D6-F Operational Combination in Radial Coherential Dynamics

This paper is the technical foundation of a Zenodo series of three notes on tachyonic stability (T3) under the D6-F operational combination of Radial Coherential Dynamics (RCD), within the LB-04 extended regime (decoupling limit, strict quasi-static approximation, Brown-Schutz dust matter, |xi|<1, Z_0>0). We establish the operational combination of potential, conformal, and disformal sectors that supports the companion notes on inverse construction [9] and forward-bank diagnostics [10]. Four options for V(C), three for A(C), three for the background C_0(x) are systematically enumerated under five cross-criteria and five kill-switches. After classification by traceability under the current framework, two operative combinations survive. We select the kernel-aligned choice V(C) = V_0(1-C)^2, A(C) = 1 + alpha(1-C)^2, B(C) = -(1-C)^2/mu^4 — a triple structural alignment on the kernel K(C) = (1-C)^2 of Notebook 8. This choice produces the exact cancellation A_0'^2 - 2A_0''A_0 = -4*alpha, C_0-independent to all orders in alpha. From the effective mass eigenvalue M^2_eff = 8X_0 + 2(1-C_0)Box C_0 - 2V_0 - alpha*rho_hat*sqrt(Z_0/A_0), imposing M^2_eff >= 0 yields the master bound V_0 <= V_0^max(y) = 4X_0 + (1-C_0)Box C_0 - (alpha*rho_hat/2)*sqrt(Z_0/A_0). Equivalently, V_0 <= Phi[C_0](y) - (alpha*rho_hat/2)*sqrt(Z_0/A_0) with kinetic-geometric functional Phi[C_0] = 2(C_0')^2 + (1-C_0)C_0''. This is the starting equation of the companion notes. The firm-seal criterion CC4 is preserved: no f_0' or f_0'' reappears in M^2_eff. A four-sector anatomy is provided (kinetic-favorable, geometric-tensioning, potential, conformal-matter), with explicit verification of the cancellation identity. An auxiliary leading-order expansion applies on local quasi-homogeneous backgrounds. The result is operationally viable conditioned, not a claim of global RCD stability. Eight inherited flags are registered for future fronts; one (quantitative T3) is discharged by the companion notes. Companion notes:- Paper 1 (inverse construction): A. Cerezo García, doi:10.5281/zenodo.20262975 (May 2026).- Paper 2 (forward-bank diagnostics): A. Cerezo García, doi:10.5281/zenodo.20263139 (May 2026). Draft v1, May 2026. Internal Panel Cerezo review (Claude, ChatGPT, Gemini, Grok, Perplexity, DeepSeek) consolidated, with explicit critical correction of the distinction between the effective mass M^2_eff and the master bound V_0^max. All algebraic derivations symbolically verified with SymPy.