blochFold11_axisTTPlus_waveStar_ne_zero

The module studies the exact phase-decorated Bloch fold of the committed true-weight flat Hessian on type-(1,1) triangle hinges in one Kuhn cell, under the midpoint plane-wave convention. Scope is the (1,1) orbit only (72 oriented slots per cell). The fold sums transported slot terms over those slots for a given 4×4 probe matrix and wavevector.

The probe here is the axis TT plus polarization: the unnormalized matrix with sole nonzero entries $+1$ and $-1$ on the last two diagonal slots. The evaluation point is the star momentum $m^\star=(\pi/2,\pi/2,\pi/2,0)$, chosen so every midpoint phase is a natural multiple of $\pi/4$ and each slot term reduces to an integer combination of $1$ and $\sqrt{2}$.

An upstream closing theorem already evaluates the fold exactly at this point: it equals $-3$. The present claim records nonvacuity of that value.

One-line wrapper. Rewrite by the upstream closing evaluation that the fold equals $-3$, then apply norm_num to conclude $-3\neq 0$.

Module documentation lists this among the closing values for the (1,1) campaign: the axis-TT fold at $m^\star$ equals $-3$ (nonzero: nonvacuity), paired with the decoy-gauge fold equaling $-4+4\sqrt{2}$ (nonzero: discrete gauge invariance at finite momentum holds only up to the finite-difference identity). Together they certify that the finite-momentum symbol is nontrivial on the physical TT sector and is not killed by phase cancellation.

No downstream consumers are recorded yet; the result is a terminal nonvacuity gate inside the QG full-theory lane for the (1,1) orbit. It does not compare the $m^2$ Taylor coefficient to the Einstein–Hilbert TT continuum symbol, does not prove $S_{RS}$ converges to EH in 4d, and does not flip gap-action recovery.