The LB-04 Extended Regime in Radial Coherential Dynamics

This methodological note declares the LB-04 extended regime — decoupling limit, strict quasi-static approximation, Brown-Schutz dust matter, |xi|0 kinetic positivity — under which the program Radial Coherential Dynamics evaluates ghost-freedom (T1), gradient stability (T2), and tachyonic stability (T3) for the disformal family B (C) = -beta*f (C) sealed in Notebook 9 §9. 3. T4 (subluminality) is inherited from the LB-03 result published in CQG-115997 (Zenodo doi: 10. 5281/zenodo. 20173399), not re-derived here, and its validity is restricted to the same eikonal/decoupling regime. T5 (isocurvature decay) and T6 (anisotropic stress) lie outside the regime as they require scalar-tensor coupled perturbations. The firm-seal property is stated explicitly: under strict QS, contributions of B (C) to the effective mass eigenvalue depend on f₀ but not on f₀' or f₀'', by exact cancellation through Jᵐu * partialₘu C₀ = 0. This is the structural basis of cross-criterion CC4 in the companion paper on the D6-F operational combination. The on-shell B ↔ D translation strategy for comparison with the disformal literature is declared, with the schematic on-shell mapping Dₑff (X) = B (C₀ (X) ) on locally invertible backgrounds. Three structural risks of false equivalence — pointwise identification, mechanical transfer of the disformal index nD, automatic inheritance of stability tests — are identified, together with four operational kill-switches. The note is the operational reference companion of the previously published trilogy on T3 under the D6-F combination: - Paper 3 (master bound): doi: 10. 5281/zenodo. 20263306- Paper 2 (forward diagnostics): doi: 10. 5281/zenodo. 20263139- Paper 1 (inverse construction): doi: 10. 5281/zenodo. 20262975 With this fourth preprint, the published series achieves a first public operational closure at the level of the LB-04 extended regime. The internal cuadernos LB-04 and LB-05 remain sealed in v0. 1 and will be published as standalone notes in future versions. This note does not extend the D6-F/T3 trilogy; it declares the regime in which that trilogy is valid. Draft v1, May 2026. Internal Panel Cerezo review (Claude, ChatGPT, Gemini, Grok, Perplexity, DeepSeek) consolidated.