{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2IAMVTQ6I2JSDDFPJM25HYLT53","short_pith_number":"pith:2IAMVTQ6","canonical_record":{"source":{"id":"2504.16229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-04-22T19:49:52Z","cross_cats_sorted":[],"title_canon_sha256":"689b76b1631f2a721788de85eaae5a8fb3188867353496d502f10418487ea4b4","abstract_canon_sha256":"421fdd1b0181d144521215ea7fbc98838670a3ff98dc3abae2f6ba531f2b07f4"},"schema_version":"1.0"},"canonical_sha256":"d200cace1e4693218caf4b35d3e173eee6a91940ebf0c81f4419864769dd7440","source":{"kind":"arxiv","id":"2504.16229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16229","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16229v1","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16229","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"2IAMVTQ6I2JS","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"2IAMVTQ6I2JSDDFP","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"2IAMVTQ6","created_at":"2026-07-05T10:52:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2IAMVTQ6I2JSDDFPJM25HYLT53","target":"record","payload":{"canonical_record":{"source":{"id":"2504.16229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-04-22T19:49:52Z","cross_cats_sorted":[],"title_canon_sha256":"689b76b1631f2a721788de85eaae5a8fb3188867353496d502f10418487ea4b4","abstract_canon_sha256":"421fdd1b0181d144521215ea7fbc98838670a3ff98dc3abae2f6ba531f2b07f4"},"schema_version":"1.0"},"canonical_sha256":"d200cace1e4693218caf4b35d3e173eee6a91940ebf0c81f4419864769dd7440","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:52:43.546255Z","signature_b64":"KG5SrXf0xMWRYVI/jGxQAi1JnRCTbQHkcM+x2rSq3khAGS47bUbcR/nXtrA7qxnYsd6zA4EjfR2iJ5386oJVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d200cace1e4693218caf4b35d3e173eee6a91940ebf0c81f4419864769dd7440","last_reissued_at":"2026-07-05T10:52:43.545821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:52:43.545821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.16229","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":"2026-07-05T10:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ph7i+V9B/Q7tx7H2XzGrTMDQVpZJAC9s4QY/Jy4T+PzXur5EkM0oQdQ7lmfmOxHRjmUU9LVGAsxWmsFr/OnDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:05:10.504459Z"},"content_sha256":"c542421f46e33f56cba0f26112966832bbf4009c536d5a2484120748a2ec9662","schema_version":"1.0","event_id":"sha256:c542421f46e33f56cba0f26112966832bbf4009c536d5a2484120748a2ec9662"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2IAMVTQ6I2JSDDFPJM25HYLT53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast, Space-Optimal Streaming Algorithms for Clustering and Subspace Embeddings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Liudeng Wang, Samson Zhou, Vincent Cohen-Addad","submitted_at":"2025-04-22T19:49:52Z","abstract_excerpt":"We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting.\n  For $(k, z)$-clustering in the streaming model, we achieve a number of words of memory which is independent of the number $n$ of input points and the aspect ratio $\\Delta$, yielding an optimal bound of $\\tilde{\\mathcal{O}}\\left(\\frac{dk}{\\min(\\varepsilon^4,\\varepsilon^{z+2})}\\right)$ words for accuracy parameter $\\varepsilon$ on $d$-dimensional points. Additionally, we obtain amortized update time of $d\\,\\log(k)\\cdot\\text{polylog}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16229","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16229/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":"2026-07-05T10:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeP0hj/TZH7ELyUw3sfQJi05jaoZ+w2zZM8rzY7z1M06GyOWzqrQt4nlvaSZERwruaNWdkiW+BCC77Yswud6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:05:10.504835Z"},"content_sha256":"5876f484f40a5a58f30615229ce3530ffbf6ab4a29891b4fa741af02629a91e3","schema_version":"1.0","event_id":"sha256:5876f484f40a5a58f30615229ce3530ffbf6ab4a29891b4fa741af02629a91e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/bundle.json","state_url":"https://pith.science/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/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":"2026-08-17T19:05:10Z","links":{"resolver":"https://pith.science/pith/2IAMVTQ6I2JSDDFPJM25HYLT53","bundle":"https://pith.science/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/bundle.json","state":"https://pith.science/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IAMVTQ6I2JSDDFPJM25HYLT53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2IAMVTQ6I2JSDDFPJM25HYLT53","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":"421fdd1b0181d144521215ea7fbc98838670a3ff98dc3abae2f6ba531f2b07f4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-04-22T19:49:52Z","title_canon_sha256":"689b76b1631f2a721788de85eaae5a8fb3188867353496d502f10418487ea4b4"},"schema_version":"1.0","source":{"id":"2504.16229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16229","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16229v1","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16229","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"2IAMVTQ6I2JS","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"2IAMVTQ6I2JSDDFP","created_at":"2026-07-05T10:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"2IAMVTQ6","created_at":"2026-07-05T10:52:43Z"}],"graph_snapshots":[{"event_id":"sha256:5876f484f40a5a58f30615229ce3530ffbf6ab4a29891b4fa741af02629a91e3","target":"graph","created_at":"2026-07-05T10:52:43Z","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/2504.16229/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting.\n  For $(k, z)$-clustering in the streaming model, we achieve a number of words of memory which is independent of the number $n$ of input points and the aspect ratio $\\Delta$, yielding an optimal bound of $\\tilde{\\mathcal{O}}\\left(\\frac{dk}{\\min(\\varepsilon^4,\\varepsilon^{z+2})}\\right)$ words for accuracy parameter $\\varepsilon$ on $d$-dimensional points. Additionally, we obtain amortized update time of $d\\,\\log(k)\\cdot\\text{polylog}","authors_text":"David P. Woodruff, Liudeng Wang, Samson Zhou, Vincent Cohen-Addad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-04-22T19:49:52Z","title":"Fast, Space-Optimal Streaming Algorithms for Clustering and Subspace Embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16229","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:c542421f46e33f56cba0f26112966832bbf4009c536d5a2484120748a2ec9662","target":"record","created_at":"2026-07-05T10:52:43Z","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":"421fdd1b0181d144521215ea7fbc98838670a3ff98dc3abae2f6ba531f2b07f4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-04-22T19:49:52Z","title_canon_sha256":"689b76b1631f2a721788de85eaae5a8fb3188867353496d502f10418487ea4b4"},"schema_version":"1.0","source":{"id":"2504.16229","kind":"arxiv","version":1}},"canonical_sha256":"d200cace1e4693218caf4b35d3e173eee6a91940ebf0c81f4419864769dd7440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d200cace1e4693218caf4b35d3e173eee6a91940ebf0c81f4419864769dd7440","first_computed_at":"2026-07-05T10:52:43.545821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:43.545821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KG5SrXf0xMWRYVI/jGxQAi1JnRCTbQHkcM+x2rSq3khAGS47bUbcR/nXtrA7qxnYsd6zA4EjfR2iJ5386oJVCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:43.546255Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c542421f46e33f56cba0f26112966832bbf4009c536d5a2484120748a2ec9662","sha256:5876f484f40a5a58f30615229ce3530ffbf6ab4a29891b4fa741af02629a91e3"],"state_sha256":"a759f92a990b2e5b62ddf62ff09747db404e19b12c02f849a00677f241b4b432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2vL4TrtB051Bbk0gdMrAD3w0dMZ9LlNphNTWtHHaawlsVxfYU6812VLzlUWml9RJX6HFSS5mcL8SC9pSqgHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T19:05:10.507343Z","bundle_sha256":"ced8027b570124aedb89e6cf210ee1477ce354ed8e20edb0958052dac4ade6ee"}}