Minimal Effective Action of the Interface Layer Σ in FBS Theory : Observable Finite Sectors and the Connection to a 7×7 Effective Matrix
Yoshihito Ookawa
Description This record contains the revised version of Paper 15 in the Fundamental Being Space (FBS) Theory series. In this revision, the updated contents of Papers 12–14 are reflected, and state formation on the Σ side, state projection to the ordinary-spacetime side, observation-output formation after projection, and the classification of multiple identical projected states are reorganized as distinct stages. The basic relation is organized as follows: internal responses in Σ→ψΣ→ψSi→Xi Here, state projection and observation-output formation are not treated as the same process. The classification of exchange, occupation, and effective projected modes for multiple identical projected states is also positioned as a subsequent stage. On this basis, this paper organizes observability, phase and rotational responses, stabilization and retention, consistency with state projection, and constraint conditions as having distinct roles within the minimal effective action of the interface layer Σ. Furthermore, a finite effective sector is extracted from the broad operator-response structure on the Σ side and connected to a finite-dimensional representation as AΣ→PeffAΣPeff→MΣeff As a specific candidate for this finite-dimensional representation, the 4+3 block structure of a 7×7 response matrix is used. By applying the Schur complement, a general form is shown in which the influence of one finite effective sector remains as a correction to the other effective response through off-diagonal responses. However, the dimension 7 is not regarded as having been newly derived from the minimal effective action or from the selection of the finite effective part. Through this revision, the role of Paper 15 within the FBS Theory research program has also been clarified. The observability structure, spinor-type responses, and classification of multiple identical projected states organized in Papers 12–14 are connected in Paper 15 to the framework of the minimal effective action and finite effective sectors. This provides a bridge to the next stage, Paper 16, where the physical specification of the 7×7 response structure and the connection between quantum-type and gravity-type responses will be examined. This paper does not derive the complete internal structure of Σ, standard quantum mechanics, the Dirac equation, or the spin-statistics relation from first principles. Its purpose is to reorganize the response structures developed in the revised Papers 12–14 under the minimal effective action and to present a finite effective structure that connects to Paper 16. Related Papers The present revision of Paper 15 directly reflects the revised contents of Papers 12–14. Paper 12 — From General Σ Responses to Hermitian Pairing: Born-Type Probability and Observability in FBS TheoryConcept DOI: https://doi.org/10.5281/zenodo.20784611 Paper 13 — Spinor Structure and 4π Symmetry as Σ-to-Si Projection in FBS TheoryConcept DOI: https://doi.org/10.5281/zenodo.20793474 Paper 14 — Effective Projected-Mode Classification in the Interface Layer in FBS TheoryConcept DOI: https://doi.org/10.5281/zenodo.20797474 Regarding Paper 16 Paper 16 will be revised to reflect the updated contents of Papers 12–15. After the revision is completed, a link from this Paper 15 record to the revised Paper 16 will be added. Complete FBS Theory Series Paper 1 serves as the main entry point for the overall FBS Theory series, including the series overview, the position of each paper within the research program, and the latest organization of the series. Paper 1 — General Discussion on the Reality of Fundamental Being Space (FBS)Concept DOI: https://doi.org/10.5281/zenodo.18220714 Versioning This preprint may be updated in revised versions as the research progresses. When citing, please specify the DOI and version. Author informationIndependent Researcher, Japanyosihitoookawa@gmail.comORCID: 0009-0006-8294-5738
•Jul 21, 2026•0 citations