🔢 Kaprekar Spectral Geometry — 54‑State Gap Automaton

Enter any 4‑digit integer to trace its path through the 54‑state gap space directly to the famous fixed point 6174.

The map is a deterministic finite automaton with a unique sink SCC {(6,2)}.

🧭 Full automaton structure

Regimes: 🔄 Swap (permutation) | ⚙️ Shear (carry‑coupling) | 📉 Contract (basin collapse)