Mass as Trans-Dimensional Binding: A Dimensional-Accessibility Account of Measurement, the Dark Sector, Space, and Time

This work develops a framework in which physical measurement is treated as a dimensional cross-section of reality rather than a complete registration of it. Two distinct operations are formalised: an observer of dimensionality n images an object of dimensionality x through the Visualization Function V(n,x) = max(0, min(n,x) − 1), and interacts with its mass through a separate Accessibility relation k ≤ min(n,x). Mass is modelled not as an intrinsic scalar but as a single conserved binding quantity distributed across a finite ladder of k-dimensional spaces. On this reading the dark sector is an accessibility class of ordinary mass — real and gravitating, but inaccessible to a three-dimensional observer — rather than a new substance. Space is generated as the join of one-dimensional energetic entities; the join of two skew lines spans exactly three dimensions, which is verified by rank computation and is the only claim in this work carrying the status of proof. The distribution of binding across the ladder is obtained from a bidirectional flow whose direction is set by local gravitational compactness: concentration dominates at high compactness, dispersion at low. The steady state of this flow is geometric rather than a power law, which supersedes the exponent that earlier formulations postulated and could not derive. Conservation of total binding fixes the direction of the primordial cascade as downward, from the dimensional ceiling toward k = 1, with a per-step transfer efficiency below unity. Two variants are examined: one with a single fitted transfer parameter, and one in which transfer is set entirely by hypersphere geometry and contains no free parameters. The parameter-free variant predicts a two-component dark-matter split of exactly 3 : 4 in the binding partition, corresponding to an observable energy-density ratio of 9 : 16, both following from the identity A₅/A₄ = 4/3. A parity property of the Gamma function identifies rungs 4 and 5 as the placement for which this ratio is rational at all. An exhaustive scan of 216 alternative label maps finds that only seven reproduce the observed cosmic energy budget, and that the assignment adopted is the unique best fit at the stated dimensional ceiling. Fifteen falsification criteria are stated, the framework's failure to reproduce horizon thermodynamics is declared explicitly, and one earlier formulation is documented as falsified by its own first confrontation with data.