Relational-Sector Pregeometry: The Unknown Ground and the Emergence of Physical Structure

This work investigates the foundational problem of why the observable universe possesses its particular spacetime structure, gravitational interaction, matter content, and physical laws, rather than another possible configuration. The investigation introduces a deliberately minimal conceptual framework involving an unknown ground, denoted by S, whose manifestations are assumed to underlie the observable physical world. No intrinsic spatial, temporal, mathematical, informational, or dynamical properties are attributed to S. Mathematical structures are introduced only as candidate descriptions of manifested physics. The study examines the logical limits of deriving physical laws from minimal premises and develops several conditional mathematical approaches to the emergence and selection of physical structure. The principal topics include spacetime dimensionality, causal ordering, the distinction between geometric and non-geometric causal systems, gravitational universality, massless spin-2 dynamics, chiral matter, fermion-family multiplicity, compactification, and coupled physical sectors. A series of mathematical models is analysed, including cosmological fronts, compact spatial topology, tensor-field propagation, stochastic causal models, internal geometric dimensions, and symmetry-breaking mechanisms. Their mathematical consequences, physical consistency requirements, and limitations are examined. The investigation also derives and organises twenty families of model-dependent observable relations. These include quantitative spectral relationships, propagation effects, geometric correlations, coupling sum rules, and other potential experimental signatures. For each model, the underlying assumptions and possible tests are distinguished from conclusions supported by established observations. Computational reproducibility is supported by accompanying Python source code and numerical verification results. The study does not claim to establish the fundamental nature of S, to derive all observed physical laws from first principles, or to provide experimental confirmation of the proposed mechanisms. Its purpose is to develop a logically controlled mathematical research framework, identify viable and non-viable explanatory mechanisms, and formulate physically testable consequences for further investigation.