{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SZODTX3NKXS3PWNCSUMT7MI7OH","short_pith_number":"pith:SZODTX3N","canonical_record":{"source":{"id":"1406.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-10T15:49:05Z","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"title_canon_sha256":"81b7d98cd7c4c35e2a91c69f7ebd2d94703df2b8c4cb4380421045d8d79755f1","abstract_canon_sha256":"1cbedf5bb85bb4c89febe44d7f6dac0ebb84685cc4b72e1017b181f13b65fa52"},"schema_version":"1.0"},"canonical_sha256":"965c39df6d55e5b7d9a295193fb11f71d8817df11370344ec6ca7ff077ad9b01","source":{"kind":"arxiv","id":"1406.2602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2602","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2602v1","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2602","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"SZODTX3NKXS3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZODTX3NKXS3PWNC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZODTX3N","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SZODTX3NKXS3PWNCSUMT7MI7OH","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-10T15:49:05Z","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"title_canon_sha256":"81b7d98cd7c4c35e2a91c69f7ebd2d94703df2b8c4cb4380421045d8d79755f1","abstract_canon_sha256":"1cbedf5bb85bb4c89febe44d7f6dac0ebb84685cc4b72e1017b181f13b65fa52"},"schema_version":"1.0"},"canonical_sha256":"965c39df6d55e5b7d9a295193fb11f71d8817df11370344ec6ca7ff077ad9b01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:01.368450Z","signature_b64":"oKsyQc13kKdZo5lT4jqBcFlNs5zNY4jdLa71bDkcAXohp4+WUWQvjQTyQm/2/IPDWLQpBhDfELcrUibFHk29Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"965c39df6d55e5b7d9a295193fb11f71d8817df11370344ec6ca7ff077ad9b01","last_reissued_at":"2026-05-18T02:50:01.367963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:01.367963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2602","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":"2026-05-18T02:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rdp30OqqCBAlXbv1WUO8mrjCJ5Qp6HkJIMhLpsj49gWm5vodfYQoYgqukAxGZHJrTMIvDcyKeslJ4UC8L9icBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:22:53.284926Z"},"content_sha256":"cadbe8cd47d628637a37f71e7cef8523a8555e347dd5fc6850fe7ccdaebbf9a3","schema_version":"1.0","event_id":"sha256:cadbe8cd47d628637a37f71e7cef8523a8555e347dd5fc6850fe7ccdaebbf9a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SZODTX3NKXS3PWNCSUMT7MI7OH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Approximation and Clustering on a Budget","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CV","cs.LG"],"primary_cat":"stat.ML","authors_text":"Ethan Fetaya, Ohad Shamir, Shimon Ullman","submitted_at":"2014-06-10T15:49:05Z","abstract_excerpt":"We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly generalizing previous results (which focused on spectral clustering with two clusters). We also propose a new algorithmic approach based on adaptive sampling, which experimentally matches or improves on previous methods, while being considerably more general and computationally c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2602","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":"2026-05-18T02:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OQ+T5F9eVwrAW65100HyL3SV+CQP9vjoBzHfy4jmH94VXcjOqx6nZAZtRV1ItsQSgSTmBpDl/8vqcAJxX1hAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:22:53.285566Z"},"content_sha256":"4c924e1ddd1d1f76d0cb77cd6fefa3c2216d1d12ebf410b8cc6f99ba787b2e47","schema_version":"1.0","event_id":"sha256:4c924e1ddd1d1f76d0cb77cd6fefa3c2216d1d12ebf410b8cc6f99ba787b2e47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/bundle.json","state_url":"https://pith.science/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/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":"2026-06-09T01:22:53Z","links":{"resolver":"https://pith.science/pith/SZODTX3NKXS3PWNCSUMT7MI7OH","bundle":"https://pith.science/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/bundle.json","state":"https://pith.science/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZODTX3NKXS3PWNCSUMT7MI7OH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SZODTX3NKXS3PWNCSUMT7MI7OH","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":"1cbedf5bb85bb4c89febe44d7f6dac0ebb84685cc4b72e1017b181f13b65fa52","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-10T15:49:05Z","title_canon_sha256":"81b7d98cd7c4c35e2a91c69f7ebd2d94703df2b8c4cb4380421045d8d79755f1"},"schema_version":"1.0","source":{"id":"1406.2602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2602","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2602v1","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2602","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"SZODTX3NKXS3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZODTX3NKXS3PWNC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZODTX3N","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:4c924e1ddd1d1f76d0cb77cd6fefa3c2216d1d12ebf410b8cc6f99ba787b2e47","target":"graph","created_at":"2026-05-18T02:50:01Z","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 learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly generalizing previous results (which focused on spectral clustering with two clusters). We also propose a new algorithmic approach based on adaptive sampling, which experimentally matches or improves on previous methods, while being considerably more general and computationally c","authors_text":"Ethan Fetaya, Ohad Shamir, Shimon Ullman","cross_cats":["cs.AI","cs.CV","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-10T15:49:05Z","title":"Graph Approximation and Clustering on a Budget"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2602","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:cadbe8cd47d628637a37f71e7cef8523a8555e347dd5fc6850fe7ccdaebbf9a3","target":"record","created_at":"2026-05-18T02:50:01Z","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":"1cbedf5bb85bb4c89febe44d7f6dac0ebb84685cc4b72e1017b181f13b65fa52","cross_cats_sorted":["cs.AI","cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-10T15:49:05Z","title_canon_sha256":"81b7d98cd7c4c35e2a91c69f7ebd2d94703df2b8c4cb4380421045d8d79755f1"},"schema_version":"1.0","source":{"id":"1406.2602","kind":"arxiv","version":1}},"canonical_sha256":"965c39df6d55e5b7d9a295193fb11f71d8817df11370344ec6ca7ff077ad9b01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"965c39df6d55e5b7d9a295193fb11f71d8817df11370344ec6ca7ff077ad9b01","first_computed_at":"2026-05-18T02:50:01.367963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:01.367963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oKsyQc13kKdZo5lT4jqBcFlNs5zNY4jdLa71bDkcAXohp4+WUWQvjQTyQm/2/IPDWLQpBhDfELcrUibFHk29Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:01.368450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cadbe8cd47d628637a37f71e7cef8523a8555e347dd5fc6850fe7ccdaebbf9a3","sha256:4c924e1ddd1d1f76d0cb77cd6fefa3c2216d1d12ebf410b8cc6f99ba787b2e47"],"state_sha256":"f22f602e1024a3e15629bac1c17f6848caf3971681b433638138d934421c57bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dssTLanXRrlKjdnxB67DaNKW4BO6sCp+YsewSQVhQ7EDvmqodWi/fk77ik4BmGDBruJO6o3e1lPbx2pNfJonCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:22:53.288916Z","bundle_sha256":"817d1291d76f23f71b8d1d31fa2d5e94da931e943a0c721ab16ef1593128d50c"}}