An end-to-end photonic audit carries source counts into a click floor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The audit feeds bright-port counts into the detector

The end-to-end audit ties energy, splitter, interferometer, detector, and rail sources together.

m=NclickNminm=N_{\text{click}}-N_{\min}
Audit below click floorThe source chain is valid but the click floor is not met.singletotal1/2upper1/2lowersplitter1/2upper1/2lower1bright0dark0lostphase1/2clicked1/2misseddetector1upper0lowerdual rail

Three audited source counts bracket the click floor

The middle row reaches the click floor while preserving every source reference.

NsrcNclickmgate422fail840pass1262pass\begin{array}{c|c|c|c}N_{\text{src}}&N_{\text{click}}&m&\text{gate}\\4&2&-2&\text{fail}\\8&4&0&\text{pass}\\12&6&2&\text{pass}\\\end{array}
Audit boundaryThe audited detector count exactly meets the floor.singletotal1/2upper1/2lowersplitter1/2upper1/2lower1bright0dark0lostphase1/2clicked1/2misseddetector1upper0lowerdual rail

The larger audited packet clears the click floor

The photonic audit helper checks the same count fields that the table compares.

m=2passm=2\quad \text{pass}
Audit above click floorThe checked source chain clears the floor.singletotal1/2upper1/2lowersplitter1/2upper1/2lower1bright0dark0lostphase1/2clicked1/2misseddetector1upper0lowerdual rail