Nonna Functions: An Experimental Study of Information Loss and Inversion Complexity

We introduce Nonna functions — a class of iterated mappings combining permutations with compression operations over finite fields. This experimental study investigates the relationship between information loss (measured discretely through preimage counting) and inversion complexity. Key findings:- Information loss grows linearly with iteration depth: I_lost ≈ λ·n (R² > 0.92 for all tested configurations)- Naive inversion complexity scales as 2I_lost with stable multiplier k ≈ 5.35 (95% CI: [5.20, 5.51])- Results are universal across different compression functions (x², x³, x⁴, x²+x) Experiments span field sizes from p = 127 to p = 10,007. STATUS: Experimental observations, not theorems. We do NOT prove lower bounds, cryptographic security, or connections to complexity classes. The results may guide future theoretical work on one-way function construction. Reproducible code is included in the appendix.