{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:W5YQCSIWRRKK7H75NRPDFBAG6A","short_pith_number":"pith:W5YQCSIW","canonical_record":{"source":{"id":"2211.00876","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-02T04:53:54Z","cross_cats_sorted":[],"title_canon_sha256":"c7417ba3fe86da46171dbe0bdc30758121fb33c833a547525c20a394fd55541e","abstract_canon_sha256":"7a7732c703fb5d0663280b5853f0dca504266664fc16364ae4bd2c021f586f10"},"schema_version":"1.0"},"canonical_sha256":"b7710149168c54af9ffd6c5e328406f023fa1c444b84d0b7c1ecfec7afcd98b5","source":{"kind":"arxiv","id":"2211.00876","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.00876","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"arxiv_version","alias_value":"2211.00876v3","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.00876","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_12","alias_value":"W5YQCSIWRRKK","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_16","alias_value":"W5YQCSIWRRKK7H75","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_8","alias_value":"W5YQCSIW","created_at":"2026-07-05T06:42:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:W5YQCSIWRRKK7H75NRPDFBAG6A","target":"record","payload":{"canonical_record":{"source":{"id":"2211.00876","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-02T04:53:54Z","cross_cats_sorted":[],"title_canon_sha256":"c7417ba3fe86da46171dbe0bdc30758121fb33c833a547525c20a394fd55541e","abstract_canon_sha256":"7a7732c703fb5d0663280b5853f0dca504266664fc16364ae4bd2c021f586f10"},"schema_version":"1.0"},"canonical_sha256":"b7710149168c54af9ffd6c5e328406f023fa1c444b84d0b7c1ecfec7afcd98b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:42:17.986630Z","signature_b64":"EY19AOuh8wOp/QHOa9a9HDqo3oMkklLYvO0dcMlXqKsjzRXa4I0wQPGVmRyrcUnE/6MSows5md3eVydxus1tAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7710149168c54af9ffd6c5e328406f023fa1c444b84d0b7c1ecfec7afcd98b5","last_reissued_at":"2026-07-05T06:42:17.986151Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:42:17.986151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.00876","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":"2026-07-05T06:42:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPhKjOBYRVtawjik8ijVEoYBLtezBYN5H4n+X8DqgV+UJ7l5vNZMgWb8pgNuFoSVaICHDIO51nsgz59JjWxdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:48:35.198867Z"},"content_sha256":"78c0a3cfc01b00350ef6ca103808533a72075d01bfce64b839c38d8ef4fd3640","schema_version":"1.0","event_id":"sha256:78c0a3cfc01b00350ef6ca103808533a72075d01bfce64b839c38d8ef4fd3640"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:W5YQCSIWRRKK7H75NRPDFBAG6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas B\\\"armann, Benjamin Beach, Lukas Hager, Robert Burlacu, Robert Hildebrand","submitted_at":"2022-11-02T04:53:54Z","abstract_excerpt":"We study mixed-integer programming (MIP) relaxation techniques for the solution of non convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for nonconvex quadratic products of the form z=xy, called hybrid separable (HybS). Additionally, we introduce a logarithmic MIP relaxation for univariate quadratic terms, called sawtooth relaxation. We combin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00876","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/2211.00876/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":"2026-07-05T06:42:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06KRqrWSQfNF3HIH9yEV2OZ1y7Iqmt2wfFbqqJo4m2BVRrGwF9lFUxRBQitILZCnkueQ6hOP73k4zBTzTYX+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:48:35.199447Z"},"content_sha256":"7d909ec00693bd1a39854527a58adf1aab903dee0625ad2e74f80558affd0a4d","schema_version":"1.0","event_id":"sha256:7d909ec00693bd1a39854527a58adf1aab903dee0625ad2e74f80558affd0a4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/bundle.json","state_url":"https://pith.science/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/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":"2026-08-03T18:48:35Z","links":{"resolver":"https://pith.science/pith/W5YQCSIWRRKK7H75NRPDFBAG6A","bundle":"https://pith.science/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/bundle.json","state":"https://pith.science/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5YQCSIWRRKK7H75NRPDFBAG6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:W5YQCSIWRRKK7H75NRPDFBAG6A","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":"7a7732c703fb5d0663280b5853f0dca504266664fc16364ae4bd2c021f586f10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-02T04:53:54Z","title_canon_sha256":"c7417ba3fe86da46171dbe0bdc30758121fb33c833a547525c20a394fd55541e"},"schema_version":"1.0","source":{"id":"2211.00876","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.00876","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"arxiv_version","alias_value":"2211.00876v3","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.00876","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_12","alias_value":"W5YQCSIWRRKK","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_16","alias_value":"W5YQCSIWRRKK7H75","created_at":"2026-07-05T06:42:17Z"},{"alias_kind":"pith_short_8","alias_value":"W5YQCSIW","created_at":"2026-07-05T06:42:17Z"}],"graph_snapshots":[{"event_id":"sha256:7d909ec00693bd1a39854527a58adf1aab903dee0625ad2e74f80558affd0a4d","target":"graph","created_at":"2026-07-05T06:42:17Z","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/2211.00876/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study mixed-integer programming (MIP) relaxation techniques for the solution of non convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for nonconvex quadratic products of the form z=xy, called hybrid separable (HybS). Additionally, we introduce a logarithmic MIP relaxation for univariate quadratic terms, called sawtooth relaxation. We combin","authors_text":"Andreas B\\\"armann, Benjamin Beach, Lukas Hager, Robert Burlacu, Robert Hildebrand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-02T04:53:54Z","title":"Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00876","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":"sha256:78c0a3cfc01b00350ef6ca103808533a72075d01bfce64b839c38d8ef4fd3640","target":"record","created_at":"2026-07-05T06:42:17Z","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":"7a7732c703fb5d0663280b5853f0dca504266664fc16364ae4bd2c021f586f10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-02T04:53:54Z","title_canon_sha256":"c7417ba3fe86da46171dbe0bdc30758121fb33c833a547525c20a394fd55541e"},"schema_version":"1.0","source":{"id":"2211.00876","kind":"arxiv","version":3}},"canonical_sha256":"b7710149168c54af9ffd6c5e328406f023fa1c444b84d0b7c1ecfec7afcd98b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7710149168c54af9ffd6c5e328406f023fa1c444b84d0b7c1ecfec7afcd98b5","first_computed_at":"2026-07-05T06:42:17.986151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:42:17.986151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EY19AOuh8wOp/QHOa9a9HDqo3oMkklLYvO0dcMlXqKsjzRXa4I0wQPGVmRyrcUnE/6MSows5md3eVydxus1tAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:42:17.986630Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.00876","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78c0a3cfc01b00350ef6ca103808533a72075d01bfce64b839c38d8ef4fd3640","sha256:7d909ec00693bd1a39854527a58adf1aab903dee0625ad2e74f80558affd0a4d"],"state_sha256":"d8b10a34136de43b4298bc9b9027a1615b7b2809245f18f118103a7c0a57d945"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nW0i5SVjLCCds+3tMuUCEH1ZU2SiRGGRFKyBpC4n1HXXoG6LqKHAwalBXVG/Jirvyw43YdBS9CRYBJQ8b8TGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:48:35.203579Z","bundle_sha256":"1694596c5858bcbb505f58a0fe697921f1614ce2a82e209e8db9faa6d122140d"}}