CAL-L4: The Meta-Inference Layer — L4 Efficiency Hypothesis and the Representational Convergence Conjecture

Working paper v0.4 for Layer 4 (L4) of the Cognitive Abstraction Layers (CAL) architecture: meta-inference M(V) over compressed tensor volumes without human working memory as a substrate. The paper formalizes the L4 Efficiency Hypothesis (the cost of M(V) scales with the structural complexity κ(V), growing far slower than O(n²) in raw-artifact count n) and the Representational Convergence Conjecture (RCC). Results (June 2026): conditions (a) operator C with κ(V)=1296 (195.6× compression, from L3) and (b) the O(n²) flat-context baseline on MI300X (n^1.90–1.91, R²≈0.997) are met, and the κ vs n² cost contrast was executed on AMD Instinct MI300X (S5): the governance-state inference cost is bounded by κ(V) and independent of n while flat-context grows ~n^1.91 — the decoupling ratio reaches 52.8× at sequence length 4096. This confirms the cost mechanism (coupling vs decoupling), not a production-scale or accuracy claim. The compression residual was then characterized (L4-B0): ~81% of it is non-linear, so a single low-rank linear volume V′ cannot carry the governance state's causal content — the dual representation (V_Tucker, G_pruned) is terminal at this rank, and the single-V operator (L4-B) is a clean NO-GO. This is the second time the ordering causality ≻ reconstruction prevents a representational collapse. The sole remaining gate is condition (c), governance accuracy of M(V) vs flat-context, which is bound to the L2 randomized controlled trial. Hardware collaboration: AMD-Instinct Labs (MI300X, ROCm). All experiments were pre-registered before data collection. Part of the CAL five-level (L0–L4) research agenda. See companion CAL pre-paper, concept DOI 10.5281/zenodo.20430343.