A computer-assisted well-founded descent for Collatz components under dyadic leaf certificates in the 6-bit hierarchy Mt = 9 · 214+6t

Abstract. We present a component-wise descent scheme for the Collatz
map based on the odd accelerated map and an “anti-9” lift that sends
any odd non-multiple of 3 to an odd multiple of 3 in the same connected
component of the Collatz graph. The core step is a well-founded descent
on the odd parameter u associated to odd multiples 3u: for every odd
u > 1 we produce a strictly smaller u∗ < u such that 3u and 3u∗
belong to the same component. The descent is analytic when e(u) :=
v2(9u +1) ≥ 7 and is certified by a finite table of dyadic leaf certificates
when e(u) ≤ 6. The remaining regime e(u) ≤ 6 is discharged by a
f
inite leaf-wise verification. The certificate tables covering all dyadic
leaves modulo M = 9 · 220 with e(c) ≤ 6 have been constructed and
verified by a deterministic verifier; all four reference logs end with RESULT:
OK