test: add POST-G shear initialization counterfactual

docs/validation/taylor_green.md

@@ -480,3 +480,31 @@ can support a descriptive timing contrast, but cannot establish a crossing
 or reflection coefficient. Changed-level probes must not be treated as
 collocated samples. `rho-1` remains raw density deviation; do not substitute
 the 24-probe mean for the global pressure gauge.
+
+### POST-G initialization counterfactual (`postg_shear_n128`)
+
+Exactly three fresh Re100 cases are admitted: U128, U512, and projected R128
+depth 3 with the original nested rectangles. Each requires `--flow shear_wave
+--diagnostic postg_shear_n128 --probe-trace`; snapshots and early-pressure mode
+are excluded. Geometry, physical velocity/density, viscosities, collisions,
+five main times and the 24 signed probes/windows are unchanged. Total work is
+2,952,265,728 active updates, with 15 main rows, 774 trace rows and five builds.
+
+Only initialization changes. At level spacing h, k_level = h k and
+A_i = 3 w_i U cos(theta) (c_i dot e) (c_i dot k_level). Initialize physical
+FP64 **POST G = feq - (tau - 1) A**, then use the existing shifted FP32 codec.
+This is the first-gradient, low-Mach Chapman-Enskog approximation, not an
+exact discrete eigenstate. The PRE coefficient is -tau; the physical viscous
+stress coefficient tau - 1/2 must not replace the raw POST-G coefficient.
+The correction has zero mass/momentum before encoding; FP32 introduces normal
+roundoff. U512 uses its native k and tau, matching nested L2 physical spacing.
+
+Receipts pin the new initializer module and identify `postg_first_gradient_v1`,
+with `qualification_eligible=false`. Existing scalar screens remain visible
+as descriptive outcomes, including failures; no new pass gate or assessor is
+introduced. Historical assessors reject the new diagnostic and initialization
+identities. Compare raw rows and signed traces with the retained equilibrium
+receipts as a startup-state counterfactual. The host first-interval pressure
+RMS reduction is not a prediction of long-time improvement, and individual
+probe errors can increase. All equilibrium paths and historical verdicts stay
+unchanged.