{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:L3NDWDJCO74TWHOJPWJIHQKQHJ","short_pith_number":"pith:L3NDWDJC","canonical_record":{"source":{"id":"1502.01403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-05T00:53:01Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"2eafdaf961f02705eff630dfd4b03efc3d96d79ce26e1a53198c8dc33ee7ce2b","abstract_canon_sha256":"111827ec88afe6ea352530ec48a2b545b1f8763d9a2d087521f79ce7d2e6776b"},"schema_version":"1.0"},"canonical_sha256":"5eda3b0d2277f93b1dc97d9283c1503a613b2efca95aa60a824967d04b00b6a9","source":{"kind":"arxiv","id":"1502.01403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01403","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01403v2","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01403","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"L3NDWDJCO74T","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3NDWDJCO74TWHOJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3NDWDJC","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:L3NDWDJCO74TWHOJPWJIHQKQHJ","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-05T00:53:01Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"2eafdaf961f02705eff630dfd4b03efc3d96d79ce26e1a53198c8dc33ee7ce2b","abstract_canon_sha256":"111827ec88afe6ea352530ec48a2b545b1f8763d9a2d087521f79ce7d2e6776b"},"schema_version":"1.0"},"canonical_sha256":"5eda3b0d2277f93b1dc97d9283c1503a613b2efca95aa60a824967d04b00b6a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:50.781169Z","signature_b64":"FvzlJwwuxiRCGBRSol/Gx0EVbLED9qesDEszOMemJfk5/oJQ1/2cCEreEPboWBvWkuyzypkUNFj/GFysBSZ2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eda3b0d2277f93b1dc97d9283c1503a613b2efca95aa60a824967d04b00b6a9","last_reissued_at":"2026-05-18T02:27:50.780784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:50.780784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01403","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":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxeDX+R6Y32TysK73ZFUUoA1/sICbqxBYFR0Vk1Y3AeD0nypeyW/gGqCbd0GnH6otEDHpU+i463H+9vxM79KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:06:39.048673Z"},"content_sha256":"f3dc90267768977c658941405360ea697b96bec002c37f6c196c4c74820523ed","schema_version":"1.0","event_id":"sha256:f3dc90267768977c658941405360ea697b96bec002c37f6c196c4c74820523ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:L3NDWDJCO74TWHOJPWJIHQKQHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML"],"primary_cat":"cs.DS","authors_text":"Martin J. Wainwright, Michael I. Jordan, Yuchen Zhang","submitted_at":"2015-02-05T00:53:01Z","abstract_excerpt":"We study the following generalized matrix rank estimation problem: given an $n \\times n$ matrix and a constant $c \\geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is the sum of $m$ matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate $\\Omega(n^2)$ bits, which is order-equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only $\\widetilde O(n)$ bits. The upper bound is matched by an $\\Omega(n)$ lower bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01403","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":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFILX+9v2lnWV1qktkTBOLq3kn3Vsl1fp+fTXToiqXtSoYu8aoTJrxSHYUwziV2pt2K2NfL0sj8RYsdxRnD7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:06:39.049014Z"},"content_sha256":"6dfa749415bca932c1c410be9460272abd9fcab13ae7f7394356b22a560438ed","schema_version":"1.0","event_id":"sha256:6dfa749415bca932c1c410be9460272abd9fcab13ae7f7394356b22a560438ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/bundle.json","state_url":"https://pith.science/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/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":"2026-06-02T00:06:39Z","links":{"resolver":"https://pith.science/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ","bundle":"https://pith.science/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/bundle.json","state":"https://pith.science/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3NDWDJCO74TWHOJPWJIHQKQHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L3NDWDJCO74TWHOJPWJIHQKQHJ","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":"111827ec88afe6ea352530ec48a2b545b1f8763d9a2d087521f79ce7d2e6776b","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-05T00:53:01Z","title_canon_sha256":"2eafdaf961f02705eff630dfd4b03efc3d96d79ce26e1a53198c8dc33ee7ce2b"},"schema_version":"1.0","source":{"id":"1502.01403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01403","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01403v2","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01403","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"L3NDWDJCO74T","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3NDWDJCO74TWHOJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3NDWDJC","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:6dfa749415bca932c1c410be9460272abd9fcab13ae7f7394356b22a560438ed","target":"graph","created_at":"2026-05-18T02:27:50Z","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 study the following generalized matrix rank estimation problem: given an $n \\times n$ matrix and a constant $c \\geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is the sum of $m$ matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate $\\Omega(n^2)$ bits, which is order-equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only $\\widetilde O(n)$ bits. The upper bound is matched by an $\\Omega(n)$ lower bound ","authors_text":"Martin J. Wainwright, Michael I. Jordan, Yuchen Zhang","cross_cats":["cs.CC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-05T00:53:01Z","title":"Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01403","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:f3dc90267768977c658941405360ea697b96bec002c37f6c196c4c74820523ed","target":"record","created_at":"2026-05-18T02:27:50Z","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":"111827ec88afe6ea352530ec48a2b545b1f8763d9a2d087521f79ce7d2e6776b","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-05T00:53:01Z","title_canon_sha256":"2eafdaf961f02705eff630dfd4b03efc3d96d79ce26e1a53198c8dc33ee7ce2b"},"schema_version":"1.0","source":{"id":"1502.01403","kind":"arxiv","version":2}},"canonical_sha256":"5eda3b0d2277f93b1dc97d9283c1503a613b2efca95aa60a824967d04b00b6a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5eda3b0d2277f93b1dc97d9283c1503a613b2efca95aa60a824967d04b00b6a9","first_computed_at":"2026-05-18T02:27:50.780784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.780784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FvzlJwwuxiRCGBRSol/Gx0EVbLED9qesDEszOMemJfk5/oJQ1/2cCEreEPboWBvWkuyzypkUNFj/GFysBSZ2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.781169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3dc90267768977c658941405360ea697b96bec002c37f6c196c4c74820523ed","sha256:6dfa749415bca932c1c410be9460272abd9fcab13ae7f7394356b22a560438ed"],"state_sha256":"b4ff54d899d568888f1f17609e50e954f74ab8813931bacf8adc191c5317e1ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xwqhCieGps//hDr9OQ2Tvwlu9TcU2w9zPsFtaLg4rVGBri2Mq59ybPIx3omVAmWpTkOdxtAo+ubzFHJBXYFKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:06:39.050854Z","bundle_sha256":"b5dc25fc9fa41b096b70833832c5b981355fac48765b835f2c3269aa891bd981"}}