OpenIE · Physical AI Library · Rust

Math-Ground AI

Physical AI that tells you what it just cost.

A Rust library where every call returns a picojoule receipt. Closed-form physics where it exists. Derived safety envelopes. Lyapunov-traced controllers. Anytime-valid verification.

live · fft · 256-pt
method · tdp_estimate + landauer_floor · this device
wall_ns / op
E_floor / op
E_tdp / op
μ apparent
~ above Landauer floor

Closed-form · mgai-auto

Safety envelopes are derived. Not trained.

The RSS minimum-following-distance is a function of ego velocity, reaction time, and deceleration capability. Three kinematic parameters. One formula. No training set, no weights, no out-of-distribution failure mode.

dmin(v) = v·τ + v² / (2·amin)

Mobileye RSS · Shalev-Shwartz, Shashua 2017

RSS minimum following distance vs ego velocity d = 58 m 0 30 m/s 0 120 m ego velocity safe distance τ = 0.4 s   amin = 4 m/s²

Phase portrait — trajectories spiraling into the origin x &xdot; V(x, &xdot;) decreasing along trajectory

Lyapunov-traced · mgai-control

Controllers prove their own stability.

For every controller, the algebra carries a Lyapunov function that decreases along every trajectory. That’s the proof. No emergent behavior where you needed a guarantee.

V(x, &xdot;) = ½(x² + &xdot;²)   with   dV/dt < 0

Energy accounting · mgai-telemetry

Every call emits a picojoule receipt.

A metered call returns the value and its energy cost at the call site, against a cost model tied to a specific silicon target. You know what the pipeline cost before you ship it to a battery-powered drone.

A 400-step integrated run on a mobile manipulator — RSS safety, DAM-VLA routing, digital-twin divergence — settles around 87.9 J end-to-end.

Math-Ground AI · receipt
step 207 / 400
  • RSS safety envelope 37.2 pJ
  • DAM-VLA route 6.2 µs · 4.1 pJ
  • CAD transition (closed) 1.8 ns · 0.2 pJ
  • Diffusion step 11.4 µs · 8.7 pJ
  • Verifier (e-value · accept) 0.8 µs · 0.6 pJ
  • Per-step total 219.7 pJ
total · 400 steps 87.9 J

Simply-supported beam under a centered load — closed-form deflection F L δ

Real physics · cad-future

CAD is the world model. Closed-form.

Parametric mechanics has solved engineering problems for forty years. The planner consumes CAD as ground truth, not as a learned approximation of itself. The planner trees over candidate states with the math doing the simulation.

δ = F·L³ / (48·E·I)

Composition · verity-cascade

Cheapest tier that clears the bar.

A query enters the cascade at L0 — lookup, picojoule cost. Each tier escalates only if the lower one didn’t suffice. An LLM is the escape hatch, not the default. The router picks the tier whose receipt clears the spec under the budget.

The bar lines are the energy receipts. A small LUT hit is two orders of magnitude cheaper than a small-model inference; that gap is what the cascade exists to spend wisely.

Cascade tiers L0–L5 with characteristic per-call energy L0 LUT ~ 0.2 pJ L1 Memo ~ 1 pJ L2 Heuristic ~ 50 pJ L3 Closed-form ~ 5 nJ L4 Small model ~ 5 µJ L5 LLM escape hatch · ~ 500 µJ cheaper ↑

WASM bundle size accounting 398 KB total runtime · 190 KB viewer · 36 KB scene

WASM · mgai-viz

It runs in your browser.

The full runtime plus the WebGPU viewer ship in 398 KB of WebAssembly. No cloud, no wait. Joints move, joules tick, the receipt prints client-side.


Lineage · Deep Space 1

Plan. Execute. Diagnose.

NASA flew this architecture in 1999. A constraint planner, a reactive executive with structured fallbacks, a model-based diagnoser that verifies by conflict-directed search. We picked up where they left off.

Plan / Execute / Diagnose pillars and data flow Plan CSP solver QueryPlan Execute RAPs · orchestrator RetrievedItems Diagnose conflict search VerificationReport RE_ROUTE (bounded) · recovery action Muscettola 1998 · Williams & Nayak 1996 · Pell 1997

math ground dot AI

Built on math. For the physical world.