{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YT5FKZUDXW2VBO5S63W6YZEKBT","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":"c92e5a753123796bec5a97a530b36cca2fcf61c24b3251ca88c5938c83258629","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T17:08:55Z","title_canon_sha256":"18ce7810fabf270330a1a0aae2f8771ccb66613bede46f320e9a903f9185a383"},"schema_version":"1.0","source":{"id":"2606.18173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18173","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18173v1","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18173","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_12","alias_value":"YT5FKZUDXW2V","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_16","alias_value":"YT5FKZUDXW2VBO5S","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_8","alias_value":"YT5FKZUD","created_at":"2026-06-19T16:10:50Z"}],"graph_snapshots":[{"event_id":"sha256:ddf071cdff3f3c966257d00da26a4292e04d234f66fc4ea08da6bc370bef91b1","target":"graph","created_at":"2026-06-19T16:10:50Z","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/2606.18173/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Loewner order on Hermitian matrices is a partial order that compares matrices in terms of positive semidefiniteness. The Loewner order plays a key role in many fields such as optimization, numerical linear algebra, control theory, operator theory, and quantum information. A fundamental difficulty is that two or more Hermitian matrices do not necessarily have a unique minimal upper bound (or maximal lower bound). In this paper, we propose an iterative method to exactly compute a minimal upper bound for any finite collection of $n\\times n$ Hermitian matrices. It is shown that the algorithm t","authors_text":"Adam Humeniuk, Gabriel Jarry-Bolduc, Nejaunie Williams, Patrick Pascua","cross_cats":["cs.NA","math.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T17:08:55Z","title":"An algorithm to exactly compute minimal upper bounds in the Loewner order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18173","kind":"arxiv","version":1},"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:b088b11b5b7dc0514a9f3a651bff68db9cb33c8f75523ac8bf51171b448fc53a","target":"record","created_at":"2026-06-19T16:10:50Z","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":"c92e5a753123796bec5a97a530b36cca2fcf61c24b3251ca88c5938c83258629","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T17:08:55Z","title_canon_sha256":"18ce7810fabf270330a1a0aae2f8771ccb66613bede46f320e9a903f9185a383"},"schema_version":"1.0","source":{"id":"2606.18173","kind":"arxiv","version":1}},"canonical_sha256":"c4fa556683bdb550bbb2f6edec648a0cd48cb4e09edeeeaceaf30b326e2a25de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4fa556683bdb550bbb2f6edec648a0cd48cb4e09edeeeaceaf30b326e2a25de","first_computed_at":"2026-06-19T16:10:50.249374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:50.249374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GmMHgmJ4aKU4T7iijvP0gCRci8j5zlgNWdxA8s4NUmhv22tevf8afO3ZA124hCkcvKpeBFrA//P3MTAN7rxxAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:50.249728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b088b11b5b7dc0514a9f3a651bff68db9cb33c8f75523ac8bf51171b448fc53a","sha256:ddf071cdff3f3c966257d00da26a4292e04d234f66fc4ea08da6bc370bef91b1"],"state_sha256":"4e1076bff7867c2a56c58216aff07d074620eb6824603902a60b6ac4be43a75d"}