{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7SDLPG7IEC5WGPA6U76JKLT6A4","short_pith_number":"pith:7SDLPG7I","canonical_record":{"source":{"id":"2112.04256","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-12-08T12:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"1e193c75a40c0e1e18ae11640ef2d2a4fad2e6e0408d7e0fd7a2a53054206818","abstract_canon_sha256":"ee1a569e6c4b5292496ecd8f19247992cecdcb541b2d17baf375d6fc21d56cc6"},"schema_version":"1.0"},"canonical_sha256":"fc86b79be820bb633c1ea7fc952e7e072bd57db14881d65295aa291f35b5a2a2","source":{"kind":"arxiv","id":"2112.04256","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04256","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04256v2","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04256","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"7SDLPG7IEC5W","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"7SDLPG7IEC5WGPA6","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"7SDLPG7I","created_at":"2026-07-05T04:45:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7SDLPG7IEC5WGPA6U76JKLT6A4","target":"record","payload":{"canonical_record":{"source":{"id":"2112.04256","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-12-08T12:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"1e193c75a40c0e1e18ae11640ef2d2a4fad2e6e0408d7e0fd7a2a53054206818","abstract_canon_sha256":"ee1a569e6c4b5292496ecd8f19247992cecdcb541b2d17baf375d6fc21d56cc6"},"schema_version":"1.0"},"canonical_sha256":"fc86b79be820bb633c1ea7fc952e7e072bd57db14881d65295aa291f35b5a2a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:37.280037Z","signature_b64":"xAYSj+gXkgP6AVRpSkSawZ4NpI4k/RzxGm4c/8gFYQxspK6xrCjSH3Myr9DOPkftl8GiiYxulKMYQvbrrvQcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc86b79be820bb633c1ea7fc952e7e072bd57db14881d65295aa291f35b5a2a2","last_reissued_at":"2026-07-05T04:45:37.279630Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:37.279630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.04256","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":"2026-07-05T04:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfdpUN0kfUBk/TmwxuaghmpVT8f8IFxqu11bMvG9BEeiSMryV2VfzXwywRjs7lgI36JwfGZDDK1QZhmUXEj6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:25:33.655744Z"},"content_sha256":"da7eaba5881e80422d8439232c777e9e86fa52dcf53fdaa1610170b54ad8e41f","schema_version":"1.0","event_id":"sha256:da7eaba5881e80422d8439232c777e9e86fa52dcf53fdaa1610170b54ad8e41f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7SDLPG7IEC5WGPA6U76JKLT6A4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving graph equipartition SDPs on an algebraic variety","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Tianyun Tang","submitted_at":"2021-12-08T12:30:15Z","abstract_excerpt":"Semidefinite programs are generally challenging to solve due to their high dimensionality. Burer and Monteiro developed a non-convex approach to solve linear SDP problems by applying its low rank property. Their approach is fast because they used factorization to reduce the problem size. In this paper, we focus on solving the SDP relaxation of a graph equipartition problem, which involves an additional semidefinite upper bound constraint over the traditional linear SDP. By applying the factorization approach, we get a non-convex problem with an additional non-smooth spectral inequality constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04256","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.04256/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":"2026-07-05T04:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkH8AUITbM4gpbh3D1a6oqz5RQFAOC8GrxlCo69SyvYwHlmxVHZsKu9HY65jQ3AVP9YaDJAMMKrzduffzKdkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:25:33.658388Z"},"content_sha256":"6f1dc643a328d74297c7827f8dea1a58f34ee697149d1f4fb3de082cec7ec6b5","schema_version":"1.0","event_id":"sha256:6f1dc643a328d74297c7827f8dea1a58f34ee697149d1f4fb3de082cec7ec6b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/bundle.json","state_url":"https://pith.science/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/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":"2026-08-14T02:25:33Z","links":{"resolver":"https://pith.science/pith/7SDLPG7IEC5WGPA6U76JKLT6A4","bundle":"https://pith.science/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/bundle.json","state":"https://pith.science/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SDLPG7IEC5WGPA6U76JKLT6A4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7SDLPG7IEC5WGPA6U76JKLT6A4","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":"ee1a569e6c4b5292496ecd8f19247992cecdcb541b2d17baf375d6fc21d56cc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-12-08T12:30:15Z","title_canon_sha256":"1e193c75a40c0e1e18ae11640ef2d2a4fad2e6e0408d7e0fd7a2a53054206818"},"schema_version":"1.0","source":{"id":"2112.04256","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04256","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04256v2","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04256","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"7SDLPG7IEC5W","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"7SDLPG7IEC5WGPA6","created_at":"2026-07-05T04:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"7SDLPG7I","created_at":"2026-07-05T04:45:37Z"}],"graph_snapshots":[{"event_id":"sha256:6f1dc643a328d74297c7827f8dea1a58f34ee697149d1f4fb3de082cec7ec6b5","target":"graph","created_at":"2026-07-05T04:45:37Z","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/2112.04256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Semidefinite programs are generally challenging to solve due to their high dimensionality. Burer and Monteiro developed a non-convex approach to solve linear SDP problems by applying its low rank property. Their approach is fast because they used factorization to reduce the problem size. In this paper, we focus on solving the SDP relaxation of a graph equipartition problem, which involves an additional semidefinite upper bound constraint over the traditional linear SDP. By applying the factorization approach, we get a non-convex problem with an additional non-smooth spectral inequality constra","authors_text":"Kim-Chuan Toh, Tianyun Tang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-12-08T12:30:15Z","title":"Solving graph equipartition SDPs on an algebraic variety"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04256","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:da7eaba5881e80422d8439232c777e9e86fa52dcf53fdaa1610170b54ad8e41f","target":"record","created_at":"2026-07-05T04:45:37Z","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":"ee1a569e6c4b5292496ecd8f19247992cecdcb541b2d17baf375d6fc21d56cc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-12-08T12:30:15Z","title_canon_sha256":"1e193c75a40c0e1e18ae11640ef2d2a4fad2e6e0408d7e0fd7a2a53054206818"},"schema_version":"1.0","source":{"id":"2112.04256","kind":"arxiv","version":2}},"canonical_sha256":"fc86b79be820bb633c1ea7fc952e7e072bd57db14881d65295aa291f35b5a2a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc86b79be820bb633c1ea7fc952e7e072bd57db14881d65295aa291f35b5a2a2","first_computed_at":"2026-07-05T04:45:37.279630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:45:37.279630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xAYSj+gXkgP6AVRpSkSawZ4NpI4k/RzxGm4c/8gFYQxspK6xrCjSH3Myr9DOPkftl8GiiYxulKMYQvbrrvQcDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:45:37.280037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.04256","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7eaba5881e80422d8439232c777e9e86fa52dcf53fdaa1610170b54ad8e41f","sha256:6f1dc643a328d74297c7827f8dea1a58f34ee697149d1f4fb3de082cec7ec6b5"],"state_sha256":"37a8912b9528aa938bd4ff6847cc4916a80c2c1a220141aade5d039a5897d2ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQdp71shnZD4vkZLHaJK4xtC2Eb+/+evfhI6eMBUptGhaeVUVxI6Jjq78fgH5iodVyloCt0dYqObdRSth/U5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T02:25:33.667577Z","bundle_sha256":"ad68327fd330aad81e5c6e8d9b6e93509d26817b85e6e9b414b5c3932822c254"}}