Open Research Index

CollatzPosDens

Kenny Lau

Palomar Registrypalomar/PALOMAR-2026-10-15-000013Oct 15, 2026math.NTscore 0

`CollatzPosDens` is a formal proof of the main results of *Explicit positive lower density for the Collatz Conjecture* (hexagon:2610.00249). It proves Theorem 1.3, an explicit positive density of odd starting values reaching a prescribed target $t$ with $3 \nmid t$; Remark 1.4, which replaces the odd part of $t$ by $t$ itself when $\gcd(t, 6) = 1$; and Corollary 1.2, the case $t = 1$. The Lean files were generated by AxiomProver, Axiom Math's in-house theorem proving system.

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