A Unified Higher-Layer Geometric Framework for Mode Generation and Projection into Four-Dimensional Spacetime

TOHI, TSUYOSHI

doi:10.51094/jxiv.4741

##article.authors##

TOHI, TSUYOSHI Independent Researcher https://orcid.org/0009-0001-3043-5967 https://tohi308.github.io/R-layer-Mode-Theory/index.html

DOI:

https://doi.org/10.51094/jxiv.4741

キーワード:

tension field、 minimal excitation modes、 projection operato、 RLMT、 higher-layer geometry、 black-hole shadow distortions、 neutrino effective masses、 gravitational-wave signatures、 ADM decomposition、 Ricci flow

抄録

We develop a unified geometric framework in which four-dimensional spacetime emerges as a projection of a higher-layer manifold equipped with curvature, torsion, and a stratified fiber structure. Minimal excitation modes arise from tension-field dynamics and phase alignment across layers, forming stable composite configurations when the higher-layer tension is minimized. Instabilities in the tension field lead to mode bifurcation and the appearance of asymmetric projection states in four dimensions.

We derive the generative equations governing the evolution of higher-layer geometry, the formation and collapse of stratified layers, and the projection of effective physical modes into four-dimensional spacetime. Annihilation processes are reinterpreted as geometric de-escalation into minimal excitation modes, ensuring information preservation. This framework provides a hierarchical mechanism for the emergence of matter-dominated cosmology from pre-geometric structures.

利益相反に関する開示

The author declares no conflicts of interest.

ダウンロード *前日までの集計結果を表示します

ダウンロード実績データは、公開の翌日以降に作成されます。

著者の経歴

TOHI, TSUYOSHI、Independent Researcher

Independent researcher working on higher-dimensional geometry, projection structures, and emergent spacetime. My recent work focuses on the geometric foundations of mode generation and effective field theory derived from higher-layer manifolds.

引用文献

T. Kaluza, “On the Problem of Unity in Physics,” Sitzungsber. Preuss. Akad. Wiss. Berlin (1921) 966.

O. Klein, “Quantum Theory and Five-Dimensional Theory of Relativity,” Z. Phys. 37, 895 (1926). doi:10.1007/BF01397481

D. Lovelock, “The Einstein Tensor and Its Generalizations,” J. Math. Phys. 12, 498 (1971). doi:10.1063/1.1665613

E. Cartan, “Sur une généralisation de la notion de courbure de Riemann,” C. R. Acad. Sci. Paris 174, 593 (1922).

J. M. Maldacena, “The Large N Limit of Superconformal Field Theories and Supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998). doi:10.1023/A:1026654312961

S. Ryu and T. Takayanagi, “Holographic Derivation of Entanglement Entropy from AdS/CFT,” Phys. Rev. Lett. 96, 181602 (2006). doi:10.1103/PhysRevLett.96.181602

R. S. Hamilton, “Three-Manifolds with Positive Ricci Curvature,” J. Diff. Geom. 17, 255 (1982).

R. Arnowitt, S. Deser and C. W. Misner, “The Dynamics of General Relativity,” in Gravitation: An Introduction to Current Research, Wiley (1962). arXiv:gr-qc/0405109

S. H. Strogatz, “From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators,” Physica D 143, 1 (2000). doi:10.1016/S0167-2789(00)00094-4

Y. Kuramoto, “Self-entrainment of a population of coupled nonlinear oscillators,” in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics 39, Springer (1975).

H. Haken, Synergetics: An Introduction, Springer (1983). doi:10.1007/978-3-642-45507-5

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851 (1993). doi:10.1103/RevModPhys.65.851