{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PAPBQFXBOMQABO63OF5FKR6YAU","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":"8bc6c08314a3eef1190e76e7ffcedf226dcebb69772184bab6be8cfe34f726b6","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-22T17:23:30Z","title_canon_sha256":"77216e28e9bdddfaf080cf1db4d7ff1ff4607225c531bceeb527bb5cf6dee398"},"schema_version":"1.0","source":{"id":"2606.23632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23632","created_at":"2026-06-23T03:14:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23632v1","created_at":"2026-06-23T03:14:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23632","created_at":"2026-06-23T03:14:32Z"},{"alias_kind":"pith_short_12","alias_value":"PAPBQFXBOMQA","created_at":"2026-06-23T03:14:32Z"},{"alias_kind":"pith_short_16","alias_value":"PAPBQFXBOMQABO63","created_at":"2026-06-23T03:14:32Z"},{"alias_kind":"pith_short_8","alias_value":"PAPBQFXB","created_at":"2026-06-23T03:14:32Z"}],"graph_snapshots":[{"event_id":"sha256:55b52b3278912c30edeb2a4f0a42865e118eb09b252850edf6a6594d36b1dbf8","target":"graph","created_at":"2026-06-23T03:14:32Z","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/2606.23632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study sharp inequalities for ratios of products of principal minors of real positive definite matrices. Our main result gives a closed-form solution to a family of nonconvex optimization problems over the positive definite cone. As a special case, we prove that the infimum of the Ingleton ratio over $4\\times 4$ positive definite matrices is $16/27$, confirming a conjecture of Hall and Johnson. We also show that the cone of absolutely bounded ratios of products of principal minors is not polyhedral for $n\\ge 4$, and that it is not semialgebraic over $\\mathbb{Q}$.","authors_text":"Ludovick Bouthat, Tobias Boege","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-22T17:23:30Z","title":"Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23632","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":"sha256:70e9fdc11cd01b7746e4fbf52a9045bcb5c3eb07a6768a4cf6e58773d823dfcc","target":"record","created_at":"2026-06-23T03:14:32Z","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":"8bc6c08314a3eef1190e76e7ffcedf226dcebb69772184bab6be8cfe34f726b6","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-22T17:23:30Z","title_canon_sha256":"77216e28e9bdddfaf080cf1db4d7ff1ff4607225c531bceeb527bb5cf6dee398"},"schema_version":"1.0","source":{"id":"2606.23632","kind":"arxiv","version":1}},"canonical_sha256":"781e1816e1732000bbdb717a5547d8052c211711cb0675740f86bfca26ba360d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"781e1816e1732000bbdb717a5547d8052c211711cb0675740f86bfca26ba360d","first_computed_at":"2026-06-23T03:14:32.850622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:32.850622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOwZt5RJRvt1rrn5ZLK61pH8jWdHI+Ra4HeA60fhRuNSG2JB7qE3Vn4/debn3byJWN5PZ6S0lydjeEL88fVcAg==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:32.851007Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70e9fdc11cd01b7746e4fbf52a9045bcb5c3eb07a6768a4cf6e58773d823dfcc","sha256:55b52b3278912c30edeb2a4f0a42865e118eb09b252850edf6a6594d36b1dbf8"],"state_sha256":"641b69f1ac341100feb4c5f63f1ca703bff427e5168045bdbbb326a57a651e77"}