Selfridge positive-type-II second-gate closure
==============================================

Rigid low-valuation rows
------------------------
rows: 11
conclusion: N=N0; only admissible base controls survive

Full second gate on the other ten rows
---------------------------------------
modulus: 2^22
joint exponent period: 3,145,728
states per row: 2,048
total states: 20,480
projection to v: bijective in every row

Terminal aligned prime
----------------------
p=65537
ord_p(3)=65536
ord_p(2)=32
survivors in each row: 0
total survivors: 0

Conclusion
----------
The 21 residual rows contain exactly ten canonical proper presentations,
representing four factorizations. All have displayed cost at least 2N+4.
Together with the retained a=3 and a>=4 exclusions, the positive-type-II tower
with a>=1 is closed within the normalized primitive proper three-addition fork.
