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|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 C₀ (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) = V₀ (1-C) ², A (C) = 1 + alpha (1-C) ², B (C) = - (1-C) ²/mu⁴ — a triple structural alignment on the kernel K (C) = (1-C) ² of Notebook 8. This choice produces the exact cancellation A₀'² - 2A₀''A₀ = -4*alpha, C₀-independent to all orders in alpha. From the effective mass eigenvalue M²ₑff = 8X₀ + 2 (1-C₀) Box C₀ - 2V₀ - alpha*rhoₕat*sqrt (Z₀/A₀), imposing M²ₑff >= 0 yields the master bound V₀ <= V₀ᵐax (y) = 4X₀ + (1-C₀) Box C₀ - (alpha*rhoₕat/2) *sqrt (Z₀/A₀). Equivalently, V₀ <= PhiC₀ (y) - (alpha*rhoₕat/2) *sqrt (Z₀/A₀) with kinetic-geometric functional PhiC₀ = 2 (C₀') ² + (1-C₀) C₀''. This is the starting equation of the companion notes. The firm-seal criterion CC4 is preserved: no f₀' or f₀'' reappears in M²ₑff. 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 M²ₑff and the master bound V₀ᵐax. All algebraic derivations symbolically verified with SymPy.