The capstone joins energy, split, interference, detector, and rail checks through typed source references. 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 starts with the photon energy source

The conserved spine uses 8 photons at 6 joules each, so the cited total is 48 joules.

86=488\cdot6=48
Photonic audit sourcesEnergy, split, phase, detector, and rail sources are present.singletotal1/2upper1/2lowersplitter1/2upper1/2lower0bright1dark0lostphase3/4clicked1/4misseddetector0upper1lowerdual rail

The split and phase sources keep the same count

The splitter cites 8 to 4 plus 4. Opposite phase sends 8 counts to the dark detector.

4+4=84+4=8
Photonic count spineThe audit joins splitter and interferometer counts.singletotal1/2upper1/2lowersplitter1/2upper1/2lower0bright1dark0lostphase3/4clicked1/4misseddetector0upper1lowerdual rail

Detector and rail claims are source-bound

The dark-port detector receives 8 photons and records 6 clicks. The rail source reports logical 1.

6+2=86+2=8
Photonic capstone auditDetector arrivals bind to the dark port.singletotal1/2upper1/2lowersplitter1/2upper1/2lower0bright1dark0lostphase3/4clicked1/4misseddetector0upper1lowerdual rail