{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4Z6CIU2PTMEAWPSCT2RXQAOTOI","short_pith_number":"pith:4Z6CIU2P","canonical_record":{"source":{"id":"1311.4643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-11-19T08:00:50Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT","stat.ML"],"title_canon_sha256":"778e6ca347ddc73a68caa7377f41b29aba8b18ba330c9a21e28bd625acd55a13","abstract_canon_sha256":"d5521e763bf734fba9d26c764ce87a447f1893cc39617dc09f08e35bab88d3bf"},"schema_version":"1.0"},"canonical_sha256":"e67c24534f9b080b3e429ea37801d3721b88cc7a04960b33467fd04cea36261d","source":{"kind":"arxiv","id":"1311.4643","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4643","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4643v1","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4643","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"4Z6CIU2PTMEA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4Z6CIU2PTMEAWPSC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4Z6CIU2P","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4Z6CIU2PTMEAWPSCT2RXQAOTOI","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-11-19T08:00:50Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT","stat.ML"],"title_canon_sha256":"778e6ca347ddc73a68caa7377f41b29aba8b18ba330c9a21e28bd625acd55a13","abstract_canon_sha256":"d5521e763bf734fba9d26c764ce87a447f1893cc39617dc09f08e35bab88d3bf"},"schema_version":"1.0"},"canonical_sha256":"e67c24534f9b080b3e429ea37801d3721b88cc7a04960b33467fd04cea36261d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:43.797763Z","signature_b64":"JBXrMC8AGO7Dj2cqj+eY39q+HW49qi328Uqt/Ti0vJpPZuBxFwjnhneGYjRM3YdGz/zjrU8ylnHQ9nQFzO0CAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e67c24534f9b080b3e429ea37801d3721b88cc7a04960b33467fd04cea36261d","last_reissued_at":"2026-05-18T03:06:43.797410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:43.797410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4643","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":"2026-05-18T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gk/T+ZIJoLUVPI41Jmhak2Z535Bq6z056P1fqEZJmxjepTuIcD5C/dpCh8BJWpxvmRbC/c48dGJAWiUSoICQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:32:24.184158Z"},"content_sha256":"b0fc102925c1698c8a2b6100d2812b498cd440d50886b8d62620b9495d373412","schema_version":"1.0","event_id":"sha256:b0fc102925c1698c8a2b6100d2812b498cd440d50886b8d62620b9495d373412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4Z6CIU2PTMEAWPSCT2RXQAOTOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near-Optimal Entrywise Sampling for Data Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Dimitris Achlioptas, Edo Liberty, Zohar Karnin","submitted_at":"2013-11-19T08:00:50Z","abstract_excerpt":"We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\\|A-B\\|_2$. For large $m \\times n$ matrices, such that $n \\gg m$ (for example, representing $n$ observations over $m$ attributes) we give sampling distributions that exhibit four important properties. First, they have closed forms computable from minimal information regarding $A$. Second, they allow sketching of matrices whose non-zeros are presented to the algorithm in arbitrary order as a stream, with $O(1)$ computation per non-zero. Third, the resulting sketc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4643","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":"2026-05-18T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eh7c3Vnk1+D/H7YhpvEgE61cpY0Y3qnZeESoA1BCWI7slp5dQfWdnp4aiBZUrCejsGLnuQjULwaRGz05mM+UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:32:24.184536Z"},"content_sha256":"eb0bbf0d56731be15aa6f622da66f3d8c3b63c34ef1a43a69da60b2f82edfec4","schema_version":"1.0","event_id":"sha256:eb0bbf0d56731be15aa6f622da66f3d8c3b63c34ef1a43a69da60b2f82edfec4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/bundle.json","state_url":"https://pith.science/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/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":"2026-05-28T04:32:24Z","links":{"resolver":"https://pith.science/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI","bundle":"https://pith.science/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/bundle.json","state":"https://pith.science/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Z6CIU2PTMEAWPSCT2RXQAOTOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4Z6CIU2PTMEAWPSCT2RXQAOTOI","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":"d5521e763bf734fba9d26c764ce87a447f1893cc39617dc09f08e35bab88d3bf","cross_cats_sorted":["cs.IT","cs.NA","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-11-19T08:00:50Z","title_canon_sha256":"778e6ca347ddc73a68caa7377f41b29aba8b18ba330c9a21e28bd625acd55a13"},"schema_version":"1.0","source":{"id":"1311.4643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4643","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4643v1","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4643","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"4Z6CIU2PTMEA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4Z6CIU2PTMEAWPSC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4Z6CIU2P","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:eb0bbf0d56731be15aa6f622da66f3d8c3b63c34ef1a43a69da60b2f82edfec4","target":"graph","created_at":"2026-05-18T03:06:43Z","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"},"paper":{"abstract_excerpt":"We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\\|A-B\\|_2$. For large $m \\times n$ matrices, such that $n \\gg m$ (for example, representing $n$ observations over $m$ attributes) we give sampling distributions that exhibit four important properties. First, they have closed forms computable from minimal information regarding $A$. Second, they allow sketching of matrices whose non-zeros are presented to the algorithm in arbitrary order as a stream, with $O(1)$ computation per non-zero. Third, the resulting sketc","authors_text":"Dimitris Achlioptas, Edo Liberty, Zohar Karnin","cross_cats":["cs.IT","cs.NA","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-11-19T08:00:50Z","title":"Near-Optimal Entrywise Sampling for Data Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4643","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:b0fc102925c1698c8a2b6100d2812b498cd440d50886b8d62620b9495d373412","target":"record","created_at":"2026-05-18T03:06:43Z","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":"d5521e763bf734fba9d26c764ce87a447f1893cc39617dc09f08e35bab88d3bf","cross_cats_sorted":["cs.IT","cs.NA","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-11-19T08:00:50Z","title_canon_sha256":"778e6ca347ddc73a68caa7377f41b29aba8b18ba330c9a21e28bd625acd55a13"},"schema_version":"1.0","source":{"id":"1311.4643","kind":"arxiv","version":1}},"canonical_sha256":"e67c24534f9b080b3e429ea37801d3721b88cc7a04960b33467fd04cea36261d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e67c24534f9b080b3e429ea37801d3721b88cc7a04960b33467fd04cea36261d","first_computed_at":"2026-05-18T03:06:43.797410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:43.797410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JBXrMC8AGO7Dj2cqj+eY39q+HW49qi328Uqt/Ti0vJpPZuBxFwjnhneGYjRM3YdGz/zjrU8ylnHQ9nQFzO0CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:43.797763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0fc102925c1698c8a2b6100d2812b498cd440d50886b8d62620b9495d373412","sha256:eb0bbf0d56731be15aa6f622da66f3d8c3b63c34ef1a43a69da60b2f82edfec4"],"state_sha256":"4fb3fe0796a71901a87a0adcfa535c64c4b9750d02cbf5e9950d108718956c22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dkGL3eVEsBT4TBV+ZggaVAH/OT4by0nI3PJTt3KJnGACLLR9GdJnJ4mCXYo5ohRdpnUaV8e0hEoP5VtoGEYvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:32:24.186571Z","bundle_sha256":"bfbcdfea32e39262ab19a69d39fa25f36ec18e706c28931d1c89ded0c9687c16"}}