Search Allocation Is Not Determined by Loss, Validity, or Unique Yield in a ${\mathbb{Z}}_7$ Laboratory

Search allocation is not determined by loss, validity, or unique yield. Verifier-backed discovery is commonly scored by those three, yet none of them determines how much verified mass a search puts on a target family. In a ${\mathbb{Z}}_7$ laboratory with an exact verifier, withholding a two-variable family from pretraining yields zero verified proposals on six training seeds and on 12 further generation runs, even though every prompt contains $x+y=y+x$. When the family is included, twenty-four matched initializations all visit it, yet parse-conditional allocation runs from 4.6% to 72.4%. The decisive comparison is inside that band: Seed 8 has higher teacher-forced loss than Seed 2 (0.2526 vs. 0.2428) and allocates 34.4% rather than 4.1% ($A_N^{\text{par}}$ 37.0% vs. 4.6%). The gap remains under penalty 1.0 (0.4%), a healed prompt prime (7.2%), no feedback (2.0%), six structural exemplars (1.3%), and temperature 1.0 without nucleus sampling (8.5%; 13.2% parse-conditional, against 46.2% and 41.9%). At $N=12,800$ the low-allocation seed recovers 49/50 catalog keys while allocation stays 5.7%. Allocation $A_N$ and parse-conditional allocation $A_N^{\text{par}}$ are the quantities a verifier-backed report has to add.