A Uniform 14--18 Carry Bound in Fibonacci Digit Lifts

This paper establishes a uniform bound on the number of carries arising in complete 32-fold lifts of consecutive Fibonacci additions in base 32. For every digit depth and every starting index, consider 32 Fibonacci additions whose indices are separated by the Pisano period corresponding to the lower digit depth. Although the lower digits remain unchanged under these period shifts, the next higher digits evolve according to an exact recursive lifting rule. The main theorem proves that among these 32 additions, at least 14 and at most 18 produce a carry across the next higher digit boundary, independently of the starting index and digit depth. A stronger result holds for three of the six index classes modulo 6: for starting indices congruent to 0, 4, or 5 modulo 6, the number of carries is always between 15 and 17. The proof is entirely algebraic. It combines Fibonacci matrix recurrences, modular arithmetic progressions, greatest common divisors, and a classification of six reachable index classes. This reduces an infinite family of digit-depth problems to a finite, depth-independent arithmetic structure. The paper includes a reproducible Python verification program that independently checks the finite matrix computations and compares the recursive generation of Fibonacci residues with the exact lifting formulas. All results concern complete modular lift groups. They do not assert equidistribution over short intervals or normality of Fibonacci digit concatenations. The contribution is an exact structural theorem on carry behavior in Fibonacci recurrences, obtained through a recursive-dynamic approach without statistical assumptions.