Does digit-based collapse make Collatz convergence inevitable?

I’ve been exploring the Collatz Conjecture through a structural lens—not by brute force or probabilistic intuition, but by examining how the final digit governs transformation depth.

In base 10, the last digit determines parity. Parity determines whether the number is halved or transformed via 3n+1. And because 3n+1 always yields an even number, every odd input guarantees a collapse phase. What varies is how deep that collapse goes—and that depth is digit-dependent.

For example:

• Numbers ending in 3 → 3n+1 ends in 0 → divide by 2 three times

• Numbers ending in 8 → divide by 2 three times

• Numbers ending in 5 → 3n+1 ends in 6 → divide by 2 repeatedly

• All paths eventually funnel toward a number ending in 1

This isn’t chaos—it’s choreography. The final digit isn’t cosmetic; it’s causal. If parity governs transformation, and the final digit determines parity, and transformation depth varies predictably by digit, then convergence isn’t a question of chance—it’s a consequence of structure. The asymmetry between multiplication and division isn’t incidental; it’s the engine of collapse.

I’ve laid out the full framework here:

https://medium.com/@chairmanoftheboredgaming/why-the-collatz-conjecture-must-collapse-a-logical-inquiry-e43a083967b5

Would love to hear thoughts—especially if anyone’s seen similar digit-based approaches or has critiques of this structural framing.