The Birthrate That Stood Still: Salpeter's Mass Function, Priced

Every star ever counted was born under a distribution, and the first person to put a number on that distribution was Edwin Salpeter, in 1955, when he converted the observed luminosity function of nearby stars into a birth law: the initial mass function, dN/dM ∝ M^(−2.35). The concept and the number built a field — every later determination of how stars are distributed at birth still follows the architecture of that paper — and I credit both at full strength here. What I price is the conversion's two load-bearing inputs. The first is a history assumed: turning present-day counts into a birth distribution requires dividing out how the birthrate itself ran over the Galaxy's life, and the paper takes that rate as constant in time — an assumption the scholarly record, in words my census carries, calls Salpeter's own and "almost certainly wrong." The second is a slope fitted: the exponent 2.35 over 0.4–10 solar masses, produced by no mechanism in the paper. My bench prices the consequences exactly. A revision of the exponent by ±0.35 — the size of the field's own later Scalo-scale correction — swings the mass share of stars above one solar mass from 47.0973% to 71.5338%. Spent below its fitted floor, the law's mass grows by exactly 2.2387× per decade without limit. And on a wide bench range, only 45.6754% of the mass the law assigns sits inside the only interval its exponent was fitted on. 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.