (i.e., when the expert conforms to a solution of $k$-means), havi","authors_text":"Hassan Ashtiani, Shai Ben-David, Shrinu Kushagra","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-08T05:28:14Z","title":"Clustering with Same-Cluster Queries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02404","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":"sha256:44c78440c6876f020c549bca76f5b957c4d08a9ea06b8bb610b210be065dbeac","target":"record","created_at":"2026-05-18T00:57:30Z","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":"bd86e7f760c5d8ade47b5667cb32ecb29eaabd30448b73ff7ed0aa95c87bfbd6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-08T05:28:14Z","title_canon_sha256":"bc6514e7be263bf21db4a270196fcf7404ce95990b659f48f62ff316416b601d"},"schema_version":"1.0","source":{"id":"1606.02404","kind":"arxiv","version":2}},"canonical_sha256":"ff36c5f7f62b25be56508543fb55f2d758d9924bf3dccf998eed6c3f7347499d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff36c5f7f62b25be56508543fb55f2d758d9924bf3dccf998eed6c3f7347499d","first_computed_at":"2026-05-18T00:57:30.740611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:30.740611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uD9E/2RPRaGW7Nd+U5ziqLBqy56qZAWNUJSphH4t8U1+zYcRbwlJMDe2J2Niux0/XP0B9CQdYR9a+z8cXsSwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:30.741099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44c78440c6876f020c549bca76f5b957c4d08a9ea06b8bb610b210be065dbeac","sha256:9059ae2447954a904252eea50b976f4f846743a319f4c8b93296498c8c25bc2b"],"state_sha256":"b0378f73b56ae298859f89843810ff330670bbef4f6c03f0c8f12e823d3033c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSoivs1NrMqov3gkcwFhjjNvzdl8LGRK5WDKtxcZqrjMfFwijGb52EgHcD9yWSWCzDYhNt+XA8fTEcQhJEPhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:39:50.896906Z","bundle_sha256":"e7619f130583960e30dee7cba6e9f50f4aedeb3ca6ff797cf8b822635004158b"}}