Which direction does the scatter point? A direction-lock census of published ferroelectric domain-wall tension and width records

Abstract

Published tensions σ and widths ξ of ferroelectric domain walls span more than an order of magnitude for nominally identical walls, usually reported by different methods under different model assumptions. We re-examine the record through a direction-lock statistic: within Ginzburg–Landau–Devonshire kinematics, any attribution difference between two reports of the same wall is a vector in the (Δ ln σ, Δ ln ξ) plane whose direction identifies its channel — slope +1 for the gradient coefficient κ (exact), −1/3 for the harmonic coefficient a, 0 for the quartic coefficient b, and vertical for width-definition bias. Auditing the literature yields seven wall-level records and twelve inter-report vectors. Ten lie within ±15° of an artifact axis; two fall in the inter-axis wedges, consistent with channel superposition; none lies on the kinematic +1 ray (95% upper bound 0.26), a result stable under bin-width variation and record-level resampling. The naive inter-report slope is Fieller-unstable, while the de-mixed estimator (X+3Y)/4 has noise amplification √10/4 ≈ 0.79. The record is thus dominated by attribution scatter, and independent (σ, ξ) pairs barely exist; we propose a paired-reporting standard. This Zenodo deposit contains the analysis script reproducing Tables 2–4 and Figure 1 of the associated manuscript.