System-Relative Dimensionality in Registration Theory

This paper is an addendum to The Canonical Foundations of Registration Theory, Version 1.0. It addresses a central unresolved question in the framework: if primitive physical registration is pre-geometric, how does conventional dimensionality become available to a particular physical system?

The paper distinguishes the underlying registration tensor from a system-specific awareness tensor, understood more generally as an awareness-resolution structure. The registration tensor represents physically available relational organization without presupposing an ordinary spacetime manifold. The awareness tensor describes how a particular registering system selects, weights, integrates, and preserves aspects of that organization. “Awareness” is used here in a general physical sense and does not require consciousness.

Effective dimensionality is proposed to arise through the constrained interaction of these two structures. Different systems may therefore resolve different effective degrees of freedom from the same underlying registration structure without arbitrarily creating different physical realities. A shared macroscopic geometry emerges when compatible systems repeatedly cross-register and stabilize mutually translatable dimensional resolutions. Familiar 3+1-dimensional Lorentzian spacetime is thereby interpreted as a robust intersystem registration result rather than an unexplained primitive container.

The paper introduces a preliminary mathematical framework for system-relative dimensional resolution, cross-registration maps, intersystem compatibility, and the reconstruction of an effective metric. It also explains how this proposal remains compatible with Version 1.0’s rejection of a single universal awareness tensor.

The proposed mechanism is presented as a constitutive extension and research program, not as a completed derivation of three spatial dimensions, Lorentzian signature, Lorentz symmetry, or the physical metric. The paper concludes with explicit theorem obligations, compatibility classifications, and criteria for possible falsifiable registration-resolution residuals.