Boundary-Condition Quantum Mechanics VII: Emergent Coarse Spatial Cloth from Cross-Linked Event Bundles

This record contains BCQM VII (v1.0) — Boundary-Condition Quantum Mechanics VII: Stage–2 “cloth” results. The paper advances the BCQM programme by moving beyond the short, fast-mixing active slice (Stage–1) and defining a persistent coarse spatial cloth that can be analysed with stable, reproducible diagnostics without assuming an underlying manifold. Time and ordering (the clock) BCQM retains a mechanistic separation between (i) an operational time/ordering signal and (ii) emergent spatial adjacency. The v_glue module supplies an operational clock-quality observable Q_{\mathrm{clock}} that tracks ordered time/temporal coherence. In Stage–2 we use Q_{\mathrm{clock}} as a stability and sanity check: the clock signal remains robust while the spatial cloth develops a structured core + halo organisation at larger N (notably N=32). What the paper does Builds a Stage–2 cloth object using a Path A cross-link layer on top of the v_glue clock engine (primitive ontology remains pre-spacetime: events + directed connections). Shows why strict edge-level persistence tends to isolate motifs rather than a spanning backbone, motivating a community coarse-graining and a community super-graph representation. Establishes stability of the cloth and super-graph across seeds and through scale-ups to N=32 in the high-coherence regime (n=0.8), including stable geometry diagnostics alongside a growing halo. Demonstrates that thread trajectories are local on the emergent coarse geometry (small hop distances on the community super-graph), supporting the interpretation that particle-like threads “respect” the cloth. What this is not yet This paper establishes a spatial cloth (persistent adjacency and robust diagnostics) with an independent operational ordering/clock signal. It does not yet extract a unified spacetime metric, causal structure, or a continuum limit; those are deferred to later stages. Reproducibility Repository artefacts (configs, CSV tables, and figure-generation scripts) are archived separately as a code release: Code DOI (v1.0): 10.5281/zenodo.18505934 Concept DOI (all versions): 10.5281/zenodo.18497216