Saved in:
| Hovedforfatter: | |
|---|---|
| Format: | Recurso digital |
| Sprog: | |
| Udgivet: |
Zenodo
2026
|
| Online adgang: | https://doi.org/10.5281/zenodo.18517517 |
| Tags: |
Tilføj Tag
Ingen Tags, Vær først til at tagge denne postø!
|
Indholdsfortegnelse:
- <p>We present a complete and self-contained derivation of the Transverse Projection Operator ˆQ, the fundamental dynamical generator in the Operator-Derived Dimension (ODD) framework. Unlike conventional higher-dimensional models where<br>dimensional reduction is assumed, the ODD framework derives observable dimensionality as the projection residue of a higher-dimensional geometric constraint system.</p> <p>Starting from a non-perturbative five-dimensional action with warped geometry, we derive ˆQ as a geometric supercharge acting on bulk fields. We demonstrate that the operator is uniquely fixed by three necessary physical requirements: causality<br>(existence of directed evolution), stability (localization of matter), and chirality (fermionic asymmetry). We prove via variational analysis that vacuum stability fixes the topological index to μ = 2, which rigidly enforces exactly three localized fermionic generations.</p> <p>The associated eigenvalue problem reduces to the exactly solvable P¨oschl–Teller potential, yielding a finite bound spectrum and a continuum of delocalized resonances. This structure predicts both the observed three-generation structure of<br>matter and a sharp dark-sector threshold. The operator does not literally slice or disconnect the bulk, but enforces compatibility constraints that select stable lower-dimensional projection residues. This work establishes ˆQ as the mathematical engine underlying dimensional emergence, mass spectra, and coherence limits in the ODD framework.</p>