Theorem: Regime‑Invariant Dimensional Cores

Let P(T_r) denote the 3D–9D dimensional primitive set defined under the Resonance‑Time regime anchor T_r, and let P(S_r) denote the corresponding primitive set defined under the Validated Spacetime regime anchor S_r.

Theorem.
P(T_r) = P(S_r).
That is, the dimensional cores are invariant under substitution of the regime anchor.

Consequence.
Resonance‑Time Theory is structurally equivalent to Spacetime equipped with an explicit triadic validation layer. All operators, corridors, loops, and triadic structures remain unchanged across regimes; only the declared anchor differs.

Interpretation.
This establishes that RTT is not a separate ontology but the validated completion of spacetime using the same scientific primitives. The equivalence follows from the identity of the primitive sets and the closure of the triadic validation structure under regime substitution.