Mersenne Exponents Structured Calculus - novel framework

"We define a reverse-decimal evolution on digit strings. Starting from a one-digit seed written with a leading zero, digits evolve independently according to a fixed reverse cycle. At selected evolution levels, a leading zero is inserted, creating a new level of the process. Each initial seed generates a distinct family of values. Empirically, the union of these families coincides with the 52 known Mersenne prime exponents."

We start: 00, 01, 02, 03, 04, 05, 06, 07, 08, 09.

The cycle: `1 → 0 → 9 → 8 → 7 → 6 → 5 → 4 → 3 → 2 → 1`

We apply the operation to each digit counting backward so each column repeat the cicle.

Example:

02

91

80

79

68

57

46

35

24

13

"This provides an alternative structural framework for studying integers."

"Within this framework, the known Mersenne exponents occupy reproducible positions that merit further investigation."

Factorization describes the multiplicative structure of integers. My research investigates whether integers also possess a deterministic structural organization under decimal evolution

Can numbers be organized by a deterministic decimal evolution in a way that reveals meaningful structure, with the Mersenne exponents serving as one well-known reference set?