The Watch Fit Geometry Framework — Axis 3: Strap Thickness as a Third Axis (Problem Statement and Open Constraint)

This paper formally establishes strap thickness as the third axis of the Watch Fit Geometry Framework. It defines the previously unnamed measurement lug clearance height (H), distinguishes between the attachability constraint (H₁ — spring bar clearance height) and the flush-wearing constraint (H₂ — lug tip clearance height), and proposes the provisional formula T ≤ H₂ as the Axis 3 constraint.

The paper identifies a material compliance factor for flexible strap materials, establishes the dependency of Axis 3 on Axis 1 (circumferential centering), and states four open problems that must be resolved before Axis 3 can be published as a complete empirically validated formula: an H₂ dataset, H₁/H₂ ratios by lug style, a material compliance allowance, and a strap thickness measurement standard.

The framework's fit vector remains [ (C − L − ΣK) ÷ 2 , (D − W) ÷ 2 ] pending resolution of Axis 3. This paper plants the flag — the territory is claimed, the measurement is named, and the path to resolution is mapped.

Related publications: DOI 10.5281/zenodo.20389138 (Axis 1 — Centering), DOI 10.5281/zenodo.20449108 (Axis 2 — Overhang), DOI 10.5281/zenodo.20496188 (Fit Vector), DOI 10.5281/zenodo.20449213 (Framework v2).