Temporal Co-Orientation from Compact Scalar Phase: A Coframe-Reconstruction Criterion

This paper develops a conditional reconstruction theorem for emergent temporal structure within parent-response theories. A parent-selected compact scalar coherence channel provides a premetric phase co-orientation that precedes Lorentzian geometry and is subsequently promoted to the temporal leg of a reconstructed coframe. The work identifies the finite parent-response data required for this reconstruction—including scalar-channel selection, phase admissibility, normalization, coframe completion, and physical current-branch selection—and distinguishes premetric temporal ordering from post-reconstruction notions of causality and proper time. Although motivated by the Axis Model, the reconstruction criterion is formulated independently as a general differential-geometric interface between compact scalar coherence and emergent Lorentzian spacetime.