t=2: lam=3/2, sqrt(lam^2+4)=5/2: 4 local cases OK; ground-state identity lhs=rhs=42818439079/4831838208
t=3: lam=8/3, sqrt(lam^2+4)=10/3: 4 local cases OK; ground-state identity lhs=rhs=256975973/12
t=4: lam=15/4, sqrt(lam^2+4)=17/4: 4 local cases OK; ground-state identity lhs=rhs=119398409/9437184
t=7/2: lam=45/14, sqrt(lam^2+4)=53/14: 4 local cases OK; ground-state identity lhs=rhs=73924303756441/3100448333024
t=11/5: lam=96/55, sqrt(lam^2+4)=146/55: 4 local cases OK; ground-state identity lhs=rhs=5897872622/2578125
RESULT: all exact checks passed
