Abstract. We study the Collatz-type mapT3, 5 (n) = n/2, n even, 3n +5, n odd. We formalize a conditional convergence strategy based on: (i) a reduction to sources 3u (with u odd) via an anti-9 lifting, (ii) a component-wise well-founded descent on the sourceparameter u produced by dyadic leaf certificates modulo Mt = 9 · 2L+6t (with L = 3), and (iii) a terminating certificate forest with six roots U0 = 1, 3, 5, 17, 41, 57. Under these hypotheses, every trajectory reaches one of the six empirically known positive terminal cycles (seed values1, 5, 19, 23, 187, 347)
julian redero (Mon,) studied this question.