<b>UTTU: Weaving Frequency Into Curvature: </b>An SI-Operational Closure That Converts Spectral Structure Into Geometric and Energetic Curvature, Certified by a Woven-Depth Invariant

UTTU (Universal Threaded Topology Unifier) turns clocks into rulers—and thermometers. It is an SI-operational framework that converts measured spectral structure on a chip into geometric curvature and energy density with instrument-grade fidelity. On a 1,999-point dataset, UTTU achieves R² = 0.9859 (correlation 0.9929), validates a horizon thermometer with K = 0.999781 ≈ 1, and certifies a woven-depth invariant of 0.599431 μm that remains constant under depth rescaling—creating a direct, SI-traceable bridge from time (frequency standards) to length. The method is plug-and-play: single-port spectra, precise gap control, lightweight preprocessing, and a preregistered replication protocol. Beyond the foundational result, a precision extension (“UTTU-2”) delivers decisive model-selection gains (ΔBIC ≈ −785). Practically, UTTU enables programmable-curvature devices, absolute thermometry from dynamics (no external calibration), and cross-platform calibration standards that align laboratories using different wave species. It is immediately implementable with today’s tools and establishes a clean path for species universality tests (e.g., TE/TM, acoustic), positioning frequency metrology as a primary route to geometry and energy on chip.