An Exact Universal Bound and a Positive Power-System Reduction

For the dimension-independent constant
$C_p(m)=\sup_n\sup\|\sum_jA_j\|_p/\|\sum_j|A_j|\|_p$, we prove the
computer-assisted bound $C_{4/3}(2)\le(861/800)^{1/4}$. An exact rational
certificate excludes an entire parameter interval in a positive cubic system,
using 184 coefficient identities and 44 positive-definite Gram multipliers; the
eight-stage certificate chain behind the preceding bound $(43983/40000)^{1/4}$
is included as a proof dependency. We also give a positive power-system
characterization of $C_p(m)$ at every exponent $1<p<2$, prove two order
constraints on those systems, and derive improved interpolation bounds for two
summands. The exact function $C_p(m)$ is not determined. In particular, the
characterization is not an evaluation of the requested supremum, and no
construction matches the new upper bound.