The Postulated Equilibrium: Saha's Stars, Priced

A star's atmosphere is not a reaction vessel, and in 1920 and 1921 Saha read its ionisation as one anyway — and the reading worked. I credit what that move bought at full strength: the founding move of quantitative stellar spectroscopy, in which ionisation read as a chemical equilibrium governed by temperature and density ordered the Harvard spectral sequence as a temperature sequence rather than a composition sequence, and inside its premises the formula is exact — it is the equilibrium constant of the reaction it postulates, in the ideal gas it imports. What I price is the warrant for spending those premises on stars generally: the equilibrium is postulated, with no ionisation rate and no recombination rate anywhere in the 1920/21 step, and the chemical potentials are imported from the ideal, dilute gas, with no interaction term and no domain fence drawn in either paper. My bench prices what the postulate buys and where the import runs out. At a declared density of 10¹⁷ cm⁻³ the entire neutral-to-ionised swing of hydrogen is compressed into a temperature width of 6385.776456 K about a midpoint of 13260.610254 K — a fractional width of 0.481560 — because the elasticity of the equilibrium constant is 13.401522 at the midpoint, driven by the exponential at χ/k_B = 157821.446456 K for the declared input χ = 13.6 eV. That narrowness, not any composition change, is the arithmetic that lets one formula order the spectral sequence. The premise's own machinery fences the import: the Debye-length fence and the Γ = 1 fence stand a fixed (4π)³ = 1984.401708 apart, at 1.080025×10¹⁷ cm⁻³ and 2.143203×10²⁰ cm⁻³ at 10,000 K, both scaling as T³ — and a routine bench density of 10¹⁷ cm⁻³ sits essentially on the Debye fence at transition temperatures, with λ_D/d = 1.012913 at 10,000 K. Above the fences the premise fails, never the algebra, and neither fence is drawn in 1920/21. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**