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This https://arxiv.org/abs/2501.03470 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positivstellensätze for polynomial matrices with universal quantifiers
This paper investigates Positivstellensätze for polynomial matrices subject to universally quantified polynomial matrix inequality constraints. We first establish a matrix-valued Positivstellensatz under the Archimedean condition, incorporating universal quantifiers. For scalar-valued polynomial objectives, we further develop a sparse Positivstellensatz that leverages correlative sparsity patterns within these quantified constraints. Moving beyond the Archimedean framework, we then derive a se…

Got a new phone, had an upgrade available. Best thing about it is USB-C. Finally moving away from lightning cables. The last one left in my arsenal is for my MagSafe Duo Charger.