This dataset contains an Isabelle/HOL formalization of information-theoretic barriers for trace-based proof strategies for the Collatz conjecture. The development formalizes several structural properties of the Collatz map, including parity vectors, affine representations of iterates, two-adic invariance, and the realizability of arbitrary finite parity traces. Building on these results, it introduces an abstract class of proof systems in which computational trace information is represented explicitly. Under explicit assumptions concerning the representation and preservation of parity information, the formalization proves a conditional barrier theorem showing that no finite proof can establish global convergence for all inputs within the corresponding class of proof systems.
The work is inspired by the author's earlier paper, "The Collatz 3n+1 Conjecture is Unprovable" (arXiv:math/0312309), and makes the assumptions underlying that argument precise within a machine-checked Isabelle/HO…
This dataset contains an Isabelle/HOL formalization and accompanying PDF document related to information-theoretic barriers for trace-based proof strategies for the Collatz conjecture. The development formalizes structural properties of the Collatz map and proves a conditional theorem showing that, under explicit assumptions about the representation and preservation of parity-trace information, no finite proof can establish global convergence for all inputs within the corresponding class of proof systems.
