spectralLoad_pos

In the Alpha Genesis module, inverse fine structure is defined forward from the EM recognition loop, before any comparison with measurement. The loop has three pieces: a channel budget $S=\Omega(\partial Q_3)\times E_{\mathrm{passive}}=4\pi\times 11$ (discrete Gauss-Bonnet curvature of the D=3 voxel boundary times passive edge count), a spectral load per channel, and a dressing weight from the T9 forced measure.

The spectral load is the gap weight $w_8$ (Parseval-normalized DFT-8 projection of the forced $\varphi$-pattern from M2/T6 self-similarity on the T7 eight-tick carrier) divided by that channel budget, in rung units. Both factors are already known positive: $w_8>0$ by a coarse rational-bound argument on the eight-tick formula, and $S>0$ by rewriting to $4\pi\times 11$ and positivity.

Positivity of the load is the domain hypothesis needed to evaluate any self-similar dressing response at that point.

One-line term proof. Unfold the definition spectralLoad = w8_from_eight_tick / channelBudget and apply div_pos to the two upstream positivity theorems w8_pos and channelBudget_pos. No further algebraic work.

Feeds the calibration theorem alphaInvGenesis_from_selfSimilar, which states that the forward α object equals $S\cdot D.g(w_8/S)$ for every self-similar dressing $D$. That proof applies the forced-response identity at the spectral load and therefore needs le_of_lt spectralLoad_pos to discharge the nonnegativity side condition.

In the broader Alpha Genesis story this is a tiny but mandatory positivity gate on the M3 loop certificate: without it the T9 dressing cannot be evaluated at the load, and the proved band $(137.030,137.039)$ cannot transfer from the forward object. It sits downstream of T6/T7 (φ-pattern and eight-tick) and T8 (D=3 cube theorems that fix the budget), and upstream of the no-fit claim that α⁻¹ is forced once the channel-budget bridge is granted.