We establish a complete, rigorous, and extensible multi-layer classification system for the theory of relativity, systematically generalizing the formal methodology previously developed for quantum mechanics and the Standard Model. The system comprises seven hierarchical layers: Kingdom (gravitational framework), Phylum (spacetime topology and causality), Class (symmetries and anomalies), Order (conserved charges and topological numbers), Family (dimension and dynamics), Genus (singularities and horizons), and Species (explicit metrics and observables). Each layer is equipped with explicit axioms (totaling 97), compatibility conditions (R1)–(R12), and fundamental theorems, all proved with at least 4 steps (important theorems ≥ 8 steps). We prove the uniqueness of general relativity within this classification. We identify infinitely many gaps in the parameter space and derive 28 predictive branches (4 per layer). Each prediction includes a complete axiom system, a main theorem, and a rigorous proof of at least 12 steps. All predictions are compatible with current data and provide testable signatures for future experiments (LISA, Einstein Telescope, CMB-S4, LiteBIRD, LIGO/Virgo/KAGRA, EHT, LSST, Euclid, etc.). The system is shown to be arbitrarily extendable, computationally NP-complete and QMA-complete, and admits an ∞-categorical lift. Forcing constructions produce non-standard relativistic spacetimes with infinitesimal parameters. This classification provides a periodic table for relativity, unifying all major branches from special relativity to quantum gravity.
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