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Foundational Analysis Of The Solvability Complexity Index: The Weihrauch-SCI Intermediate Hierarchy
Announce Type: replace-cross Abstract: The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map $\Xi$ from finite samples of an evaluation interface $\Lambda\subseteq\mathbb C^\Omega$ by finite-height towers of pointwise limits. We first give a foundational analysis of what this extensional framework does and does not determine. We show that the SCI separation axiom is equivalent to a factorization of $\Xi$ through the full evaluation...