physics.gen-ph

The weak-field, quasi-static regime of gravity is commonly described by the Newton–Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1–AX5 (including conservation) and standard DEC refinement, the Newton–Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency–wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source–potential relation characterized by a power-law kernel w ker ( k ) = 1 + C ( k 0 / k ) α in Fourier space. The kernel exponent α = 1 2 ( 1 − φ − 1 ) ≈ 0.191 , where φ = ( 1 + 5 ) / 2 , is derived from self-similarity of the discrete ledger closure; the amplitude C = φ − 2 ≈ 0.382 is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed M / L = 1 , no per-galaxy tuning, conservative σ tot ), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves median ( χ 2 / N ) = 3.06 over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening.