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

The Absolute Relativity Conjecture (ARC) formulates the observed Universe as a Fun-damental Inverse Problem. The Observer (O) and the Universe (U ) arise as spatio-evolutivemanifestations of a single four-dimensional Continuum governed by an isochoric and bijec-tive law. Its admissible finite-scale deformations are described by the Z-Scale Tensor andsubject to the isochoric admissibility condition det(Z) = 1. Isochoricity makes any spatialdeformation inseparable from its Evolutive and mixed spatio-evolutive counterparts, so phe-nomena conventionally treated as independent become mutually constrained manifestationsof one common geometry.ARC reconstructs candidate geometries whose calculated datasets DC (U, O) must con-verge toward observed datasets DX (U, O). Prediction arises when a geometry constrainedby one subset of the observational dataset determines phenomenology withheld from thatreconstruction; unification is therefore defined as reciprocal reconstructibility under a com-mon identifiable admissible geometry. Successful reconstruction necessarily preserves estab-lished empirical results by reproducing them within DC (U, O); validation need not awaitnew phenomenology, because known observations withheld from the reconstruction can in-dependently test new predictions about the underlying geometric nature of already observedphenomena, including dark-matter-like and dark-energy-like regimes, while newly observedphenomena provide additional independent tests.A spherical and cyclic Elementary Absolute Relativistic Particle (EARP) provides a con-crete candidate realization. Under progressive reconstruction, the same morphology is in-dependently constrained by particle, gravitational, electromagnetic, dark-regime, compact-object, and statistical phenomenology. For unresolved EARP populations, each repetition ofan experiment corresponds to a definite absolute spatio-evolutive configuration that is gen-erally not reproduced across observer-equivalent repetitions; the resulting ensemble there-fore manifests observer-relative statistical outcomes, whose calculated distributions mustconverge toward the corresponding observed distributions. ARC is falsified if increasinglyprecise and diverse independent datasets persistently require mutually incompatible geome-tries, preventing reciprocal reconstruction under one common admissible geometry withoutsectorial ad hoc prescriptions.