Proto-Field Gravity II: 3PN/4PN Conservative Dynamics and Binary Diagnostics

This paper extends the weak field analysis of the Proto-Field GravityModel (PFGM) to compact binaries. The effective geometry is givenby the rank one disformal update gμν = ημν + α ∂μΦ∂νΦ, posed in thecausal domain 1 + αX > 0 with X = ημν∂μΦ∂νΦ. All conservativepost-Newtonian (PN) coefficients coincide with general relativity (GR)through 2PN. The first departures appear dissipatively at 2.5PN (flux)and conservatively at 3PN/4PN. The 3PN/4PN sector is constructed fromminimal near zone sources S3 = U|∇U|2 and S4 = |∇U|4. Using a zeromean Poisson solver, inner zone subtraction, and finite radius/polytropesweeps, re-normalized coefficients Cren3,4 are extracted via R⋆ → 0 fits.Mapping the conservative series to gauge invariant diagnostics yields δK(x)and δz1(x) with the expected x3/x4 scaling; across pulsar and early inspiralbands the 4PN/3PN ratio remains ∼ x ≪ 1, ensuring predictability. Onthe dissipative side, the stationary phase approximation (SPA) introducesa leading v5 ln v (and v5) imprint normalized by α/M2, expressed in adata ready form. O3 inspiral posteriors for the 2.5PN–log deformationcoefficient already imply α ≲ 10–20km2 for binary neutron stars [48],with stronger bounds expected from the ongoing O4a catalog [49]. Allcodes, tables, and figures including the Poisson pipeline with zero moderemoval, interaction only ring averages, renormalization fits for Cren3,4 , andSPA summary panels are released for full reproducibility.