TWO ROOTS. ONE LANDING.
The Meeting.
Follow two different starting integers
to the same landing.
MOVE THROUGH THE PROVED FAMILY
N = 739 + 1024q
H = 725 + 1024q
Common landing = 13 + 18q
CERTIFIED FAMILY · REPLAY READY
The halving order changes the path.
Source word [1, 8]. Teacher word [7, 2]. Both spend nine halvings over two accelerated steps; their affine constants are 5 and 131.
M = 13
The replay verifies a meeting with H < N. Under the induction hypothesis that smaller positive odd sources reach 1, the certificate transfers termination to N.
Five whole turns are still between them.
121 − 1 = 120 = 5 × (8 × 3). The phases agree; the strict radius condition fails because 120 is not smaller than 24. These endpoints do not meet.
The equality criterion needs both phase agreement and |y − x| < 2ᵈ3ᵏ. The signed winding changes sign if the arms are exchanged; the nonzero gap remains.