URTD: Dynamics of the Uncertainty Boundary

This release replaces the original v1.0 manuscript and represents a major structural revision of the URTD paper within the Unified Recursion Theory (URT) program.

The paper develops the dynamical interpretation of the uncertainty boundary derived in the companion URTC work. Within URT, physical evolution is modeled as a sequence of admissible compressive recursion events acting on informational state structure. The URTC paper establishes that admissible recursion events must possess finite two-direction support in conjugate coordinates, producing a minimal symplectic recursion cell that corresponds empirically to the quantum action scale.

URTD extends this result by introducing recursion cadence, interpreting the minimal recursion event as a finite energetic–temporal support scale linking informational compression, thermodynamic bandwidth, and action. Under empirical correspondence with the quantum action constant, the uncertainty boundary emerges as the physical realization of the minimal admissible recursion event.

Version 2.1 introduces several improvements over the original v1.0 release:

• Structural reorganization of the derivation chain from distinguishability floor to action scale

• Explicit statement of the positive distinguishability floor proposition

• Separation of geometric constraint results (URTC) from dynamical interpretation (URTD)

• Clarification of the recursion cadence concept and minimal temporal support scale

• Expanded empirical analysis using IBM Quantum hardware datasets and a delay-controlled single-qubit experiment

• Clear scope discipline and falsification criteria

The empirical section identifies an observational hierarchy of operational and coherence timescales above the structural recursion cadence scale, consistent with the URT measurement-admissibility principle.

The manuscript also identifies the remaining mathematical closure of the program: proving that the minimal recursion action cell is invariant under admissibility-preserving canonical transformations.

URTD therefore provides the dynamical bridge between recursion admissibility, thermodynamic cadence, and the emergence of the uncertainty boundary within the URT framework.