MID/QC Foundation Series 8 - The Substrate Geometry Primitives: Polarity, Coherence, and Torsion

This paper introduces the substrate geometry primitives—polarity, coherence, and torsion—as the minimal geometric degrees of freedom required to describe MID/QC substrates. Rather than treating fields, particles, or forces as fundamental, the framework anchors dynamics in how a substrate can be oriented, aligned, and twisted relative to its own internal reference structure. Polarity captures directional asymmetry across a substrate, defining how “sidedness” and sign structure emerge from geometry rather than being imposed as external labels. Coherence formalizes the degree to which local substrate elements share a common geometric phase, providing a native measure of alignment that underwrites interference, pattern formation, and information-bearing structure. Torsion encodes how substrate elements can twist through and around one another, enabling chiral, helical, and rotational behaviors without invoking separate force laws. Together, these primitives define a compact, substrate-native basis for constructing MID/QC models across scales. The paper situates polarity, coherence, and torsion within the broader MID/QC lexicon, clarifies their relationships to familiar physical quantities, and outlines how they propagate into applied arcs, including thermal, mechanical, electromagnetic, and device-level engineering. By fixing these primitives early and explicitly, the work provides a stable geometric backbone for subsequent MID/QC papers and protects the conceptual provenance of substrate-native modeling.