Data and reproducibility files for "Statistical admissibility and long-wavelength structural convergence determine representative support in granular materials"

This dataset contains the image data, numerical material-property maps, statistical-admissibility masks, reference calculation outputs, manuscript figures, and software used in the study “Statistical admissibility and long-wavelength structural convergence determine representative support in granular materials”. The BSE archive contains seven full-resolution backscattered-electron images of Arabian dune-sand polished sections. These images support the identification of statistically admissible structural domains and the determination of representative support through persistent convergence of the apparent gray-level mean and the low-wavenumber covariance spectrum. The QEMSCAN archive contains numerical two-dimensional thermal-conductivity, Young’s-modulus, and Poisson-ratio maps derived from mineralogical classification. These maps preserve the physical values required for periodic thermal and elastic homogenization. Intensity-rescaled visualization images cannot substitute for these numerical inputs. The reference-output archive contains the statistical-admissibility masks, window-level diagnostics, structural statistics and spectra, property-homogenization results, uncertainty and parameter-sensitivity analyses, and execution logs. It also includes the assembled manuscript Figures 1–3, the scripts and plotting data used to generate them, and a complete software snapshot. Under the documented study protocol, the selected structural support has a side length of 1536 BSE pixels, corresponding to 2.01216 mm, assessed against a finite 2048-pixel reference. Physical validation uses a nominal support of 204 property-map pixels, corresponding to 2.04 mm. This nominal support is distinct from the exact calibration-based conversion of the structural length, which is 201.216 property-map pixels. The archive documents the sampling uncertainty of the structural selection. In 10,000 whole-image bootstrap draws, 33.10% yield no selected support; the percentile range reported for successful draws is conditional on selection. The results concern statistically admissible domains in two-dimensional sections. Thermal calculations describe in-plane conduction, and elastic calculations assume plane strain. Image-resolution convergence and three-dimensional bulk representativeness have not been established. The accompanying software supports user-provided collections of N two-dimensional images, with configurable inputs and analysis parameters. README_DATA.md explains the dataset organization, physical units, calibration, installation, and workflows for reproducing the calculations and assembling the manuscript figures. The software is maintained at https://github.com/Christian48596/representativeness-emerges, with the corresponding snapshot included in the reference-output archive.