Type II: exact positive stationary state; 64 principal minors checked.
det(-H)=90368/1125; lower bound=36.
Type V: 8 literal species reduce to three base variables with exact reconstruction.
An internal-only loss gives two endpoint leaks of 1/3, even when both direct endpoint losses vanish.
Fixed-rate continuation: 41/41 numerical roots.
At most one positive root is the theorem; existence, stability at arbitrary loss and global continuation are not asserted.