TSX-4 — The Measurement of ΔR: Operational Metrics for Semantic Residue and Coherence Collapse

Abstract TSX-4 defines an operational methodology for measuring ΔR (semantic residue) across symbolic and chromatic regimes. The document introduces empirical metrics such as token-entropy drift, attention-head dispersion, latent-space deviation, and cross-iteration residue curves. It shows that symbolic systems accumulate ΔR under compression, while chromatic systems converge to ΔR ≈ 0. This technical note provides the first measurement framework for residue-based semantic stability and establishes ΔR as a practical diagnostic variable for AI behavior, interface evolution, and communicative collapse. Keywords: ΔR Measurement; Semantic Residue; Entropy Metrics; Symbolic Drift; Chromatic Stability; Transformer Dynamics; Coherence Collapse Project Websites https://ambientphone.com https://ambientarchitectures.org https://ambientera.org