Use direct momentum in opt-in shifted blocked equilibrium

docs/shifted_blocked_candidate.md

@@ -41,3 +41,21 @@ this is not full-solver validation. Host algebra/storage/remap tests and staged
 GPU continuation, three-grid cylinder physics, raw budgets, Couette helper
 stress and measured runtime are separate gates. Original failed experiments
 remain evidence; no acceptance threshold is relaxed.
+
+## Direct-input-momentum equilibrium candidate
+
+The shifted BlockStep now constructs the linear equilibrium term from input
+momentum j, without reconstructing rho*u. For opposite axis pairs the odd term
+is j/3; for diagonal pairs it is (jx +/- jy)/12, evaluated with explicit
+round-to-nearest division. The even term is
+w*[delta + 4.5*(c dot j)*(c dot u) - 1.5*(j dot u)].
+This is the same second-order D2Q9 equilibrium in exact arithmetic. Original SRT,
+storage, boundaries, and transfers are unchanged. No collision residual or force
+is corrected afterward. Existing four/five-argument equilibrium APIs are retained;
+only shifted blocked collision calls the new six-argument momentum helper.
+
+The all-fluid read-only CUDA replay reduced signed x-momentum error by 120–2285x
+at five sampled states, with lower mass/momentum and second-moment RMS errors.
+Signed mass bias was larger (~1e-12/cell/hop), so full evolving mass budgets remain
+mandatory. This local evidence does not establish physical convergence or speed.
+The unshifted default and its arithmetic path remain unchanged.