Calculation record
Necessary positive-frequency support bound from all retained bands.
A separating source functional provides an analytic lower bound. This is
an integrated, time-averaged test, not a claim of pointwise equilibrium.
Research context
- Complete positive-band source balance and its energy cost
Frequency-weighted occupation cancels every centered source in the time-averaged retained multiplet, while an explicit dual inequality prevents such support from preserving the small frequency's energy per canonical charge.
Interpret numerical checks within the assumptions and limitations documented in these notes.