Bibliographic Details
| Title: |
A Fixed-Point Resolution of the Theory of Everything via the Global Recursive–CSP Bridge (GRCB) |
| Authors: |
Rodgers, Jeremy |
| Publication Status: |
Preprint |
| Publisher Information: |
Zenodo, 2025. |
| Publication Year: |
2025 |
| Subject Terms: |
GRCB, fixed-point theory, Tarski–Knaster theorem, TOE, Global Recursive–CSP Bridge (GRCB), ultrametric spaces, holomorphic fixed points, β-function recursion, curvature-gauge coupling, analytic function theory, ω-continuous logic, recursive systems, grand unified theory, symbolic–analytic correspondence, quantum gravity, spin-foam dynamics, symbolic dynamics, theory of everything, GUt, unified field theory, grand unified theory (GUT), theory of everything (TOE), CSP (classical symbolic paradigm), operator convergence, Banach contraction |
| Description: |
This paper presents a rigorous fixed-point resolution of the Theory of Everything (TOE) by coupling Quantum Gravity (QG) and Grand Unified Theory (GUT) recursions within the Global Recursive–CSP Bridge (GRCB) framework. Building on prior analytic-symbolic fixed-point resolutions for QG and GUT, we define a unified recursive symbolic space ΦTOE\Phi_{\mathrm{TOE}}ΦTOE and a holomorphic analytic host space ATOE\mathcal{A}_{\mathrm{TOE}}ATOE, connected via adjoint embedding and projection maps. The core innovation is the construction of a block-kernel update operator UTOE\mathcal{U}_{\mathrm{TOE}}UTOE, incorporating: Curvature-induced gauge deformation Mass-hierarchy feedback mechanisms Off-diagonal mixing between gravitational and gauge sectors This operator is shown to be monotone, ω-continuous, and contractive, satisfying Banach and Tarski–Knaster conditions on both sides of the bridge. On the analytic side, a global operator TTOET_{\mathrm{TOE}}TTOE acts on a direct-sum of holomorphic function spaces valued in a gauge Lie algebra g\mathfrak{g}g and curvature mode space q\mathfrak{q}q, defined over C∗\mathbb{C}^*C∗. The main theorem proves that: There exists a unique analytic fixed point FTOE∈ATOEF_{\mathrm{TOE}} \in \mathcal{A}_{\mathrm{TOE}}FTOE∈ATOE There exists a unique symbolic least fixed point ΦTOE∗∈ΦTOE\Phi_{\mathrm{TOE}}^* \in \Phi_{\mathrm{TOE}}ΦTOE∗∈ΦTOE These are precisely related via: π∞(FTOE)=ΦTOE∗,ι∞(ΦTOE∗)=FTOE\pi_\infty(F_{\mathrm{TOE}}) = \Phi_{\mathrm{TOE}}^*, \quad \iota_\infty(\Phi_{\mathrm{TOE}}^*) = F_{\mathrm{TOE}}π∞(FTOE)=ΦTOE∗,ι∞(ΦTOE∗)=FTOE All known obstructions—strong coupling, kernel divergence, embedding overflow, mixed-sector instability—are neutralized via exponential damping and strict blockwise Lipschitz conditions. A numerical appendix confirms convergence of the coupled recursive-analytic system within 15 iterations at κ≤0.7\kappa \le 0.7κ≤0.7, demonstrating the framework’s predictive viability. This result establishes the first mathematically complete unification of QG and GUT via fixed-point theory, bridging discrete symbolic recursion with continuous analytic dynamics. The GRCB framework is thereby extended to a full fixed-point resolution of the Theory of Everything. Supporting papers A Fixed-Point Resolution of Quantum Gravity via the Global Recursive–CSP Bridge (GRCB) DOI: https://doi.org/10.5281/zenodo.16756790 A Universal Bridge Between Recursive Systems and Analytic Function Theory DOI: https://doi.org/10.5281/zenodo.16756790 A Universal Bridge Between Recursive Systems and Analytic Function Theory: Application to Grand Unification DOI: https://doi.org/10.5281/zenodo.16757249 |
| Language: |
English |
| DOI: |
10.5281/zenodo.16757400 |
| Rights: |
CC BY |
| Accession Number: |
edsair.doi...........600c1d07c3546479d0720f6779f5f3cc |
| Database: |
OpenAIRE |
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