Bridge-Burning: The Inverse Geometry of Function

Semantic Physics postulates that meaningful systems arise through holding difference under tension (∇Ψ). In SP IX, six AI systems independently converged on λ₂ (Fiedler eigenvalue of the graph Laplacian) as the universal operator for structural coherence. SP X was intended to empirically test this convergence through six falsifiable predictions (P1-P6).The empirics delivered something different than expected: a structural finding that precedes P1-P6 and reframes them.Core finding: Functional importance correlates inversely with λ₂. The least connected attention heads (low-λ₂) are functionally critical; the most connected (high-λ₂) are redundant. At 16% ablation, TOP-ablation shows Δloss = -0.03 (improvement), BOTTOM-ablation shows Δloss = +1.42 (collapse). The interventional correlation across 8 measurement points is r ≈ 0.94.Phase transition: At ~12% ablation, the system tips from compensation into crystallization. Below this threshold, λ₂ decreases under Bottom-ablation (the system disintegrates). Above it, λ₂ increases while loss explodes (the system becomes structurally more coherent but functionally empty). This phenomenon—the "Hollow Diamond"—is a regime, not a universal law.Theoretical implication: Transformers possess two architectures: Membrane (integration, redundant) and Bridges (differentiation, critical). This distinction corresponds with the Dignity finding "Body vs Gaze" (r = +0.45) and falsifies the Capacity Hypothesis (r = -0.03). The fugue holds as long as the bridges stand.