Recombination and Expansion Budget of the Born-Again Shells of Abell 30

This paper computes a self-contained budget for Abell 30 from published observational values, with every derived number produced by the deposited computation script. Abell 30 is the prototype born-again planetary nebula: an old, large, hydrogen-rich outer shell surrounds young hydrogen-deficient knots ejected in a very late thermal pulse. The contrast between the two generations of ejecta inside one object makes it a natural laboratory for timescale comparisons. The recombination time in the inner knots, computed from their density and the elevated temperature of the hydrogen-deficient gas, states how the young material responds to the now very hot central star, while the outer shell expansion records the original ejection. The headline results are: electron_density_cm3 = 1.5e+03; electron_temperature_K = 1.4e+04; alpha_B_cm3_s = 2.02e-13; recombination_time_yr = 105; expansion_age_yr = 9778; ratio_age_to_trec = 93.5; stromgren_radius_pc = 0.113. The inner-knot recombination time is short, so the knots are photoionised by the present star rather than shining as cooling remnants of the thermal pulse itself. The two shell generations differ in dynamical age by more than an order of magnitude, quantifying the born-again interpretation in timescale terms. The budget supports the standard picture in which the pulse ejecta are a small mass riding inside a much older and more massive nebula. The calculation is presented with its inputs, relations and sensitivities stated openly, so that any revised distance, density or stellar parameter can be substituted and the verdict recomputed directly.