Mass Without the Higgs: A Structural Consequence of Finite-Speed Causality

How can persistent memory coexist with the fading requirement of completely monotone kernels? We resolve this apparent tension through a principled sector separation: dissipative response governed by CMF kernels (which must fade) is distinguished from persistent records (which need not fade). This separation is not ad hoc but structurally necessary—conflating the two sectors leads to either violation of the CMF necessity theorem or loss of persistent information. Our main contributions are threefold: (i) we prove that sector separation is **necessary** for systems requiring both dissipation and persistence under S3 constraints; (ii) we construct **capacity-limited records** with barrier functions that induce emergent inertia as records approach saturation; (iii) we establish **well-posedness** of the coupled system, proving existence, uniqueness, and invariance of the admissible domain. The key insight is that resistance to change (inertia) emerges from informational saturation, not from non-fading tails in the dissipative kernel. As records approach capacity, effective inertia diverges: $M_{\text{eff}}(R) \to \infty$ as $R \to C_{\max}$. This provides a mechanism for mass-like behavior without violating the fading memory condition established in S3.