{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OCRHX2FEHFSNL3E36LINFI6VYC","short_pith_number":"pith:OCRHX2FE","canonical_record":{"source":{"id":"1406.7274","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-27T19:18:21Z","cross_cats_sorted":[],"title_canon_sha256":"2d5c2d4ada30bb0bbcc511d650a62a35cb8377102b6e40003f44cda0b7e125b4","abstract_canon_sha256":"63ff0329db0a390c685c8f50ef26c7701fb73f6f070ca7660d5f3eff10bea79e"},"schema_version":"1.0"},"canonical_sha256":"70a27be8a43964d5ec9bf2d0d2a3d5c092fd7fe8a16d456ea86b08a1518ea8d2","source":{"kind":"arxiv","id":"1406.7274","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7274","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7274v3","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7274","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"OCRHX2FEHFSN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OCRHX2FEHFSNL3E3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OCRHX2FE","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OCRHX2FEHFSNL3E36LINFI6VYC","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7274","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-27T19:18:21Z","cross_cats_sorted":[],"title_canon_sha256":"2d5c2d4ada30bb0bbcc511d650a62a35cb8377102b6e40003f44cda0b7e125b4","abstract_canon_sha256":"63ff0329db0a390c685c8f50ef26c7701fb73f6f070ca7660d5f3eff10bea79e"},"schema_version":"1.0"},"canonical_sha256":"70a27be8a43964d5ec9bf2d0d2a3d5c092fd7fe8a16d456ea86b08a1518ea8d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:42.639180Z","signature_b64":"NU81NQ5p6/15nl++wJXnNcDTM07teYQfNnujfN0H2aD7jZyXwtQ5CJyrDcWagKe5QjVkDMUJ6wJvQkSD58RHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70a27be8a43964d5ec9bf2d0d2a3d5c092fd7fe8a16d456ea86b08a1518ea8d2","last_reissued_at":"2026-05-18T02:19:42.638720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:42.638720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7274","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":"2026-05-18T02:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYPGO0O7lkx7/YoyQkdvt/cwROmIByCs+bvnP+Rn5TgLpioQB269b0cdWhRmGKq3OAgREJ/zvwaWaFLmdNzaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:35:43.229299Z"},"content_sha256":"c90ff41b4e793f26ae2a4b855a1eebbb37c084de68fafca38065b8c3871c0e81","schema_version":"1.0","event_id":"sha256:c90ff41b4e793f26ae2a4b855a1eebbb37c084de68fafca38065b8c3871c0e81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OCRHX2FEHFSNL3E36LINFI6VYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact duality in semidefinite programming based on elementary reformulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabor Pataki, Minghui Liu","submitted_at":"2014-06-27T19:18:21Z","abstract_excerpt":"In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite system of the form Ai*X = bi (i=1,...,m) (P) X >= 0 using only elementary row operations, and rotations. When (P) is infeasible, the reformulated system is trivially infeasible. When (P) is feasible, the reformulated system has strong duality with its Lagrange dual for all objective functions.\n  As a corollary, we obtain algorithms to generate the constraints "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7274","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":""},"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":"2026-05-18T02:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N9SQ5ijHnmmNO/bJYiIybEWrYwd2vBP572WDzTrsBnrGLQU3i9gsaTZY+QmhJh41uXoGmGX9K//3FD8dUajjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:35:43.229983Z"},"content_sha256":"1d27aa3f8dd5732750a46f6c13ea12a7364ea0b064e87eea752e116d2495e53a","schema_version":"1.0","event_id":"sha256:1d27aa3f8dd5732750a46f6c13ea12a7364ea0b064e87eea752e116d2495e53a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OCRHX2FEHFSNL3E36LINFI6VYC/bundle.json","state_url":"https://pith.science/pith/OCRHX2FEHFSNL3E36LINFI6VYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OCRHX2FEHFSNL3E36LINFI6VYC/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":"2026-06-05T05:35:43Z","links":{"resolver":"https://pith.science/pith/OCRHX2FEHFSNL3E36LINFI6VYC","bundle":"https://pith.science/pith/OCRHX2FEHFSNL3E36LINFI6VYC/bundle.json","state":"https://pith.science/pith/OCRHX2FEHFSNL3E36LINFI6VYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OCRHX2FEHFSNL3E36LINFI6VYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OCRHX2FEHFSNL3E36LINFI6VYC","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":"63ff0329db0a390c685c8f50ef26c7701fb73f6f070ca7660d5f3eff10bea79e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-27T19:18:21Z","title_canon_sha256":"2d5c2d4ada30bb0bbcc511d650a62a35cb8377102b6e40003f44cda0b7e125b4"},"schema_version":"1.0","source":{"id":"1406.7274","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7274","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7274v3","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7274","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"OCRHX2FEHFSN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OCRHX2FEHFSNL3E3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OCRHX2FE","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:1d27aa3f8dd5732750a46f6c13ea12a7364ea0b064e87eea752e116d2495e53a","target":"graph","created_at":"2026-05-18T02:19:42Z","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":"In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite system of the form Ai*X = bi (i=1,...,m) (P) X >= 0 using only elementary row operations, and rotations. When (P) is infeasible, the reformulated system is trivially infeasible. When (P) is feasible, the reformulated system has strong duality with its Lagrange dual for all objective functions.\n  As a corollary, we obtain algorithms to generate the constraints ","authors_text":"Gabor Pataki, Minghui Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-27T19:18:21Z","title":"Exact duality in semidefinite programming based on elementary reformulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7274","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:c90ff41b4e793f26ae2a4b855a1eebbb37c084de68fafca38065b8c3871c0e81","target":"record","created_at":"2026-05-18T02:19:42Z","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":"63ff0329db0a390c685c8f50ef26c7701fb73f6f070ca7660d5f3eff10bea79e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-27T19:18:21Z","title_canon_sha256":"2d5c2d4ada30bb0bbcc511d650a62a35cb8377102b6e40003f44cda0b7e125b4"},"schema_version":"1.0","source":{"id":"1406.7274","kind":"arxiv","version":3}},"canonical_sha256":"70a27be8a43964d5ec9bf2d0d2a3d5c092fd7fe8a16d456ea86b08a1518ea8d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70a27be8a43964d5ec9bf2d0d2a3d5c092fd7fe8a16d456ea86b08a1518ea8d2","first_computed_at":"2026-05-18T02:19:42.638720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:42.638720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NU81NQ5p6/15nl++wJXnNcDTM07teYQfNnujfN0H2aD7jZyXwtQ5CJyrDcWagKe5QjVkDMUJ6wJvQkSD58RHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:42.639180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7274","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90ff41b4e793f26ae2a4b855a1eebbb37c084de68fafca38065b8c3871c0e81","sha256:1d27aa3f8dd5732750a46f6c13ea12a7364ea0b064e87eea752e116d2495e53a"],"state_sha256":"e4147e2cf09e42adfa3111aecbef24e78f0c4987e2cbd3163eb6469e01440c64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyzCGkz07LXvdWjplO26BziaUs4vMzhG8ttOmUTv1d+Q72ot74OSFQhS9P9TMYISKmTiXjwFRAs1v4hzKibfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:35:43.233605Z","bundle_sha256":"7f97371805a3aaef9cd661cc144533ed1a69a67cd5c7a3da6dab179979a927cf"}}