At depth one the finite continuous source layer is the literal initial
function (3-s)/s throughout the low strip.
The Section 13 plus-hat initial condition at β=2, written in the
normalization occurring in the depth-one error envelope.
On the low strip the exact hat initial value gives the uniform lower bound
1/s for the depth-one production error envelope.
A completely explicit eventual comparison of the local depth-one remainder
with the same fixed C error budget. The threshold is chosen before s, so
this is uniform on 1 < s ≤ 3.
The Euler product multiplying both base-one brackets is nonnegative.
Actual Case-II N=1 closure with one fixed C. A single threshold is
chosen before the low-strip parameter s; it simultaneously enforces the
source value 3 ≤ sourceSigma D d, the natural-ceiling base geometry, and the
uniform absorption of 9K/(s log D).
The exact producer requested by the Case-II dispatcher, now discharged
from source data. It is a specialization of the stronger threshold-before-s
uniform theorem above and therefore uses the identical constant C.