Boundary-Condition Quantum Mechanics VI: Emergent (1+1)-Dimensional Spacetime Islands from Cross-Linked Bundles

Boundary-Condition Quantum Mechanics VI — Stage-1: Dynamic Islands and Ball-Growth Geometry from Cross-Linked Bundles This record archives the compiled paper PDF for Boundary-Condition Quantum Mechanics (BCQM) VI. BCQM VI continues the BCQM I–V programme by combining a clock-coherence (v_glue) mechanism with a Path A cross-link layer on a pre-spacetime primitive (events + directed connections only). The goal of this Stage-1 paper is operational: identify what emerges, in what order, and by which mechanisms, without assuming an embedded manifold or a priori metric. Main findings (Stage-1) Two-step emergence: connectivity (“space”) turns on first as cross-link pressure increases; island coherence strengthens later and is threshold-sensitive. Mechanism separation (ablations): nospace prevents percolation and confirms the scan parameter does not leak into the clock engine; glue-off shows connectivity can percolate while clock quality collapses, demonstrating separability of space-connectivity and clock coherence. Dynamic islands: time-resolved (binned) diagnostics show “space on, islands fluctuating” at intermediate overlap threshold. The effect is reproducible in ensembles and across N = 8 and N = 4. Geometry on the active slice: return-probability spectral-dimension fits are structurally unstable on finite, rapidly mixing active slices; ball growth is used as the robust Stage-1 geometry diagnostic. Ball-growth ensembles show a clear tightening (“channels + shortcuts”) as cross-link pressure increases. Reproducibility The full reference implementation (code, configs, pipelines, and figure regeneration scripts) is available separately: GitHub: https://github.com/PMF57/BCQM_VI Code archive (release DOI): 10.5281/zenodo.18403109 (tag v0.1.0)