Absolute Relativity Conjecture (ARC): The Z-Scale Tensor and The Isochoric Morphology of the Universe

AbstractThe unification of General Relativity and quantum mechanics remains a central openproblem in fundamental physics. The perturbative non-renormalizability of gravity andunresolved conceptual issues concerning time, observation, and formal description suggestthat a deeper reformulation of the relation between geometry and physical law may berequired.The Absolute Relativity Conjecture (ARC) recognizes current physical laws as the besteffective description of perceived reality and is not formulated as an attempt to further refinethat description. Instead, ARC attempts to identify the underlying generative structure fromwhich reality can be reconstructed: not only the reality perceived by the observer, but alsothe reality inaccessible to that observer, both of which are essential for a coherent descriptionof reality as a whole.Motivated by a geometric reinterpretation of classical and contemporary physical de-scriptions, the ARC develops an observer-invariant framework in which both the observerand the observed Universe emerge as spatio-evolutive manifestations of a four-dimensionalgeometric Continuum governed by an isochoric and bijective law. These structures are notintroduced as fixed axioms, but as falsifiable hypotheses whose validity depends on their re-constructive capacity. The formalism introduces the Z-Scale Tensor, a non-linear finite-scaledescriptor that replaces infinitesimal differential descriptions with scale-dependent relationsdefined over finite domains, without assuming local linearity or morphologic evanescence inthe infinitesimal limit.Within this framework, a single admissible permanent geometric state is specified by amutually constrained set of geometric descriptors that operationally define the morphologicalqualities of spatial substance, evolutive rhythm, anatopicity, and anachronicity. Together,these geometric descriptors and morphological qualities serve as precursors to phenomeno-logically accessible physical properties and quantities. The Relativistic Elemental Particle(REP ) is introduced as a candidate finite four-dimensional domain whose admissible mor-phological states provide a common geometric basis for interpreting particle-like, thermo-dynamic, gravitational, and cosmological phenomenology.ARC is empirically constrained through candidate metrics whose finite-scale projec-tions generate calculated datasets DC (U, O) that can be compared with observed datasetsDX (U, O). It is therefore presented as a falsifiable geometric reconstruction framework, de-veloped to test whether a single isochoric spatio-evolutive law can reconstruct reality and tosubject its foundational geometric hypotheses to empirical validation through their recon-structive capacity. ARC is not contingent upon dedicated new experiments or observations,since the empirical record—both as presently available and as it continues to expand—constitutes a single joint reconstruction target whose complete empirically resolved content,at any specified finite level of precision, must be recovered within the calculated datasetDC (U, O), against which the framework is constrained and validated.The present work implements the first stages of this necessary metric refinement. Be-ginning with an observer-relative reinterpretation of the observed dataset DX (U, O), itprogressively constrains the admissible metric class toward the target of a single coherentcandidate geometry, obtains a first set of mutually connected and observationally recogniz-able consequences across otherwise distinct phenomenological domains—including regimeswhose common underlying interpretation remains open or fragmented across current physicaldescriptions—and defines a concrete path toward their progressively quantitative reconstruc-tion. These results constitute an initial, non-trivial validation of the ARC program at thestructural and qualitative phenomenological levels, without claiming the complete empiricalconvergence that remains its ultimate criterion.