Manuscript XVI-M@1 · XVI-M.tex · section · 7346c909

Time-only universal Helmholtz classification (work package C)

M.4 Contact collapse and Helmholtz conditions › Time-only universal Helmholtz classification (work package C) · lines 1256–1262

Back to manuscript

Everything in this subsection is relative to the current coherent presentation of M.2 (, , K block of dimension ); since Gate S-bv is certified (Theorem thm:wpA-Sbv), no (S-bv) condition remains. Gate V is unchanged: ; with on the diagonal and off it; symmetric lowered ; and are fixed under the variation, and their derivatives are retained in every integration by parts. The collapse is the single-switch collapse of Definition def:collapse, with , and there is no second . This subsection supplies the time-only analysis that Proposition prop:fixed-crit (time-only caveat) had left Unresolved.

Nearby in this section