One integrality test, not many

Enter positive division exponents separated by commas. This verifies exact numerator identities, not the Collatz conjecture. Negative denominators are algebraically permitted but cannot certify a positive cycle.

For k exponents with sum A, D = 2^A − 3^k and C = Σ 3^(k−1−j) 2^(a₀+…+aⱼ₋₁). Each rotation satisfies 2^a₀ C_next = 3C + D. Since D is coprime to 6, divisibility by D is equivalent at adjacent rotations. Repeated rotation checks add no independent integrality constraint.