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checkable.

What the paper establishes

The study maps structural domains in LESCO using scanning 3D X-ray diffraction. The ~150 nm width is a reported structural scale at 300 K, not a NetPhysics measurement. The paper discusses possible consequences for coherence and local pathways; a direct local structure–electronic-response relationship remains to be tested.

This work adds spatial detail to an existing literature on cuprate heterogeneity. We do not describe it as the first evidence of inhomogeneity, a universal explanation of superconductivity, or validation of NetPhysics. Physical memory requires a separate history-controlled experiment.

Evie Ladbrook, Jon P. Wright and Mark S. Senn, “Giant Domain Walls and Intrinsic Heterogeneity in 214 Cuprate Superconductors,” Physical Review Letters 137, 126504 (2026). DOI: 10.1103/r62x-kt5j. CC BY 4.0. Extracted from published figure 2; temperature images are crops of panel (a). Original map colors and scale bars retained.

Published article · Author preprint · ESRF dataset record

Raw-data status, checked 21 October 2026

The DataCite record identifies collection on 19 July 2024 and gives 2027 as the publication/issued year. That metadata alone does not establish an embargo. Current raw-file access has not been confirmed; no raw ESRF data were downloaded or reprocessed for this release. The displayed maps are attributed figure crops, and the analyzer opens with synthetic data.

Archived DataCite metadata · Source and transformation record

Boundary lab: ordinary conduction

J = −σ ∇V
∇ · (σ ∇V) = 0
V(left) = 1; V(right) = 0
J · n = 0 at top and bottom
Grelative = total incoming current / all-host current

A square domain is divided into 64 × 64 cell-centered finite volumes. Host conductivity is 1; the selected band conductivity is the positive ratio you choose. Interior face conductance is the harmonic mean 2σ₁σ₂/(σ₁+σ₂). Half-cell distances at the left and right electrodes give conductance 2σ. A diagonally preconditioned conjugate-gradient solver uses a relative residual tolerance of 10⁻⁹ and a 1,200-iteration cap.

The exported calculation includes the grid, potential, current estimates, conductance, residual, current mismatch and dissipation check. Dissipation is Σ g(ΔV)²; at unit applied voltage it should match incoming current. Reported current directions are cell-centered averages of face currents.

The periodic synthetic geometry is defined in source code. Band direction is relative to x; width is a percentage of band spacing. Gap percentage removes segments along a repeating coordinate. Actual selected area is measured after rasterization and can differ from the nominal width fraction.

Analytic uniform, series-layer and parallel-layer cases test the solver. Conservation, potential bounds and monotonicity are also checked. A small residual measures solver convergence on this grid, not convergence to the continuum or fidelity to a material. Narrow bands and gaps remain resolution-sensitive.

No zero resistance, superconducting order parameter, pairing mechanism, magnetic field, temperature law, quantum phase coherence or calibrated LESCO conductivity is included.

Map analyzer: explicit definitions

The selected mask is |value| ≤ threshold. Area fraction counts selected cells. Components use four-neighbor connectivity (horizontal and vertical only). A spanning component must touch opposite image edges. The largest component’s orientation is the principal axis of its cell-center covariance, measured clockwise from image-right, modulo 180°. Orientation is omitted for fewer than three cells or a covariance anisotropy below 0.1.

A transect run is a consecutive sequence of selected cells along one chosen row or column. Its width is cell count × supplied pixel pitch. Runs touching either end of the line are marked truncated and excluded from the median. This is neither a fitted wall profile nor a normal-direction boundary width.

The synthetic map has 96 × 72 cells with values 0.007 tanh[1.2 sin((x + 0.28y)π/18)]. Its default 50 nm pitch is illustrative. The ±20% threshold analysis is sensitivity, not statistical uncertainty. Instrument resolution, point-spread function, projection effects and uncertain pixel calibration are not corrected.

Prediction workbench: compare at the specimen level

MSE(specimen, model) = mean of squared errors within that specimen
RMSE(model) = sqrt(mean of specimen MSEs)
Candidate improvement (%) = 100 × [1 − RMSE(candidate) / RMSE(reference)]

All models use the same test observations. Training rows are ignored for scoring, and a specimen ID appearing in both splits is rejected. Equal specimen weighting prevents repeated observations on one specimen from increasing its weight. This does not prove that different identifiers represent independent samples.

Uncertainty uses 1,000 paired bootstrap resamples of whole specimens, with the same draws for every model; seed 20261021. The displayed interval is the 2.5th–97.5th percentile of improvement. Intervals are omitted with fewer than three specimens or when fewer than 95% of draws have a positive reference error. Fewer than ten specimens triggers a small-sample warning. A zero reference RMSE makes percentage improvement undefined.

Intervals omit measurement error, calibration uncertainty and model-selection uncertainty. They do not establish prospective validation or correct data leakage in how predictions were generated. There is no automatic scientific pass/fail decision. Use a strong conventional rival, record prediction freezing independently, and publish all preregistered comparisons.

Reproducibility and local processing

CSV files are parsed and calculated in the browser. The tools do not upload their contents. Existing site analytics still applies to visits. JSON exports include software version, settings and results; input SHA-256 is included when the browser’s secure-context crypto API is available. A hash identifies bytes, not when predictions were made.

Download calculation and media source · Calculation verification record · Reproduction instructions

Original NetPhysics illustrations are labeled conceptual. The published figure crops retain their scientific scale bars and colors, with CC BY attribution. No endorsement or collaboration by the authors, Warwick, ESRF or APS is implied.