We report the design, verification, and first preregistered results of P2, a momentum-conserving 3D particle-mesh (PM) testbed for entropy-modulated gravity — toy models in which the effective coupling Geff(x) is modulated by local entropy gradients and vorticity while the Poisson equation is retained. A Noether analysis of the simulation domain (an expanding 3-torus) shows that the conservation gates used by a predecessor programme were inverted with respect to the actual symmetries: linear momentum is exactly conserved for any expansion history and any coupling variant, whereas angular momentum is not symmetry-protected at all. The P2 engine implements matched cloud-in-cell deposition/interpolation with an antisymmetric spectral force kernel and a charge-picture treatment of spatially varying Geff, and passes a ten-test acceptance battery at machine precision, including exact momentum conservation under the active entropic coupling (residual ~2×10−13 over 600 steps) and recovery of the inverse-square law (fitted exponent −2.003). A box-doubling test with an identically embedded compact system adjudicates the predecessor programme's angular-momentum “gate passes” as numerically dominated. Finally, a preregistered, paired, 20-seed screen (plan SHA-256 hash committed before execution; 60/60 runs momentum-clean) finds that the entropic coupling variant F suppresses structure formation relative to standard gravity: power-spectrum band amplitudes fall by 22–31% and smoothed density variance by 20–24% (Wilcoxon p ≤ 2×10−4, Bonferroni-controlled), with a bounded variant showing the same signature at half the amplitude and the effect stable under timestep halving. These are properties of the toy models as operationally defined; no claim about physical gravitation or cosmology is made.
Malin Hess (Wed,) studied this question.