Family 116: explicit ordered-algebra witnesses and large companion costs

Characteristic-zero pages 1-12, positive-characteristic pages 1-4/10-13 and rational-formula pages 1-4/16-21 were read, with five construction pages visually inspected. The family scope, two Comparators/configs and two solution entry files were read. Imported formal closure, kernel verification and complete companion proofs remain unaccepted.

The rational division-free tuple has explicit dimension 2ns^2 and entries that admit a linear-time-in-dimension structured action in rational arithmetic. A bounded visible-tree reference returns finite nonzero matrix witnesses and preserves zero/exhaustion as conditional or unknown. 726 finite controls include independent exact words, direct matrix entries, SymPy, model differences and limits. Two tiny conventional matrix presets already catch the generated errors cheaply; no commercial or general algorithm advantage is established.

The prime-field companion's dense dimension is 16,306 at n=2,s=3, while the inverse-formula list visits over 9*10^25 triples already at n=s=1. These literal backends are deferred. Keep a specialist rewrite-witness SDK at low confidence; the facility-planning product retains priority. Revised dossier, comparison.