IndisputableMonolith.Astrophysics.StellarMassFunction_FromPhiLadder
Module that derives the stellar initial mass function from the Recognition Science phi-ladder and a domain cost built on the J-functional. It packages a Salpeter-slope certificate together with nonnegativity and positivity lemmas for the domain cost and a canonical mass threshold. Astrophysicists comparing RS mass spectra to the classical Salpeter IMF would cite it. The argument is definitional plus short algebraic certificates, not a deep existence proof.
claimOn the $\varphi$-ladder, a domain cost $C$ built from the $J$-cost yields a canonical positive mass threshold $M_\ast$ and a certificate that the stellar initial mass function has Salpeter slope (power-law index near $-2.35$) in the RS-native mass variable.
background
Recognition Science places particle and stellar masses on a discrete $\varphi$-ladder, with mass proportional to $\varphi^{r_{\mathrm{rung}}-8+\mathrm{gap}(Z)}$ times a yardstick. The cost module supplies the unique $J$-cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law; Constants supplies the RS tick and related units.
This astrophysics module lifts that cost to a domain cost on stellar mass scales and isolates a canonical threshold above which the ladder population is interpreted as stars. The Salpeter IMF (classical $dN/dM\propto M^{-2.35}$) is the observational target: the module's certificate objects assert that the RS ladder plus domain cost reproduce that power-law regime rather than fitting it by hand.
Sibling definitions include nonnegativity of the domain cost, equality at evaluation points, positivity of the canonical threshold, and inhabited certificate bundles (SalpeterIMFCert, cert).
proof idea
Definition-heavy module. Domain cost is introduced as a $J$-derived functional on the mass variable; short lemmas record evaluation identities and $C\ge 0$. The canonical threshold is a positive constant cut on the ladder. The Salpeter certificate is a bundled Prop (slope and threshold side-conditions) shown inhabited by assembling those lemmas with Constants/$\varphi$ facts. No long tactic developments; structure is defs plus certificate inhabitation.
why it matters in Recognition Science
Connects the T6-forced self-similar fixed point $\varphi$ and the mass-ladder formula to a concrete galactic observable: the stellar IMF slope. Downstream graph edges are empty in the current mirror, so this sits as a leaf packaging an astrophysics claim rather than feeding a named parent theorem yet. It is the natural place to hang comparisons against Salpeter/Kroupa IMFs and to test whether RS rung spacing plus domain cost fix the high-mass exponent without extra parameters. Lands in the Astrophysics domain beside other ladder-to-sky bridges.
scope and limits
- Does not derive binary fractions, IMF turnover at low mass, or Kroupa broken-power-law segments.
- Does not prove observational uniqueness of Salpeter slope against all alternative cost functionals.
- Does not compute numerical star-formation rates or galactic chemical evolution.
- Does not discharge cosmological initial conditions or dark-matter halo mass functions.
- Does not claim a fully sorry-free end-to-end IMF theorem beyond the local certificate bundle.