Pick any number with at least five digits. Apply the right rule. Watch it converge, almost always, to 60714.
The rule depends on the input's digit length: there is one rule at d = 5, another at d = 6, and a uniform recipe extending to every higher dimension. At d = 5 and d = 6, every admissible input reaches 60714. At d ≥ 7, almost every input does, but a small, exactly characterized class of inputs collapses to zero instead. The calculator recognizes both cases.
The number 60714 is a fixed point of an explicit family of permutation-pair rules built from its native rule at d = 5, with the family extending to every higher digit length by appending pairs of coefficients that sum to zero. The fixed-point equation K(60714) = 60714 holds at every d ≥ 5.
The dynamics are strict-universal at d = 5 and d = 6: every admissible input reaches 60714. At d ≥ 7, the rule is near-universal: every admissible input outside a small structural class (the escape class of block-aligned multisets and their backward orbits) reaches 60714. Inputs in the escape class collapse to zero. The escape class has a closed-form description and at d ≤ 11 the escape orbits all reach zero within four iterations.
This is a strict generalization of Kaprekar's classical 1949 result. Kaprekar's constant 6174 is universal at d = 4; the routine "stops working" at d = 5 if you keep his rule fixed. The result extended here is that if you let the rule itself vary with d (specifically, by appending zero-sum coefficient pairs), there is a distinguished fixed point, 60714 (sharing 6174's digit multiset plus a zero), whose universality persists across infinitely many dimensions, apart from a structurally characterized escape class.
This calculator is a pedagogical companion to the paper, not a formal verifier. It demonstrates the iteration on individual inputs; the formal claims of the paper are established by the Python scripts and proofs in the repository.
Full paper, the proof, the 506-fixed-point classification at d = 6, the closed-form description of the escape class, and reproducibility scripts: github.com/clayelmore/Kaprekar-60714