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The science
Chapman cycle (1930). O₂ + hν → 2 O (rate J₂), O + O₂ + M → O₃ + M (k₂), O₃ + hν → O₂ + O (J₃) and O + O₃ → 2 O₂ (k₄). Atomic oxygen is so short lived that [O]/[O₃] = r = J₃ / (k₂ [O₂][M]). Setting production equal to loss, 2 J₂[O₂] = 2 r [O₃](k₄[O₃] + kX[X]), gives a quadratic in [O₃] that the model solves in every 1 km layer from the top of the atmosphere downward, so each layer feels the ozone column above it (Beer-Lambert shielding exp(-σ N)). That shielding is the ozone layer's self-healing.
Catalytic loss. A catalyst X (here ClO, plus a lumped natural NOx/HOx term) adds O + ClO → Cl + O₂ and Cl + O₃ → ClO + O₂: net O + O₃ → 2 O₂ with the catalyst returned, so one chlorine atom destroys on the order of 10⁵ ozone molecules before being locked in a reservoir such as HCl.
Polar vortex. In the cold lower stratosphere ice clouds activate chlorine; the rate-limiting step ClO + ClO + M → Cl₂O₂ followed by photolysis destroys two O₃ per cycle: d[O₃]/dt = -2 kd[ClO]², integrated with RK4 for the chosen number of days at an average sunlit fraction of 25 %. The dependence on [ClO]² makes the hole very sensitive to chlorine.
Column and UV. 1 Dobson unit = 2.687×10¹⁶ molecules cm-2 (0.01 mm of pure ozone at 0 C and 1 atm); the column is the sum over layers. The clear-sky UV index uses the common approximation UVI ≈ 12.5 cos2.42θ (Ω/300)-1.23.
Honest simplifications. A 1-D, isothermal-scale-height atmosphere with band-averaged effective cross sections, not a line-by-line radiative transfer. Natural NOx/HOx catalysis is one lumped parameter, tuned together with the photolysis rate so that the natural column is about 300 DU (the real global mean is about 300 DU, so this agreement is by construction, not a validation); below 20 km ozone is controlled by transport, so a fixed shape tied to the chemistry at 20 km of the chlorine-free run is used. The resulting layer is narrower and sits lower (about 18 km) than the real one (peak near 20 to 25 km) with too little ozone above 25 km, and the pure Chapman column (no other catalysts) comes out about three times too large, a known weakness of the 1930 theory. The mid-latitude chlorine effect is therefore a few percent at most, in line with the idea that the big losses are polar. Mid-latitude chlorine is a single ClO profile shape, not a chemical-transport model; the equivalent-chlorine history is an illustrative curve, not observed data; the polar vortex temperature (192 K) and ClO share are typical values; reservoir chemistry, bromine, transport and dynamics are omitted. The molecule animation is a cartoon, not to scale. Treat absolute numbers as illustrative and the sensitivities (what a chlorine change does to column and UV) as the lesson; verify typical values against an atmospheric chemistry reference before quoting them.