Tajalaei–Yazdan Manifestational Field Theory: An Equilibrium-Based Route to Unified Physics with Geometric Realization and Testable Predictions

This paper presents the complete formulation of the Tajalaei–Yazdan Manifestational Field Theory (YFT), an equilibrium-based approach to unified physics. The theory elevates equilibrium—rather than symmetry, spacetime, or fundamental particles—to the primary organizing principle of physical reality. The core structure consists of three equilibrium channels:- Scalar (linear): generates mass, inertia, and the cosmological constant.- Phase (elliptic/circular): generates spin, gauge symmetry, and quantum properties.- Geometric (hyperbolic): generates gravitation and spacetime curvature. A key conceptual advance is the background-independent formulation of the theory. The Yazdan Field is defined on an abstract equilibrium manifold, and the spacetime metric emerges as a solution to the geometric equilibrium condition δV_eq/δg_μν = 0, resolving the apparent circularity of defining dynamics without a presupposed background. The theory is closed nonperturbatively using the Functional Renormalization Group (FRG). Explicit demonstration of truncation convergence (differences <5% between 4th and 6th order) ensures numerical robustness. Testable predictions include:- A fifth force with range ℓ_eq ≈ 100–300 nm and strength A_rel(200 nm) ≈ 0.0065, consistent with Eöt-Wash bounds and accessible to next-generation experiments.- Exactly three fermion generations from the golden ratio φ = (1+√5)/2, with rigorous proof of fourth generation instability (λ₄ < 0).- A dark matter spectrum with masses ~0.5, 10, and 500 GeV, interacting via a frozen-in mechanism with cross-section σ_DM ~ 10⁻³⁴ cm² (below LHC sensitivity).- A cosmological constant Λ ≈ 1.46 × 10⁻¹² eV⁴ from vacuum fluctuations, matching observations within 25%. The theory requires no extra dimensions, supersymmetry, or anthropic tuning. All fundamental constants emerge as equilibrium numbers from fixed-point solutions of the RG flow. Version 3.0 incorporates peer review feedback: background-independent formulation, convergence analysis, detailed comparison with short-range gravity experiments, and explicit dark matter production mechanism. The article is formatted as a complete research paper suitable for submission to Physical Review D or Journal of High Energy Physics. Author: Yazdan Tajalaei (ORCID: 0009-0005-8389-4533)