nx_stem_bound_gate.nx

nx_stem_bound_gate.nx -- THE STEM RUN BOUND, PROVEN OVER EVERY TERM OF THE LIVE DICTIONARY (search prep cut, 2026-09-14). WHY. dss_stem_expand (nx_docportal_search_seg.nx) finds every dictionary term whose stem equals the query term's stem by walking the sorted run of terms sharing the stem's first 3 bytes and stemming each one. The phase timers in /api/search named that walk as 0.33-0.40 s of every cold query, CPU in nx_stem per run entry (a prefetch pass over the same run measured no gain). Widening the run key from 3 bytes to qsn-1 bytes makes the walk a SUBSET of the old run, and it is exact ONLY IF: for every dictionary term w, w and stem(w) share at least len(stem(w))-1 leading bytes. Porter rewrites suffixes only, and the rewrites that can change a byte inside the stem's span (y to i, biliti to ble) touch at most its LAST byte -- but that is an argument about the textbook, and the estate's stemmer is nx_stem. So this gate does not argue: it walks EVERY term of EVERY live segment (no sample), stems each with the same nx_stem the scorer calls, and counts the terms that violate the bound. One violation is RED and the cut does not ship; the violators are printed as the worklist. The predicate is a pure function so KAT and neg-control teeth pin its arithmetic before the census runs. The shard path probes the manifest to survive the buildroot cwd anchor (nx_livemap_fast_gate's lesson); argv[1] overrides the prefix. license_tier: ORIGINAL No hw writes (Rule 26).