The stellar-to-halo mass relation peaks near 10¹² M☉ at only 10 to 20 percent baryon conversion, declining steeply on both sides (Behroozi 2013; Moster 2018), with every feature requiring its own calibrated feedback story, and JWST's high-z galaxies breaking the assembled machine with stellar masses far too large for their assigned halos.
The relation's denominator is assumed to be a particle halo whose mass is fixed by the halo mass function, so all structure in the curve must be carved by baryonic feedback: supernovae below the peak, AGN above it, each calibrated to the data it explains. The framework fits rather than predicts, and its high-z extrapolation fails.
SCT re-reads the relation's denominator. The halo masses are inferred dynamically or through lensing, and in SCT what those methods measure is the coherently amplified baryonic mass, M_eff = A × M_baryonic, with A running to the parameter-free fixed point A* = 5.970 = 1/f_b in virialized systems (P50, P52, Paper 13, From Chaos to Coherent Gravity). Part of the famous inefficiency is therefore bookkeeping: dividing stellar mass by an amplified denominator makes every galaxy look like it wasted most of a particle halo that was never there. The registered baryon-fraction prediction pins the accounting: f_b within the virial radius should sit at 0.162 ± 0.019 for halos of all masses, because the amplification is the inverse of the cosmic baryon fraction by construction.
The curve's shape then follows from how A varies: coherence builds with virialization, so quiet intermediate-mass systems sit nearest full amplification while kinematically stirred giants and diffuse dwarfs amplify less (the same coherence dial behind rotation-curve diversity, recid 112), and the baryonic numerator varies with cascade-seeded reservoir history (P25). The high-z failure dissolves separately: collision-seeded galaxies carry stellar masses set by deposit geometry, not by a halo growth curve, so the SHMR's early extrapolation was never binding (recid 107, recid 116).
Keystone economy: P54 removes the particle, P52 fixes the amplification, P25 feeds the numerator. The efficiency report was grading against the wrong denominator.
The registered kill is the baryon fraction: simulations or observations finding f_b at the virial radius outside 0.14 to 0.19 across halo masses at >3σ breaks the A* accounting directly. Euclid and Roman lensing-calibrated SHMRs add the environment test: a relation whose shape is fully independent of coherence state and environment, matching the feedback-carved particle prediction at percent precision, would refute the amplified-denominator reading.