MathGround: joules, not tokens.

The cost of intelligence is energy, and most of what a system must decide is not a generation problem. MathGround is the substrate the rest of the lab's work runs on: every decision is priced in joules and carries a receipt, and a request resolves at the lowest tier whose grammar covers it — a deterministic lookup, then a closed-form formula, then a sparse solver, and a stochastic model only as a last resort. Every claim carries a replayability class — deterministic, retrieved-and-cited, composed, or model-generated — enforced at the type level, so a generated answer can never be relabeled as ground truth. On commodity silicon the model tier costs orders of magnitude more energy than a cited composition; declining to invoke it unless the request demands it is where the joules are saved. The same substrate carries the lab's robot-policy harness: every frontier architecture behind one action space and one energy meter.