About this Monograph This monograph presents Geometric Theory of Gravity 3. 5 as a canonically specified effective phenomenological theory for weak-field and quasistatic gravitational systems. GTG 3. 5 investigates whether part of the observed departure from purely Newtonian galactic dynamics can arise from a constitutive, compensating response of geometry itself together with the physically non-isolated character of real gravitational systems. The response introduced by GTG 3. 5 is not interpreted as additional matter, a fitted dark-matter halo, or a separate force. The theory reconstructs one physical scalar potential coupled to matter through a conditional weak-field one-metric ansatz. Its predictions are calculated from observationally reconstructed baryonic source models, a declared parent domain, fixed global parameters, boundary conditions, and an explicitly defined environmental sector. A particularly important property of GTG 3. 5 is that several well-known gravitational regularities appear as specific reductions or limiting regimes of the theory rather than as independent input laws. Under the assumptions of radial flux balance, the local sector gives the exact radial acceleration relation gₗoc = gN / 1 − exp (−sqrt (gN/a₀) ). In the deep-acceleration regime this relation produces the MOND-like scaling gₗoc² ≃ a₀ gN and, in the exterior radial limit of a finite baryonic mass, the baryonic Tully–Fisher normalization vc⁴ → G Mb a₀. At high accelerations the local solution approaches the Newtonian field exponentially. The theory also admits a conditional weak-field, static scalar metric sector with zero scalar slip and the standard leading one-metric lensing expression. This is compatible with the corresponding static weak-field limit of general relativity, but it is not presented as a derivation of full GR, full PPN, gravitational waves, strong-field dynamics, or Kerr geometry. The observational results reported in the monograph are preliminary but interesting. The main internal sample contained 30 high-quality, bulgeless SPARC galaxies and 504 accepted rotation-curve points. The calculation used a fixed acceleration scale and no galaxy-dependent parameters of the gravitational law. GTG 3. 5 obtained an RMSE of 20. 670 km/s, compared with 52. 289 km/s for the baryonic Newtonian model and 19. 611 km/s for the algebraic RAR benchmark. It performed better than the baryonic Newtonian prediction in 29 of the 30 galaxies. A separate holdout sample contained 15 galaxies and 319 points. GTG 3. 5 obtained an RMSE of 18. 620 km/s, compared with 49. 058 km/s for the baryonic Newtonian model and 17. 592 km/s for the algebraic RAR. It performed better than the baryonic Newtonian prediction in 14 of the 15 holdout galaxies. The small difference relative to the algebraic RAR may be interpreted as the cost of enforcing a globally integrable three-dimensional potential instead of applying a purely local algebraic acceleration map. One of the most notable results is the practically zero signed velocity bias. The bias was −0. 363 km/s in the main sample, +0. 364 km/s in the independent holdout, and −0. 081 km/s for the combined set of 45 galaxies and 823 points. This means that GTG 3. 5 does not show a significant global tendency to systematically overpredict or underpredict the velocity scale of the tested population. A near-zero bias does not, however, imply a small pointwise error or a completed empirical validation. The remaining residuals are structured: on average, the model tends to be too low in the inner regions and too high in the outer regions. The formal marginalized likelihood tests have not yet passed their preregistered thresholds. The current results therefore suggest that the global normalization may be close to the required level, while the detailed radial shape remains sensitive to source reconstruction, geometry, environment, or the phenomenological response law. The monograph distinguishes two levels of parameter treatment. Level 1 consists of observational and astrophysical nuisance parameters that determine the reconstruction of the baryonic source rather than the gravitational law itself. These include distance, inclination, radially varying stellar mass-to-light ratio, HI and H2 distributions, three-dimensional disk geometry, warps, non-circular motions, dust effects on the reconstructed light distribution, and baryonic masses and distances of neighbouring systems. These quantities may be marginalized using independent observational priors. Level-1 improvements can materially change the calculated field because GTG 3. 5 is sourced directly by the reconstructed three-dimensional distribution of baryonic matter. A partial marginalization over distance, inclination, and stellar mass-to-light ratio already reduced the reported statistic from χ²/N = 82. 47 to χ²MAP/Nₑff = 9. 718. This demonstrates substantial sensitivity to source quality, although it does not guarantee that more accurate data will remove all residuals. Any improvement must result from independently measured maps and priors rather than from fitting the gravitational law separately to each galaxy. Level 2 would mean a global calibration of one or a small number of universal hyperparameters of the theory, common to the entire population. It would not permit separate values of a₀, separate environmental amplitudes, or separate transmission-law shapes for individual galaxies. Any Level-2 calibration would have to be performed once on a training sample and then followed by a new, genuinely blind holdout test. The observational results presented in this monograph were obtained without using an additional Level-2 optimization of the theory against the reported galaxy samples. The global law and its active parameters remained frozen. This leaves open the possibility of testing whether a single universal recalibration could improve the population-level results, but such a step would require strict preregistration and independent validation. The accompanying canonical JSON repository and implementation-oriented files make the framework reproducible and suitable for further independent testing. They contain the active equations, global parameters, parent–child domain contract, environmental kernel, theorem registry, numerical workflow, validation rules, and the status of all claims. On this basis, researchers and developers can implement additional tests, including non-spherical three-dimensional systems, alternative baryonic source reconstructions, convergence studies, environmental reruns, radial and non-radial flux tests, lensing calculations, Solar-System weak-field checks, and new blind galaxy samples. GTG 3. 5 should therefore be understood as a falsifiable and mathematically specified quasistatic phenomenological theory with nontrivial exact reductions, promising but not conclusive observational results, and a clear path toward stronger tests. It does not yet constitute a complete fundamental or covariant theory of gravity, but it provides a concrete framework in which RAR, MOND-like behaviour, BTFR, and the static weak-field Newtonian/GR regime arise from different limits of one broader gravitational mechanism.
Maciej Mróz (Sun,) studied this question.