Barrier-Aware Merge Trees Reveal Ultrametric Organization in Nonlinear p-Spin Energy Landscapes: Code and Processed Data

This record contains the Python code, fixed random seeds, processed numerical results, validation tables, and publication figures accompanying the manuscript “Barrier-Aware Merge Trees Reveal Ultrametric Organization in Nonlinear p-Spin Energy Landscapes.” It includes results from 36 spherical  p=3  disorder realizations, matched spherical-null analyses, sampling-convergence and path-sensitivity tests, analytic geodesic validation, spherical-string calibration, a structure-preserving node-label permutation null, and processed metrics for the external Cambridge LJ13 transition-state-network benchmark. The raw Cambridge LJ13 archive is third-party material and is not redistributed in this record. Its official source and complete processing provenance are documented in the included THIRD_PARTY_DATA.md file.