FTAR v33: Unified Relational Stability Gravity — Classical Consistency, Quantum Completeness, and Observational Predictions

This paper presents the final, unified formulation of the Formal Theory of Attractor-Relational Dynamics (FTAR v33). FTAR is a fully covariant theory of gravity that derives spacetime curvature from a fundamental Relational Stability Tensor. Unlike General Relativity, which suffers from singularity pathologies and non-renormalizability, FTAR provides a mathematically complete and singularity-free framework. Key features of v33 include: Uniqueness Theorem: Formal proof that the derived regular black hole metric is the unique static, spherically symmetric solution under relational stability constraints. UV Completeness: Derivation of the Renormalization Group (RG) flow and beta functions, demonstrating that the theory reaches a stable UV fixed point via asymptotic weakening. Hamiltonian Consistency: Full ADM decomposition confirming canonical consistency and unitarity (ghost-free stability). Observational Signatures: Quantifiable predictions for Gravitational Wave Echoes (logarithmic delays) and stable Planck-scale remnants as natural candidates for Cold Dark Matter (CDM). This version synthesizes and extends the research line initiated in FTAR v18, providing a complete bridge between classical relational geometry and quantum field theory.