{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4M6NMCTMODVCFT23THA3NMIPQW","short_pith_number":"pith:4M6NMCTM","canonical_record":{"source":{"id":"1104.2502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-13T14:13:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"de12186a7539decaed1a2d4d1ec760f961aa1483737610c4463ce80128f16f8d","abstract_canon_sha256":"35219a6f4974f9d478eb5fa5228b5d8ce507a86cfc6710a8e0264bcf4329a816"},"schema_version":"1.0"},"canonical_sha256":"e33cd60a6c70ea22cf5b99c1b6b10f85926bbd2150c4de2604ba83c1f87c3970","source":{"kind":"arxiv","id":"1104.2502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2502","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2502v1","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2502","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"pith_short_12","alias_value":"4M6NMCTMODVC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4M6NMCTMODVCFT23","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4M6NMCTM","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4M6NMCTMODVCFT23THA3NMIPQW","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-13T14:13:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"de12186a7539decaed1a2d4d1ec760f961aa1483737610c4463ce80128f16f8d","abstract_canon_sha256":"35219a6f4974f9d478eb5fa5228b5d8ce507a86cfc6710a8e0264bcf4329a816"},"schema_version":"1.0"},"canonical_sha256":"e33cd60a6c70ea22cf5b99c1b6b10f85926bbd2150c4de2604ba83c1f87c3970","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:34.728655Z","signature_b64":"/dIF8Z+jgLkdqNjexF3rEG8ucZQQBK8dwGrnnn+CW11LQM8umjc32YtQ6nDZyjkZqvlqyoewoEHHqeYYywarCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e33cd60a6c70ea22cf5b99c1b6b10f85926bbd2150c4de2604ba83c1f87c3970","last_reissued_at":"2026-05-18T04:24:34.728265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:34.728265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2502","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":"2026-05-18T04:24:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mShBAEdW/2zdhOE0qIcUK0zyV/NQ9J61s+i/pn6wjYDBpN0oM4pNuNFUnQ/xV3QSbQSPapQ2o1Ba1u22BMD+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T17:57:20.266272Z"},"content_sha256":"86320bd4858fc37b40eee4bee4b68e56ce1b06fda2180e1769042544c53ec37c","schema_version":"1.0","event_id":"sha256:86320bd4858fc37b40eee4bee4b68e56ce1b06fda2180e1769042544c53ec37c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4M6NMCTMODVCFT23THA3NMIPQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Parallel Approximation Algorithm for Positive Semidefinite Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Penghui Yao, Rahul Jain","submitted_at":"2011-04-13T14:13:02Z","abstract_excerpt":"Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel algorithm, which given an instance of a positive semidefinite program of size N and an approximation factor eps > 0, runs in (parallel) time poly(1/eps) \\cdot polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1 + eps) to the optimal. Our result generalizes analogous result of Luby and Nisan [1993] for positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2502","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":"2026-05-18T04:24:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pklXxLSviqxKRiedPO5+6TEHi+7MV+YOW0KxOJhbmCuAKul+frqeuNindqtpKKUoq4raDGYUKn0ArXT89XAiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T17:57:20.266786Z"},"content_sha256":"ad367de6d35c302c1f356bf186c31ef527b9d088b36804cc8d09277b645f7c15","schema_version":"1.0","event_id":"sha256:ad367de6d35c302c1f356bf186c31ef527b9d088b36804cc8d09277b645f7c15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4M6NMCTMODVCFT23THA3NMIPQW/bundle.json","state_url":"https://pith.science/pith/4M6NMCTMODVCFT23THA3NMIPQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4M6NMCTMODVCFT23THA3NMIPQW/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":"2026-05-21T17:57:20Z","links":{"resolver":"https://pith.science/pith/4M6NMCTMODVCFT23THA3NMIPQW","bundle":"https://pith.science/pith/4M6NMCTMODVCFT23THA3NMIPQW/bundle.json","state":"https://pith.science/pith/4M6NMCTMODVCFT23THA3NMIPQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4M6NMCTMODVCFT23THA3NMIPQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4M6NMCTMODVCFT23THA3NMIPQW","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":"35219a6f4974f9d478eb5fa5228b5d8ce507a86cfc6710a8e0264bcf4329a816","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-13T14:13:02Z","title_canon_sha256":"de12186a7539decaed1a2d4d1ec760f961aa1483737610c4463ce80128f16f8d"},"schema_version":"1.0","source":{"id":"1104.2502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2502","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2502v1","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2502","created_at":"2026-05-18T04:24:34Z"},{"alias_kind":"pith_short_12","alias_value":"4M6NMCTMODVC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4M6NMCTMODVCFT23","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4M6NMCTM","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:ad367de6d35c302c1f356bf186c31ef527b9d088b36804cc8d09277b645f7c15","target":"graph","created_at":"2026-05-18T04:24:34Z","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":"Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel algorithm, which given an instance of a positive semidefinite program of size N and an approximation factor eps > 0, runs in (parallel) time poly(1/eps) \\cdot polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1 + eps) to the optimal. Our result generalizes analogous result of Luby and Nisan [1993] for positiv","authors_text":"Penghui Yao, Rahul Jain","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-13T14:13:02Z","title":"A Parallel Approximation Algorithm for Positive Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2502","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":"sha256:86320bd4858fc37b40eee4bee4b68e56ce1b06fda2180e1769042544c53ec37c","target":"record","created_at":"2026-05-18T04:24:34Z","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":"35219a6f4974f9d478eb5fa5228b5d8ce507a86cfc6710a8e0264bcf4329a816","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-13T14:13:02Z","title_canon_sha256":"de12186a7539decaed1a2d4d1ec760f961aa1483737610c4463ce80128f16f8d"},"schema_version":"1.0","source":{"id":"1104.2502","kind":"arxiv","version":1}},"canonical_sha256":"e33cd60a6c70ea22cf5b99c1b6b10f85926bbd2150c4de2604ba83c1f87c3970","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e33cd60a6c70ea22cf5b99c1b6b10f85926bbd2150c4de2604ba83c1f87c3970","first_computed_at":"2026-05-18T04:24:34.728265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:34.728265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dIF8Z+jgLkdqNjexF3rEG8ucZQQBK8dwGrnnn+CW11LQM8umjc32YtQ6nDZyjkZqvlqyoewoEHHqeYYywarCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:34.728655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86320bd4858fc37b40eee4bee4b68e56ce1b06fda2180e1769042544c53ec37c","sha256:ad367de6d35c302c1f356bf186c31ef527b9d088b36804cc8d09277b645f7c15"],"state_sha256":"9340ae4daa04d5b7696bbaf5042134a6860b4ac6d1c2eb5d87ecb37d61369c8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOIClu31rWhWGi6PlfIunDdyPM/8Jg2+1IBr+j/km85GNct7lR2rumVf9hppFvCfTXfbTmsz4tEJ8QZ+TswSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T17:57:20.268965Z","bundle_sha256":"097b843cbb5865a2fe79243a64d37fa9b9ba8230c4832078bbe433ed9d6563d8"}}