Photon energy is introduced with a toy proportionality: one declared frequency and constant set the per-photon energy. The arithmetic is exact only for the stated toy constant and frequency values; real optical photons require calibrated frequency, Planck constant units, linewidth limits, source stability, and measurement uncertainty.
A photonic ledger starts with one exact proportionality: frequency sets per-photon energy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A toy constant links frequency to energy
With toy constant h = 2 joules per hertz and frequency 3 hertz, one photon carries 6 joules.
Eγ=2⋅3=6
Doubling frequency doubles the photon energy
Keeping the same toy constant, frequency 6 hertz gives 12 joules per photon.