{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GEWYGHCNESKXWQ2C4ZLII26ACA","short_pith_number":"pith:GEWYGHCN","canonical_record":{"source":{"id":"2101.06219","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-01-15T17:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"005d20fcb1ea13c7527e615296cccf6e800d7f724c5b9993517969f1c758f757","abstract_canon_sha256":"7bdd46dd5992d0e2334787115e2c210ace8933f633555e3162ae143975a289ef"},"schema_version":"1.0"},"canonical_sha256":"312d831c4d24957b4342e656846bc01020ec39514439ad0291de4743d5161b22","source":{"kind":"arxiv","id":"2101.06219","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.06219","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"arxiv_version","alias_value":"2101.06219v3","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.06219","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_12","alias_value":"GEWYGHCNESKX","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_16","alias_value":"GEWYGHCNESKXWQ2C","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_8","alias_value":"GEWYGHCN","created_at":"2026-07-05T05:36:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GEWYGHCNESKXWQ2C4ZLII26ACA","target":"record","payload":{"canonical_record":{"source":{"id":"2101.06219","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-01-15T17:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"005d20fcb1ea13c7527e615296cccf6e800d7f724c5b9993517969f1c758f757","abstract_canon_sha256":"7bdd46dd5992d0e2334787115e2c210ace8933f633555e3162ae143975a289ef"},"schema_version":"1.0"},"canonical_sha256":"312d831c4d24957b4342e656846bc01020ec39514439ad0291de4743d5161b22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:36:28.825496Z","signature_b64":"wDgRakySxbDP/6bxVaBLVLKBd25gEAO2N36xz/DW2knxsTq3aFTz6IhFJzPfUG/jthMmVW//siC8OwwVn7KGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"312d831c4d24957b4342e656846bc01020ec39514439ad0291de4743d5161b22","last_reissued_at":"2026-07-05T05:36:28.825048Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:36:28.825048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.06219","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":"2026-07-05T05:36:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lou2LCcrI9M61rz67bZrCnNiucUiyFfUK6peKqJ3Fwm4aSHiUUJMTVBGDFTlBJTCwo5TQyJOO/y0krdCPPm/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:02:29.953813Z"},"content_sha256":"c2b9d88916b74eebacce5cec46fb8a9d290194ebbca004476dea5b34919c46b6","schema_version":"1.0","event_id":"sha256:c2b9d88916b74eebacce5cec46fb8a9d290194ebbca004476dea5b34919c46b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GEWYGHCNESKXWQ2C4ZLII26ACA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Conic Reformulation of Structured QCQPs based on Copositive Optimization with Applications in Stochastic Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Markus Gabl","submitted_at":"2021-01-15T17:06:42Z","abstract_excerpt":"In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is similar to Burer's reformulation, but lifts the variables into a comparatively lower dimensional space. The reformulation rests on a generalization of the set-completely positive matrix cone. This cone can then be approximated via inner and outer approximations in order to obtain upper and lower bounds, which potentially close the optimality gap, and hence can giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.06219","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/2101.06219/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":"2026-07-05T05:36:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFPl0YGyldB7ag+0AqhMhLJ826DhtnA980gPM0QL4an6NU5cu2pwXAvKqaL47VMkCMeOgROUNEK8PEwKaW1UCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:02:29.954188Z"},"content_sha256":"5908968c686bed5fd4a993803220cab7f3c3450f655cd6197a56532768e021df","schema_version":"1.0","event_id":"sha256:5908968c686bed5fd4a993803220cab7f3c3450f655cd6197a56532768e021df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/bundle.json","state_url":"https://pith.science/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/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":"2026-07-06T19:02:29Z","links":{"resolver":"https://pith.science/pith/GEWYGHCNESKXWQ2C4ZLII26ACA","bundle":"https://pith.science/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/bundle.json","state":"https://pith.science/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEWYGHCNESKXWQ2C4ZLII26ACA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GEWYGHCNESKXWQ2C4ZLII26ACA","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":"7bdd46dd5992d0e2334787115e2c210ace8933f633555e3162ae143975a289ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-01-15T17:06:42Z","title_canon_sha256":"005d20fcb1ea13c7527e615296cccf6e800d7f724c5b9993517969f1c758f757"},"schema_version":"1.0","source":{"id":"2101.06219","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.06219","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"arxiv_version","alias_value":"2101.06219v3","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.06219","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_12","alias_value":"GEWYGHCNESKX","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_16","alias_value":"GEWYGHCNESKXWQ2C","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_8","alias_value":"GEWYGHCN","created_at":"2026-07-05T05:36:28Z"}],"graph_snapshots":[{"event_id":"sha256:5908968c686bed5fd4a993803220cab7f3c3450f655cd6197a56532768e021df","target":"graph","created_at":"2026-07-05T05:36:28Z","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/2101.06219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is similar to Burer's reformulation, but lifts the variables into a comparatively lower dimensional space. The reformulation rests on a generalization of the set-completely positive matrix cone. This cone can then be approximated via inner and outer approximations in order to obtain upper and lower bounds, which potentially close the optimality gap, and hence can giv","authors_text":"Markus Gabl","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-01-15T17:06:42Z","title":"Sparse Conic Reformulation of Structured QCQPs based on Copositive Optimization with Applications in Stochastic Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.06219","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:c2b9d88916b74eebacce5cec46fb8a9d290194ebbca004476dea5b34919c46b6","target":"record","created_at":"2026-07-05T05:36:28Z","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":"7bdd46dd5992d0e2334787115e2c210ace8933f633555e3162ae143975a289ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-01-15T17:06:42Z","title_canon_sha256":"005d20fcb1ea13c7527e615296cccf6e800d7f724c5b9993517969f1c758f757"},"schema_version":"1.0","source":{"id":"2101.06219","kind":"arxiv","version":3}},"canonical_sha256":"312d831c4d24957b4342e656846bc01020ec39514439ad0291de4743d5161b22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312d831c4d24957b4342e656846bc01020ec39514439ad0291de4743d5161b22","first_computed_at":"2026-07-05T05:36:28.825048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:36:28.825048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wDgRakySxbDP/6bxVaBLVLKBd25gEAO2N36xz/DW2knxsTq3aFTz6IhFJzPfUG/jthMmVW//siC8OwwVn7KGAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:36:28.825496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.06219","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2b9d88916b74eebacce5cec46fb8a9d290194ebbca004476dea5b34919c46b6","sha256:5908968c686bed5fd4a993803220cab7f3c3450f655cd6197a56532768e021df"],"state_sha256":"5ab02444b599aa4c535ec3d2ebd4a2331fdf167a73b6e4679774716ea1864857"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMQ8SjDWf7ePbieiSBX5UDKTx5Ra3575wMaUnh9WH5iCW2pP3aQUnmMK+bYie7EuIdBdGPtFW2vUQrCqOUG/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:02:29.956135Z","bundle_sha256":"3ac1d5b604e7a3d851a759be8acc824a3ff78040f47fb1847d12cb27ff5fd09a"}}