### AbstractCoordinate Density Field Theory (CDFT) encodes the static gravitational sector and homogeneous cosmology in a single dimensionless field φ (x) defined on a Minkowski reference, with operational intervalsds²ₚhys = e^-2φ c² dt² − e^+2φ dx². For sourcing/variation only, matter couples universally to g̃⏛⏜ = e^+2φ η⏛⏜, yielding the trace-sourced equationβ □φ + dV/dφ = T with β = c⁴/ (4πG) > 0 on a vacuum-subtracted, flat-minimum (Yukawa-free) weak-field branch. The weak-field expansion gives γPPN = βPPN = 1 in the static isotropic sector. In the baseline non-spinning exponential exterior, the photon-ring (shadow) diameter is a +4. 6% benchmark relative to Schwarzschild at fixed (M, D), and in the adopted compact-object construction an absorbing boundary at rₕ = 2GM/c² implies no long-lived echoes. Assuming the static interior depends only on the relative compression Δφ = φ − φ_∞ (i. e. invariance under constant background shifts), compact-object sensitivities vanish (sA = 0), eliminating scalar dipole radiation; the leading scalar channel is quadrupolar and is suppressed relative to GR by EOS/trace and wave-zone factors. Cosmologically, a Λ-free FRW branch admits late-time acceleration as a boundary-fixed integration mode in H (a) ; for late-time sub-horizon checks we provide a GR-emulator dictionary under explicit dust/no-slip/Poisson closures. Galaxy phenomenology is implemented via a phenomenological one-scale μ-law with the FRW-fixed a₀ (z) = cH (z) / (2π) and is confronted with SPARC/BTFR/RAR catalog-level tests. A uniform local-domain offset φₗoc rescales ladder distances, producing an apparent H₀ split without changing the global H (z). ### Files- `CDFT. pdf` — compiled preprint- `CDFTₛourceᵥ1. zip` — LaTeX source + prebuilt bibliography (`CDFT. bbl`) + README ### Build (source ZIP) This source package compiles without running BibTeX (the bibliography is included as `CDFT. bbl`). Run: - `pdflatex CDFT. tex` (twice; a third time only if LaTeX asks to rerun for cross-references) ### Keywordsgravitation; alternative theories of gravity; quantum gravity; scalar field; cosmology; compact objects; post-Newtonian tests ### How to citeAwdhoot, T. (2026). *Coordinate Density Field Theory (CDFT): A Split-Metric Scalar Compression Framework for Gravity* (Version v1). Zenodo. https: //doi. org/10. 5281/zenodo. 18624273
Tushar Awdhoot (Thu,) studied this question.