Paper XVII — Gauge Sector Closure: Standard Model Gauge Group and Anomaly Cancellation in Radial Coherential Dynamics (v2.3)

Previous papers in the RCD series established that gauge fields emerge from the dynamics of the coherence field C(x,t) and that fermionic matter corresponds to topological defects (vortices and monopoles) in C. However, a critical gap remained: the Standard Model gauge group SU(3) × SU(2) × U(1)_Y was not derived as a closed, self-consistent structure, and anomaly cancellation was not verified. These limitations were explicitly identified in Paper XIII [1, Sec. 8]. This paper addresses both gaps through a conditional theorem. We formulate three structural hypotheses (H1–H3) on the multi-component coherence field, prove that the natural U(3) × U(2) × U(1) symmetry reduces to SU(3) × SU(2) × U(1)_Y through identification of redundant U(1) factors, and verify generation-by-generation cancellation of all five perturbative gauge anomalies and the Witten global SU(2) anomaly. The novelty is not the Standard Model anomaly algebra itself — which is textbook material — but that the RCD topological dictionary lands exactly on an anomaly-free set of representations. The dictionary was fixed before the anomaly audit; no charges were tuned to satisfy cancellation. Claim boundaries are delineated in Appendix A. Part of the Radial Coherential Dynamics (RCD) series, Papers I–XVII. AI Collaborative Panel methodology: human-led research with collaborative review from Claude (Anthropic), ChatGPT (OpenAI), Gemini (Google), Grok (xAI), and Perplexity AI.