Geometric Theory of Gravity (GTG-DC): A Constitutive-Geometry Framework for Galaxy Dynamics, Gravitational Lensing, and Cosmology

Abstract

GTG-DC — Constitutive Geometry as a Parent Theory About This Publication This record presents the current form of GTG-DC (Geometric Theory of Gravity — Dynamical/Constitutive Geometry) — an effective theory in which ordinary, observable matter remains the material source of the gravitational field, while the additional response is attributed to the state of geometry itself. The central idea of GTG-DC is not to replace one acceleration law with another, nor to introduce an additional halo, a new form of matter, or a second physical metric. Instead, the theory assumes that an additional physical layer exists between the distribution of matter and the observed dynamics: baryonic matter → excitation of geometry → constitutive state of geometry → metric readout → motion of matter and gravitational lensing. It is precisely this intermediate layer that constitutes the proposed new physics of GTG-DC. In its most concise interpretation: baryons are the source, but geometry is not a passive carrier of the field. Geometry may possess its own response state, memory of excitation, saturation, environmental response, and directional field structure. At the conceptual level, this is analogous to the situation familiar from the electrodynamics of media, where the same source can produce different responses depending on the state of the medium. In GTG-DC, however, the responding system is spacetime geometry itself. Where Exactly Is the New Physics? The new physics of GTG-DC does not reside solely in the final RAR relation or in the baryonic Tully–Fisher relation. These relations emerge only after the full theory is reduced under additional assumptions such as isolation, stationarity, and radial symmetry. The full local construction contains several coupled elements: a baryonic carrier of the Newtonian field; a nonlinear local transmission channel; a saturation state of the geometric response; a retarded, causal memory sector; a geometric compensation sector; an environmental response defined as total minus self/target; full three-dimensional information about field direction and tidal structure; a common metric readout for matter dynamics and gravitational lensing. A key feature of the theory is that the local baryonic system and its environment are not simply represented as two forces that are added together. Instead, the environment changes the state of geometry in which the local response develops. Geometry may also retain a causal memory of previous excitation. This means that the present response does not have to be determined solely by the instantaneous local acceleration. As a result, two systems with similar local baryonic acceleration may — within the full GTG-DC framework — possess different geometric states because of differences in their environment, orientation, three-dimensional structure, tidal field, and excitation history. It is precisely in such systems that one should search for possible observational differences between the GTG-DC parent theory and its simpler reductions. Reduction to AQUAL-like Dynamics, RAR, the MOND-like Limit, and BTFR One of the central properties of GTG-DC is the existence of a controlled hierarchy of reductions. In the isolated and static limit, the local theory reduces to a nonlinear two-potential AQUAL-like system. After the additional imposition of radial symmetry, the possible ambiguity associated with the solenoidal component disappears, and an exact radial acceleration relation is obtained. In the deep low-acceleration regime, this relation approaches the characteristic MOND/AQUAL-like scaling. For a finite isolated baryonic mass and asymptotically circular motion, the same limit leads directly to the baryonic Tully–Fisher relation. The reduction hierarchy can therefore be written schematically as: GTG-DC → AQUAL-like dynamics → radial RAR → MOND-like limit → BTFR. GTG-DC, however, is not identified with RAR, MOND, AQUAL, or BTFR. These are reductive descendants of the theory. Each of these reductions removes part of the information present in the full parent state, including, to varying degrees, environmental dependence, memory, non-sphericity, field direction, tidal structure, and the complete metric readout. The full equations and mathematical derivations of these reductions are provided in the accompanying monograph and in the complete research repository. The Transition Function and the Meaning of the (4/3) Limit Earlier versions of the metric-readout sector used the (4/3) factor as a convenient weak-field approximation. In the current form of GTG-DC, it is not treated as a universal constant multiplier. Instead, it appears as the limiting value of a continuous transition function. At low accelerations, the additional geometric metric response is essentially unscreened, and the corresponding readout approaches the (4/3) limit. At high accelerations, the additional contribution is progressively screened, and the metric readout approaches unity, recovering the ordinary static weak-field Newtonian/GR sector. The most important physical interpretation is therefore: (4/3) is the weak-field limit of the unscreened metric response, not an additional universal coefficient applied to RAR, BTFR, or the dynamical acceleration. The exact form of the transition function, its derivation, its relationship to the metric potentials, and the explicit origin of the (4/3) limit are presented in the accompanying monograph. Cosmological Extension and the Friedmann Sector The present publication also includes an extended GTG-DC parent containing the previously developed cosmological sector. An important distinction must be maintained: the original local GTG-DC, by itself, was not a derivation of the Friedmann equations. The cosmological sector was subsequently embedded within a broader parent-theory architecture. In the homogeneous FLRW limit, the extended parent leads to a modified Friedmann background together with a conserved geometric component that, at the background level, scales like a pressureless component. Within GTG-DC, this component is interpreted as a geometric state/current rather than material dark matter. The extended architecture therefore contains two principal classes of branches: FLRW / cosmological branch → modified Friedmann dynamics → linear cosmology and formed local/static branch → GTG-DC → AQUAL-like → RAR → MOND-like limit → BTFR. These branches belong to the same extended parent architecture, but they should not be mixed by directly inserting cosmological background components into the local acceleration equations of galaxies. The complete Friedmann equations, their reconstruction, the geometric current, the perturbation kernel, and the relationship between the cosmological and local branches are presented in the monograph and in the accompanying research materials. What Does the Monograph Contain? The PDF “GTG-DC — Constitutive Geometry as a Parent Theory” is a concise, publication-oriented presentation of the current state of the theory. The monograph describes: the physical interpretation of GTG-DC; the architecture of the constitutive response of geometry; the complete equations of the local sector; transmission, memory, and compensation; environmental and three-dimensional structure; the metric readout for dynamics and gravitational lensing; the transition function and the origin of the weak-field (4/3) limit; the extended parent and the Friedmann sector; linear cosmology; the static weak-field GR/Newtonian limit; the relationship with AQUAL-like dynamics; the exact derivation of the radial RAR; the MOND-like limit; the derivation of BTFR; the domain of applicability, predictions, and falsification criteria. The equations are presented together with their assumptions and reduction conditions, preserving a clear distinction between the full parent theory and its simpler descendants. The monograph is intended primarily for readers who want to understand what the proposed new physics may mean, what GTG-DC currently is, how its physical mechanism is organised, and how its principal reductions arise, without having to reconstruct the entire multi-stage research programme. What Is Included in the Full Research Archive? The publication also includes an approximately 80 MB research repository containing the preserved development record of the current extended GTG-DC construction. It is not merely a collection of final equations. The archive includes, among other materials: original and corrected equations; complete derivations; formal JSON representations; reports from successive development stages; algebraic and numerical tests; supporting code; proof objects; manifests and SHA-256 checksums; records of corrections and results superseded by later versions; no-go analyses; development of the parent action; the transition to the CTP/in-in formalism; worldtube and ancestry constructions; formation-history analysis; derivations of the Friedmann sector; non-regression tests of the local reductions; documents showing why particular versions of the theory were accepted, rejected, corrected, or superseded. Earlier variants and negative results are intentionally preserved. This makes it possible not only to examine the final form of the theory, but also to independently reconstruct the process that led to the current construction and to follow the alternative possibilities considered along the way. Large external observational datasets and some external source repositories are not unnecessarily duplicated inside the main archive. Their provenance and identifiers are preserved in the corresponding provenance files. Why Download Both Files? The monograph answers the question: What is GTG-DC in its current form, and how does it work? The full research repo