A sideband boundary asymmetry scan compares a red sideband at the packet-zero floor (rejected), a red sideband one packet above the floor (accepted), and a blue sideband starting from a much higher packet, 20, which still accepts and still adds one packet exactly for the stated toy sideband rule. This toy model enforces a real floor for red sidebands at packet zero, since there is no packet below zero to drop into, but enforces no matching ceiling for blue sidebands at any packet checked here; real trapped-ion systems do have a practical upper bound set by anharmonicity and heating, which this toy model does not capture.
A red sideband has a real floor at packet zero; a blue sideband has no matching ceiling in this model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Red sideband has a real floor at packet zero
Chapter two already established that a red sideband at packet index zero is rejected -- there is no packet below zero to drop into, so the accepted bit reads 0.
ni=0,nf=0,a=0
Blue sidebands never hit an equivalent ceiling in this model
One packet above the floor, red is accepted normally. Chapter five's blue-growth scan only ever checked small starting packets, up through two. Scanning a blue sideband from a much higher starting packet shows this toy model enforces a floor for red but never enforces any matching ceiling for blue.
kindredredblueni0120nf0021a011
A high-packet blue sideband is still accepted without limit
Starting from packet 20, the blue sideband still adds one packet and is still accepted. Nothing in this model's blue-sideband rule checks for an upper packet limit the way the red rule checks for the zero floor.