Boundary-Condition Quantum Mechanics VII_c - Technical Note: Knee contour sweeps for the Stage–2 cloth and an operational lock contour

This record contains BCQM VII_c (Technical Note). It extends the BCQM VII cloth programme and the BCQM VII_b knee/metastability study by mapping Stage-3 finite-N crossover contours for the Stage-2 cloth. What this technical note does Defines a cloth order parameter Phi = N_core / N_total (core fraction of the cloth). For each coherence value n, estimates the knee location Nk(n) where Phi crosses 0.5. Records an operational ordering/lock contour Nl(n) defined as the first tested N where the low-Q tail probability p_lowQ = Pr(Q_clock < 3) falls to <= 0.05 (where this is reached within the tested N grids). Method summary Uses a bracket-then-refine sweep protocol: 10 seeds for bracketing runs 20 seeds for refinement runs Standard Stage-2 cloth settings (bins=20, hits1 extraction, W_coh=100, Path A space-on with w*=0.30). Produces consolidated CSV artefacts and plots: knee_contour_summary.csv and lock_contour_summary.csv knee and lock contour PDFs (with optional bootstrap CI summaries where available) Main outcome The resulting Nk(n) contour provides a compact, reproducible map of where the cloth transitions from core-dominant to halo-dominant behaviour as a function of (N, n). The operational lock contour Nl(n) is included primarily as a planning guide in the higher-n regime; functional-form modelling of Nk(n) is deferred. Reproducibility All configs, consolidated CSV artefacts, plotting scripts, and run logs supporting this technical note are archived with the associated code/repository record (see related identifiers/links). Raw simulation output folders are kept local and are not required to regenerate the figures from the consolidated artefacts.