🔬Where Feasibility Bends: Stable 2D Interaction and the Absence of 3D Structure
First empirical demonstration that feasibility constraints compose non-additively in pairwise combinations but exhibit a dimensional cutoff at n=2
Research Program: UNNS Laboratory Phase P₀–P₂ • Status: Publication-Ready
Foundation: Axis I–V verification (Phase P₀) → Admissibility geometry (Phase P₁–P₂)
Total Evidence: 384,832 independent recursive executions • Methodology: Preregistered with transparent null results
56% non-additive volume
0.580 max residual
n≤2 dimensional bound
κ=0.309 boundary curvature
🎯 Key Discovery
Building on Phase P₀ verification of Axis I–V substrate stability, we demonstrate for the first time in a recursive substrate that
admissibility constraints do not compose independently.
When two feasibility gates interact (topological + spectral, or spectral + logical), they create measurable geometric structure:
boundaries curve, interaction volumes span 56% of parameter space, and enhancements reach 138% beyond independence predictions.
But here's the twist: this non-additivity vanishes in three dimensions. Systematic predicate relaxation across
259,200 executions shows interaction structure decreases with improved coverage, establishing a fundamental
dimensional constraint (n≤2) on admissibility composition.
This finding bounds the phenomenon, preventing speculative overclaiming, and opens new questions about why feasibility
geometry operates only in lower dimensions.
Read more: Geometric Constraints on Reality: Discovery of Dimensional Boundaries in Admissibility Composition
