{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:42AOKYKTY5LQ2KX7ZUFEGRUC52","short_pith_number":"pith:42AOKYKT","canonical_record":{"source":{"id":"2509.18911","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-23T12:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"c2d0ec02dd2ba29786f1498a526c29f1cd05cebdcb65944cf2ae34cfea3f284e","abstract_canon_sha256":"e97a68eaa71aac1b2b2a327f805e40f42114be2de4e9924950e309cf11804788"},"schema_version":"1.0"},"canonical_sha256":"e680e56153c7570d2affcd0a434682eebabe5d7d46c7f62b7da954ed593e0c16","source":{"kind":"arxiv","id":"2509.18911","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.18911","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2509.18911v2","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.18911","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"42AOKYKTY5LQ","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"42AOKYKTY5LQ2KX7","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"42AOKYKT","created_at":"2026-06-09T01:05:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:42AOKYKTY5LQ2KX7ZUFEGRUC52","target":"record","payload":{"canonical_record":{"source":{"id":"2509.18911","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-23T12:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"c2d0ec02dd2ba29786f1498a526c29f1cd05cebdcb65944cf2ae34cfea3f284e","abstract_canon_sha256":"e97a68eaa71aac1b2b2a327f805e40f42114be2de4e9924950e309cf11804788"},"schema_version":"1.0"},"canonical_sha256":"e680e56153c7570d2affcd0a434682eebabe5d7d46c7f62b7da954ed593e0c16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:09.460713Z","signature_b64":"TFbFJA+7o8VdSfHT8K5eNuiGrcBX8DTldsQ4LCw0ULkAWoOgxIVMms4zTA/aoiU39pmFuMHmFBBdkRwfTngfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e680e56153c7570d2affcd0a434682eebabe5d7d46c7f62b7da954ed593e0c16","last_reissued_at":"2026-06-09T01:05:09.460240Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:09.460240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.18911","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":"2026-06-09T01:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VvehOM09sRfFYcKsu16jUbMBzFDZOWlvTJcMRCDp95IB0A4lKywZm28zlTFRoeli2JImgH/Tc08uPL1ptFJFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:01:51.853037Z"},"content_sha256":"c98ce35c81d180fab113fcf84e181eb1cb404c0c4ad99e5de25715815637b821","schema_version":"1.0","event_id":"sha256:c98ce35c81d180fab113fcf84e181eb1cb404c0c4ad99e5de25715815637b821"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:42AOKYKTY5LQ2KX7ZUFEGRUC52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Sparse Mixed-Integer Quadratic Problems: Application to the Unit Commitment Problem with Optimal Power Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bissan Ghaddar, Ignacio G\\'omez-Casares, Julio Gonz\\'alez-D\\'iaz, Pietro Belotti","submitted_at":"2025-09-23T12:33:34Z","abstract_excerpt":"Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQP) arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions interact with nonconvex quadratic constraints. These problems are computationally challenging due to the combination of combinatorial complexity and nonconvexity, often rendering traditional exact methods ineffective for large-scale instances. We propose a solution framework for sparse MIQCQPs that integrates semidefinite programming relaxations with chordal decomposition techniques to exploit sparsity. By leveraging pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.18911","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/2509.18911/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":"2026-06-09T01:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/99Ld6/AV4IWOF6i0bDQ8PdybJZLxoRMx2F5t6UDD6f6cwJP4KI3W7yp+KwwjTcczmMHlvEb1ctc3pXDQuiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:01:51.853834Z"},"content_sha256":"396fe7b8fc58590733a95455a4f005926f8078b052babb78c98dc345e14b4d8f","schema_version":"1.0","event_id":"sha256:396fe7b8fc58590733a95455a4f005926f8078b052babb78c98dc345e14b4d8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/bundle.json","state_url":"https://pith.science/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/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":"2026-06-10T12:01:51Z","links":{"resolver":"https://pith.science/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52","bundle":"https://pith.science/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/bundle.json","state":"https://pith.science/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42AOKYKTY5LQ2KX7ZUFEGRUC52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:42AOKYKTY5LQ2KX7ZUFEGRUC52","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":"e97a68eaa71aac1b2b2a327f805e40f42114be2de4e9924950e309cf11804788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-23T12:33:34Z","title_canon_sha256":"c2d0ec02dd2ba29786f1498a526c29f1cd05cebdcb65944cf2ae34cfea3f284e"},"schema_version":"1.0","source":{"id":"2509.18911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.18911","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2509.18911v2","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.18911","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"42AOKYKTY5LQ","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"42AOKYKTY5LQ2KX7","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"42AOKYKT","created_at":"2026-06-09T01:05:09Z"}],"graph_snapshots":[{"event_id":"sha256:396fe7b8fc58590733a95455a4f005926f8078b052babb78c98dc345e14b4d8f","target":"graph","created_at":"2026-06-09T01:05:09Z","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/2509.18911/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQP) arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions interact with nonconvex quadratic constraints. These problems are computationally challenging due to the combination of combinatorial complexity and nonconvexity, often rendering traditional exact methods ineffective for large-scale instances. We propose a solution framework for sparse MIQCQPs that integrates semidefinite programming relaxations with chordal decomposition techniques to exploit sparsity. By leveraging pr","authors_text":"Bissan Ghaddar, Ignacio G\\'omez-Casares, Julio Gonz\\'alez-D\\'iaz, Pietro Belotti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-23T12:33:34Z","title":"Solving Sparse Mixed-Integer Quadratic Problems: Application to the Unit Commitment Problem with Optimal Power Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.18911","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:c98ce35c81d180fab113fcf84e181eb1cb404c0c4ad99e5de25715815637b821","target":"record","created_at":"2026-06-09T01:05:09Z","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":"e97a68eaa71aac1b2b2a327f805e40f42114be2de4e9924950e309cf11804788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-23T12:33:34Z","title_canon_sha256":"c2d0ec02dd2ba29786f1498a526c29f1cd05cebdcb65944cf2ae34cfea3f284e"},"schema_version":"1.0","source":{"id":"2509.18911","kind":"arxiv","version":2}},"canonical_sha256":"e680e56153c7570d2affcd0a434682eebabe5d7d46c7f62b7da954ed593e0c16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e680e56153c7570d2affcd0a434682eebabe5d7d46c7f62b7da954ed593e0c16","first_computed_at":"2026-06-09T01:05:09.460240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:09.460240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFbFJA+7o8VdSfHT8K5eNuiGrcBX8DTldsQ4LCw0ULkAWoOgxIVMms4zTA/aoiU39pmFuMHmFBBdkRwfTngfAg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:09.460713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.18911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c98ce35c81d180fab113fcf84e181eb1cb404c0c4ad99e5de25715815637b821","sha256:396fe7b8fc58590733a95455a4f005926f8078b052babb78c98dc345e14b4d8f"],"state_sha256":"6f386a7737a52e154005488308319341db1a0130d6933322d573014f9caa80ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wT82+xy3YWLsCj8iPEarOf5m9jVti0TKoaFZYr8/XBN2sU7p6sBnRcLYLGe3/ErISG1P/QRfFZIF6mmhDlAJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:01:51.858456Z","bundle_sha256":"939880df203783866cdbff7332455fbbbce8192bbc3546e62dbd505860dbf92a"}}