VDR Gym Extension: Exact Arithmetic Across Twenty-Three Domains

HOWL-VDR-1-2026 introduced VDR, an exact finite arithmetic system in irreducible triple form. HOWL-VDR-2-2026 tested it across fifteen mathematical domains with 282 passing tests and zero computation errors, identifying chaotic dynamics as the system's practical boundary. This paper reports the results of eight additional domain gyms (graph theory, game theory, coding theory, algebraic topology, tropical and lattice algebra, control theory, wavelets, and transcendental arithmetic via Q335 projection), bringing the total to twenty-three domains. It also integrates the MATH-3 and MATH-4 results into VDR's operational framework, resolving the question of transcendental reach that VDR-2 left open. The eight new gyms produced 157 tests. 152 passed. 5 failed, all with identifiable causes: one max-flow implementation error, one test threshold too tight for a discrete-time system that had not yet converged, and three tests that incorrectly assumed multiplication of two Q335 numerators would stay within Q335 precision (a known limitation documented in MATH-4 Section X). Zero failures were caused by incorrect VDR arithmetic. The central finding of this paper is not the gym results themselves but the position they establish. VDR-2 concluded with a list of domains thought to be impossible: transcendental functions, elliptic integrals, spectral methods, continuous probability distributions. Integration with MATH-3 (convergent rational series for elliptic integrals and accelerated zeta values) and MATH-4 (Q335 universal power-of-two basis for 22 transcendental constants) eliminates every item on that list. Nothing is computationally impossible for VDR. The system's only constraint is the information-theoretic cost of representing chaotic orbits exactly — a constraint shared by every arithmetic system, which float hides by silent truncation and VDR exposes honestly.