This preprint is published as part of the author’s theoretical series, “Fundamental Being Space (FBS) Theory.” The series proposes a three-layer structure—Fundamental Being Space (FBS), an interface layer Sigma (Σ), and ordinary spacetime S_i—and aims to reorganize key physical concepts from first principles. Reading note / recommended orderPaper 4 is intended to be read immediately before Paper 5, which develops the time-generation mechanism based on the DeltaC–DeltaT coupling introduced in the series. This paper uses the term “tachyonic” in the field-theoretic sense (tachyonic modes in a dispersion relation). Readers who prefer to start from the time-generation component may begin with Paper 5 and return to Paper 4 afterward. Overview of PaperThis paper reinterprets “tachyonic” structures not as superluminal particles propagating within ordinary spacetime, but as phase modes on the FBS–Sigma side that mediate inter-layer energy redistribution. Within this framework, the continuous velocity spectrum C' is projected and normalized through the interface layer, yielding the intrinsic light speed C_i of each spacetime and providing a mechanism for stabilizing the light-speed hierarchy. A key step is to keep the tachyon dispersion relation intact while shifting its physical interpretation: the inverse correlation between velocity and observed energy implied by the dispersion relation is mapped to an inverse correlation known in shallow-water wave dynamics (Green’s law). This mapping is used as an interpretational guide to distinguish the retained mathematical structure from conventional particle-based readings. Series connection: Paper 4 bridges Paper 2 (electromagnetism from a double-helix structure in Sigma) and Paper 3 (gravitational weakness as interface-layer filtering) by introducing tachyonic C' modes as carrier degrees of freedom underlying the stability of C_i and the mode separation that yields electromagnetic and gravitational channels. Scope and references: Consistent with the series policy, background literature is restricted to original works and representative reviews and experiments related to electromagnetism, general relativity, and quantum gravity. Series notePaper 4 of the “Fundamental Being Space (FBS) Theory” series. Recommended citationYoshihito Ookawa, Stabilization of the Light-Speed Hierarchy Ci via Tachyonic Modes, Zenodo, 2026. 10.5281/zenodo.18327253. Series navigation Paper 1 (Overview / Series map)General discussion of the “Fundamental Being Space (FBS) Theory” framework and the series-wide mapping.Zenodo: https://zenodo.org/records/18220715 Paper 2 (Electromagnetism / Double-helix → A → E,B)Derives an effective vector potential A from the geometry and phase difference of a double-helix structure in the interface layer Σ, recovering electromagnetism (E, B) and the Maxwell equations in the long-wavelength limit.Zenodo: https://zenodo.org/records/18232306 Paper 3 (Gravity channel / Interface-layer filtering)Explains gravitational weakness as a multi-stage filtering (attenuation) effect in the interface layer Σ, yielding large hierarchy ratios naturally.Zenodo: https://zenodo.org/records/18240764 Paper 5 (Paired with Paper 4: Time generation / Coupled constraint ΔC–ΔT)This paper is designed as a companion to Paper 4. It formulates time generation as a constraint/coherence phenomenon in Σ via a coupled condition between the velocity width ΔC and the time step ΔT.Zenodo: https://zenodo.org/records/18327480 Recommended paired reading: Paper 4 ↔ Paper 5, then Paper 1 → Paper 2 → Paper 3 → (Paper 4 ↔ Paper 5) VersioningThis preprint may be updated in revised versions. When citing, please specify the DOI and the version. Author informationIndependent Researcher, JapanORCID: 0009-0006-8294-5738