What does this research mean for the field?

The LB-04 extended regime establishes the strict quasi-static approximation and operational boundaries required to validly evaluate ghost-freedom, gradient stability, and tachyonic stability in Radial Coherential Dynamics. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This note introduces the LB-04 extended regime for evaluating ghost-freedom and stability in a dynamical framework.

May 20, 2026Open Access

The LB-04 Extended Regime in Radial Coherential Dynamics

Key Points

This note introduces the LB-04 extended regime for evaluating ghost-freedom and stability in a dynamical framework.
Defines strict quasi-static approximation and its implications for various stability tests.
Outlines contributions to mass eigenvalues under the proposed decoupling limit.
Identifies operational kill-switches and structural risks in stability assessments.
Establishes a framework under which the trilogy on T3 is valid within the LB-04 regime.
Identifies risks of false equivalence in stability assessments of disformal structures.
Confirms the operational closure of the trilogy with the LB-04 note.

Abstract

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.

The LB-04 Extended Regime in Radial Coherential Dynamics

Key Points

Abstract

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