FRAME-SELECTION GEOMETRY: BENCHMARKING ΔΦ-GUIDED INTERFACE RANKING IN LAYERED RECONFIGURATION SYSTEMS

This preprint introduces a frozen, fully reproducible benchmark for evaluating interface-selection strategies in layered geometric systems. The model consists of stacked two-dimensional templates connected by inter-layer hinges. At each step, a selection rule chooses which hinge to release, and the resulting system reconfiguration is measured through centroid-path exploration and related metrics.

The primary benchmark compares a local interface-tension heuristic (ΔΦ) against random selection and multiple competing heuristics. Across synthetic layered systems and a connectome-derived graph representation, ΔΦ-guided release consistently produces longer structured exploration paths than random selection while exhibiting predictable failure modes in sparse and low-complexity regimes.

The study makes no claims regarding biological, physical, or engineering mechanisms. Instead, it provides a reproducible computational benchmark for testing whether local interface-ranking strategies can predict coherent global reconfiguration in layered systems.

Key findings include:

• Large effect sizes in the canonical synthetic benchmark (Cohen's d = 1.33)

• Replication across 10 of 11 tested scenarios

• Optimizer invariance between gradient-descent and quasi-Newton minimization

• Detection of the effect within a human connectome-derived graph representation (d = 1.65)

• Explicit characterization of failure modes and performance regions