A Binary Carry Dynamics Framework for Collatz-Type Iterations: Early investigations of a subtractive bitwise iteration

This preliminary draft explores a binary carry dynamics framework for Collatz-type iterative maps on integers. We study a 2-adic subtractive bitwise iteration and analyze its bitwise borrow behaviour, potential function construction and orbit evolution. Early versions of this manuscript incorrectly labelled this subtractive iteration “Antihydra”; this naming is not correct, and the map is independent of the BB(6) Antihydra Turing machine problem from the Busy Beaver Challenge. The full termination proof and extended comparison with the 3n+1 Collatz problem appear in the revised Version 4 of this work.