{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7EMPI42SYAJE2QBV2WJP5LFQPP","short_pith_number":"pith:7EMPI42S","canonical_record":{"source":{"id":"1806.10868","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-28T10:28:27Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"cdbbd95bc111b2c6bb2fa9542f43326d77fcfd2e7361ced978eec140978aeafb","abstract_canon_sha256":"7ae60dce387f14642cea35d190626aaa042eab8b0552bab39305ecee11031441"},"schema_version":"1.0"},"canonical_sha256":"f918f47352c0124d4035d592feacb07bdef09e34fa2c843621fc56670a38e451","source":{"kind":"arxiv","id":"1806.10868","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10868","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10868v3","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10868","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_12","alias_value":"7EMPI42SYAJE","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_16","alias_value":"7EMPI42SYAJE2QBV","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_8","alias_value":"7EMPI42S","created_at":"2026-07-05T01:36:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7EMPI42SYAJE2QBV2WJP5LFQPP","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10868","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-28T10:28:27Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"cdbbd95bc111b2c6bb2fa9542f43326d77fcfd2e7361ced978eec140978aeafb","abstract_canon_sha256":"7ae60dce387f14642cea35d190626aaa042eab8b0552bab39305ecee11031441"},"schema_version":"1.0"},"canonical_sha256":"f918f47352c0124d4035d592feacb07bdef09e34fa2c843621fc56670a38e451","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:36:25.357484Z","signature_b64":"dY6ZkyxMio0ZXpj4kxZKyqiGT8rB2fFmaNUiKZF0bZ6/jqZ9TwM+rueAPXkZkLsyJuc0N+Rk485l4lrkkFVXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f918f47352c0124d4035d592feacb07bdef09e34fa2c843621fc56670a38e451","last_reissued_at":"2026-07-05T01:36:25.356862Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:36:25.356862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10868","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:36:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvhXzzeZhIeapB+tQgMYGmjucWPvZcYeGsQqlf/oOFjDQntDaZ1qb9l15fDaSvVolDxB2qMm1o3dtDspMdY+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:27:20.739874Z"},"content_sha256":"76cd3640c754d9500c34fa21a8f36891dc99e7cf2cdb54fbb70cae90c9339151","schema_version":"1.0","event_id":"sha256:76cd3640c754d9500c34fa21a8f36891dc99e7cf2cdb54fbb70cae90c9339151"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7EMPI42SYAJE2QBV2WJP5LFQPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Two-Step Pre-Processing for Semidefinite Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Jakub Marecek, Vyacheslav Kungurtsev","submitted_at":"2018-06-28T10:28:27Z","abstract_excerpt":"In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction, which reduces the dimension of the problem by removing redundant rows and columns. This paper suggest that these work in a complementary manner and that facial reduction should be used after chordal-completion procedures. In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10868","kind":"arxiv","version":3},"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/1806.10868/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":"2026-07-05T01:36:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1g135F5tBM6vJK6K5beep96U0+mAaSw25E3J6EaSzlf9tJ6lX3pVXjnwQ1coJsW4ztQazzoUfmnriH6wo2akBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:27:20.740786Z"},"content_sha256":"6a9016ebd6fbef3c605c2305a372b5d6d09100068b1d0f8806a879ba4f08a222","schema_version":"1.0","event_id":"sha256:6a9016ebd6fbef3c605c2305a372b5d6d09100068b1d0f8806a879ba4f08a222"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/bundle.json","state_url":"https://pith.science/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/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":"2026-08-15T19:27:20Z","links":{"resolver":"https://pith.science/pith/7EMPI42SYAJE2QBV2WJP5LFQPP","bundle":"https://pith.science/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/bundle.json","state":"https://pith.science/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EMPI42SYAJE2QBV2WJP5LFQPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7EMPI42SYAJE2QBV2WJP5LFQPP","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":"7ae60dce387f14642cea35d190626aaa042eab8b0552bab39305ecee11031441","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-28T10:28:27Z","title_canon_sha256":"cdbbd95bc111b2c6bb2fa9542f43326d77fcfd2e7361ced978eec140978aeafb"},"schema_version":"1.0","source":{"id":"1806.10868","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10868","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10868v3","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10868","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_12","alias_value":"7EMPI42SYAJE","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_16","alias_value":"7EMPI42SYAJE2QBV","created_at":"2026-07-05T01:36:25Z"},{"alias_kind":"pith_short_8","alias_value":"7EMPI42S","created_at":"2026-07-05T01:36:25Z"}],"graph_snapshots":[{"event_id":"sha256:6a9016ebd6fbef3c605c2305a372b5d6d09100068b1d0f8806a879ba4f08a222","target":"graph","created_at":"2026-07-05T01:36:25Z","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/1806.10868/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction, which reduces the dimension of the problem by removing redundant rows and columns. This paper suggest that these work in a complementary manner and that facial reduction should be used after chordal-completion procedures. In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic","authors_text":"Jakub Marecek, Vyacheslav Kungurtsev","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-28T10:28:27Z","title":"A Two-Step Pre-Processing for Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10868","kind":"arxiv","version":3},"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":"sha256:76cd3640c754d9500c34fa21a8f36891dc99e7cf2cdb54fbb70cae90c9339151","target":"record","created_at":"2026-07-05T01:36:25Z","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":"7ae60dce387f14642cea35d190626aaa042eab8b0552bab39305ecee11031441","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-28T10:28:27Z","title_canon_sha256":"cdbbd95bc111b2c6bb2fa9542f43326d77fcfd2e7361ced978eec140978aeafb"},"schema_version":"1.0","source":{"id":"1806.10868","kind":"arxiv","version":3}},"canonical_sha256":"f918f47352c0124d4035d592feacb07bdef09e34fa2c843621fc56670a38e451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f918f47352c0124d4035d592feacb07bdef09e34fa2c843621fc56670a38e451","first_computed_at":"2026-07-05T01:36:25.356862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:36:25.356862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dY6ZkyxMio0ZXpj4kxZKyqiGT8rB2fFmaNUiKZF0bZ6/jqZ9TwM+rueAPXkZkLsyJuc0N+Rk485l4lrkkFVXDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:36:25.357484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10868","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76cd3640c754d9500c34fa21a8f36891dc99e7cf2cdb54fbb70cae90c9339151","sha256:6a9016ebd6fbef3c605c2305a372b5d6d09100068b1d0f8806a879ba4f08a222"],"state_sha256":"40f281b9dce06c4005fcbdecc52da93e1fe7dce189ad6d7381106042dca0b78d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0PMdaVrS3SF7YExAFPdQX+JFHZcYQaASCacsjuIBlC5HAnvnm/zWHeYUpCU3qEXySBLauXUuAGEeii2LxJXpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T19:27:20.746170Z","bundle_sha256":"3239240708b00b801a126f838174e0b79b80256d8d84c85bc1bf15c0d15eaf9c"}}