Semantic Residual Theory (SRT): An Empirical Validation of Semantic Phase Transition via Cognitive Protocol Architecture (CPA v4)

We present the Semantic Residual Theory (SRT), a new theoretical framework that describes meaning in natural language as a distributed, reconstructible structure rather than a collection of discrete tokens. SRT introduces three core constructs: the Residual Semantic Field (RSF), the Reconstruction Threshold Function (RTF), and the Minimum Sufficient Structure (MSS). The theory predicts the existence of a Semantic Phase Transition: a sharp threshold δ* in the token deletion rate beyond which meaning reconstruction fails. We validate this prediction through a computational experiment using the Cognitive Protocol Architecture (CPA v4), a neurocognitively-inspired layer implementing five protocols (C1–C5). On a corpus of 100 texts (70 English, 30 Arabic), a hybrid IDF-based importance proxy for the C3 Spotlight mechanism reveals a clear δ* = 0.537 (95% CI: 0.482–0.593) for smart deletion. Crucially, the ordering Smart ≥ Random ≥ Destructive is confirmed for the first time (0.537 ≥ 0.534 ≥ 0.479), while Destructive deletion yields the worst transition point. The architecture exhibits zero NaN events across all 100 texts, confirming numerical stability. All five core claims of the SRT-CPA framework are empirically confirmed. These results establish a proof-of-concept for SRT and position CPA v4 as a viable substrate for semantic precision-weighted language processing.