URTD: Dynamics of the Uncertainty Boundary

This paper develops the URTD (Unified Recursion Theory Dynamics) extension of the uncertainty program. Building on the admissibility framework established in URTC, the work analyzes recursion cadence, recursion density, and the geometric structure of admissible recursion events. The analysis shows that compressive recursion events possess finite two-direction support and admit a minimal recursion cell in conjugate coordinates. This geometry yields a structural distinguishability constraint consistent with the uncertainty architecture of quantum theory.

Independent analysis of IBM superconducting-qubit scans (Fez and Marrakesh backends) reveals a layered observational structure above the minimal action scale. A retained-structure proxy derived from θ-sweep scans yields a stable median value χ ≈ 0.177 corresponding to a proxy action ratio R ≈ 15. Cadence analysis identifies a higher operational cadence floor near R ≈ 26 and a scheduling-scale estimator near R ≈ 187. These scales lie above the minimal quantum action bound R = 1, indicating that the minimal recursion event lies below the directly observable telemetry timescale of the current dataset.

The work therefore establishes a structural bridge between recursion geometry and the thermodynamic action scale while clarifying the observational limits of current quantum telemetry.