Digit Curvature and the Non-Scalar Content of Measured Numbers We define a second-difference operator (Δ²) on the digit sequences ofreal numbers in arbitrary bases. We show that this operator discriminatesphysical and mathematical constants from noise (z = 4.87 in base 8),that the resolution landscape across bases has a single quiet point(base 13.038) where all tested constants simultaneously resolve, andthat the full geometric product of two Δ² vectors carries non-scalarcontent — grade-2 and grade-3 components that dominate the scalartension by orders of magnitude. We demonstrate that the resultingcoupling field exhibits standing-wave structure with an emergentincompressibility surface, correlates with CIE spectral fidelitymeasurements (r = +0.467, p < 0.05), and places water's refractiveindex at the field's nodal point. All claims are falsifiable. Allcomputations are deterministic and reproducible from digits alone. All claims are reproducible from the algorithm and publicly known digit expansions. No simulation data, curve fitting, or free parameters are involved.
Hammarsten et al. (2026) studied this question.