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.
The receipt above prices one decision. This bench runs the whole loop: provable control, with the joules attached to the proof.
The same decision, priced twice: what the work costs against what the device costs →
A lookup costs about a picojoule of work and about half a millijoule of device. Both numbers are correct and they differ by nearly nine decades, because idle device-seconds dwarf the operation. An energy figure is a coordinate, plane times model, never a fact.
mathground.ai ↗Run a request: its latency is measured, its energy priced against real device power measured on silicon (macmon), and the receipt signed on-device with a real ECDSA key. Tamper with the replayability class and the signature breaks, provenance you can verify, not just assert.
In the field · the frontier is consolidating into world-action models that reason, generate, and act in one system (NVIDIA Cosmos 3, 2026), and into routing and cascades that fall back to a cheaper model when it suffices. MathGround takes the axis they leave open, energy as the unit, and a replayability class on every answer.
↓ Whitepaper · PDFRead online◆ Living paperTechnical Report TR-2026-06 · Institute for Physical AI @ JBI
Pricing a decision in joules and signing the receipt works today, and it runs the rest of this lab. What is left is agreement rather than instrumentation, which is a good position to be in. A modelled figure, a stand-in measurement and a metered one are three different claims, and most published comparisons still mix them. A shared convention for saying which is which would make a decade of results comparable to each other.
One of eight, and only one of them is physics. How we read a frontier →