Slices, Not Selves: A Non-Inducibility Separation Framework for Global Coherence in Non-Abelian Constraint Systems

Abstract: Structural Separation in Non-Abelian Constraint Systems We present a structural separation framework for verification versus construction based on the non-inducibility of global coherence in non-abelian constraint systems. Core Methodology Problem Formulation: Instances are formulated as group-valued edge-consistency (cocycle trivialization) problems on graphs. Witnesses: A witness is defined as a vertex labeling consistent with all edge constraints. Verification: This process is local and achievable in polynomial-time. Key Results In contrast to the ease of verification, we demonstrate an explicit representational lower bound. We show that any ordered read-once process constructing a global solution must maintain an internal state large enough to track a distributed non-abelian holonomy obstruction. Hardness Alignment We further embed an NP-hard label-cover family into a growing sequence of groups, aligning hardness with distributed obstruction structure: $G_N = \text{SL}_{n(N)}(\mathbb{F}_{q(N)})$ The result provides a rigorous non-inducibility mechanism for separating local slice verification from global coherent induction within a precise computational model, finalized by a synthesis theorem assembling the full chain.