Final source-pairing closure for Suzuki Proposition 11.8 #
The genuine source pairing is continuous on every [2,M] and has zero right
derivative at every point of [2,M), including the lower endpoint 2 and the
kink 3. The right-derivative constant theorem therefore proves conservation
on the whole closed interval in one step. Decay at infinity then forces the
boundary scalar, and hence Suzuki's B, to vanish.
The genuine source pairing has zero right derivative throughout [2,∞),
including both exceptional endpoints required by the one-sided argument.
Continuity of the source pairing on every compact interval of its legal range.
Conservation of the genuine source pairing on all of [2,∞).
The genuine source pairing vanishes at every legal coordinate.
Suzuki's lower-boundary constant is zero, now closed from the genuine source pairing rather than assumed.
Equivalently, the even source mass at the lower boundary is normalized to one.