Research operating system
Verified mathematics.
Verified software.
Verified hardware.
Build once. Prove once. Run everywhere.
Most systems stop at code. Monogate carries evidence — from mathematics, to software, to hardware.
The pipeline
One source, carried to hardware — proven at every step.
- EMLone source
- Forgecompile
- Leanproof ✓
- MachLibmath
- RTLsynthesis
- FPGAon silicon ◦
- ESP32byte-identical ◦
- Evidencepacket · replay
Hover a stage to trace the flow. ● Lean is machine-checked proof (formal). ◦ FPGA / ESP32 are measured — byte-identical output on real silicon, not formal equivalence.
Four ways in
Where do you want to start?
Research
Mathematics, proofs, papers. The Khovanskii results, EML foundations, and the Lean library behind every claim.
Enter → 02Engineering
Forge compiles one source to real silicon — FPGA bitstreams, byte-identical ESP32, electronics, and the reproduction zoo.
Enter → 03Explore
Interactive surfaces — the math-to-art gallery, Glass Box, the Proof-Carrying Rescue Explorer, playable simulators.
Enter → 04Build
Install the compiler, read the docs, run the examples. Published packages on PyPI, source on GitHub.
Enter →Live from CI
The verification skyline
Numbers that can go down. Emitted by the build, not by marketing.
Live from status.json (machlib CI) — the real state, in progress. FPGA count from the hardware lane.
The evidence
See it. Don’t take our word.
Real reproduction-zoo artifacts — a proof, a 32-target emit, and hardware you can re-derive yourself.
theorem pid_step_bounded
(error prev_error integral kp ki kd dt : ℝ)
(h : dt > 0) :
OUT_MIN ≤ pid_step error prev_error integral kp ki kd dt ∧
pid_step error prev_error integral kp ki kd dt ≤ OUT_MAX := by
unfold pid_step
exact ⟨clamp_ge_lower _ _ _, clamp_le_upper _ _ _⟩
fn pid_step(error, prev_error, integral,
kp, ki, kd, dt: Real) -> Real
where chain_order <= 0
requires (dt > 0.0)
ensures (result >= OUT_MIN)
ensures (result <= OUT_MAX)
{
clamp((kp*error) + (ki*integral)
+ (kd*(error - prev_error))/dt, OUT_MIN, OUT_MAX)
}
$ python -m efrog.lean_corpus # decompile every example to EML, emit the Lean # proofs, then actually run `lake env lean`: Efrog.sigmoid_eml_consistent ✓ verified (clean) Efrog.while_sum_chain_order ✓ verified (clean) … verified 32/32 theorems — Lean-checked, sorryAx-free
These are real artifacts — pid_step and rc_filter re-derive with make verify-proof; the efrog tile re-derives with python -m efrog.lean_corpus. The full tree — 32 targets, proofs, hardware captures — lives in the reproduction zoo →
Auditable by design
Every number here can go down. We publish what we retract.