Declarations

status. The claims of this manuscript are the displayed theorems on their specified domains. Standard functional-analysis inputs are cited. No unprovided result from a companion manuscript is a theorem premise.

. The finite examples and refinements are existence constructions. No hardware efficiency, energy-cost, bounded-degree continuum architecture, uniform block-cardinality bound, or arbitrary gate-library compilation theorem is claimed.

. No successful pdflatex execution, proof-assistant verification, executed numerical check, independent referee certification, journal acceptance, or laboratory implementation is asserted. The source has an internal bibliography and requires no external figures, bibliography file, or shell escape.

. No external funding is reported for this manuscript.