We validate and verifyChat assistants and coding agents are excellent general tools. Lemma adds what scientific work needs: the software, the compute, the checks and the sources, ready in your browser.
Covers maths, CS and physics. Lemma does not replace peer review. How we measured it →
Each card is a real Lemma session, with the check it passed. Click a card to see the result, what Lemma built and how it was checked. Strongest today in physics, optics and engineering.
Check a paper's references, claims and equations.
Combine solvers such as Optiland and Tidy3D in one notebook.
Turn a paper's system into a live model you can change.
Reproduce a paper's figures live, next to the original.
A short, visual, interactive lesson at your level.
Find, read and compare the key papers on a topic.
Digitise a plot, then optionally fit a model.
Start from a working notebook and make it your own.
Solve a hard problem, check it, and play with the answer.
Rebuild a paper's model, check it, then explore where the authors didn't go.
Want to look inside? Open real Lemma notebooks in the showcase →
▶Play with sound · 1:16
The code behind every number, in plain view. Move a slider and the physics recomputes.
▶Play with sound · 1:17
Write your paper next to the chat, and Lemma checks it like a careful co-author.
▶Play with sound · 0:36
Lemma looks up each citation in your paper and flags the ones that do not exist.
▶Play with sound · 1:08
Anyone can open it in their browser, with no account and no install.
Lemma turns a paper into a live notebook: the original figures beside the ones its model recomputes, with the checks that show how well they agree. Open one: it runs in your browser, with no account.
Every figure from Fig. 1 to Fig. 17 beside its twin, with sliders for the link, the power delivery and the case temperature.
Every figure panel of the paper beside its reproduction, on the same axis ranges. Sliders recompute band structures and move a crosshair over the indicator maps.
Every figure recomputed live from the paper's equations, with values read off the paper's plots beside the model's. The original figures stay on arXiv; the twin links to them.
A result you cannot inspect is a guess. Lemma recomputes the results and looks up the sources, and its report says which claims hold, under which assumptions, and what it did not check.
I want a plan to numerically solve the steady state heat equation in the unit square with dirichlet BC equal to 0 in the axis X and Y, while t=1 in the other 2. Use finite differences, confirm convergence rate, then plot in 2D and 3D. Use viridis palette
Lemma is in open beta, and you can try it free. You can obtain extra credits through referrals and by joining a user group (contact@axiomatic-ai.com).
It is strongest today in physics, optics and photonics, and engineering, where the examples above come from. The published error benchmark covers mathematics, computer science and physics.
Interactive notebooks with the code of every step, plots, sliders and 3D views; an annotated PDF when it checks a paper; a verification and validation report; LaTeX compiled to PDF; and a BibTeX file for a literature survey.
Yes. Every step is code in a notebook, and each note in a report points to the script that checked it.
Your research stays yours. Axiomatic AI does not use your private work to train models or to build capabilities for other users without your explicit opt-in, and does not use it to race you to publication or patenting. For extra data protection, you can run Lemma on open-weight models. Read our commitment: Scientists own their work →
Long jobs keep running in the background, so you can leave and come back. In verification mode, Lemma takes you through all the steps, or runs them automatically. Larger projects can take many hours.
No. It does not certify that a paper is correct. It finds errors and shows its working, so that you and your referees can judge.
Bring a paper, a question, a problem set or a device. Made by scientists and engineers, for scientists and engineers.
Build a digital twin of https://arxiv.org/pdf/1911.04959
run model exploration
17 of 17 numbers in the paper reproduced, each figure redrawn over the original.
The paper gives one number, 3.23, for the tip of the region where microwaves strengthen superconductivity. Lemma varied what the paper kept fixed: the number changes, from 3.13 to 3.90. A prediction, not in the paper.
One of 9 findings beyond the paper.
Errors slip through review: in a survey of 459 recent preprints, more than one in three had at least one reference with a small error. Attach a PDF and Lemma checks its references, claims and equations, and marks each issue where it occurs.
Check a paper's references, claims and equations.
A lens system lives in millimetres, a grating coupler in nanometres, and each needs its own solver. Lemma combines multiple tools to solve one problem: here Optiland for the optics and Tidy3D for the chip, in one notebook.
show me a notebook with a basic lens (optiland) and grating coupler (tidy3d)
about 20 short follow-up messages to steer the design, such as combining the two solvers into one coupled system
Real solvers, such as Optiland, Tidy3D, QuTiP, Qiskit and DEVSIM, combined in one notebook.
Lemma reads the paper and rebuilds its optical system as a live model you can change, checked against the paper's claims.
Easier reading: watch a paper's physics come to life.
Here: a lithography metrology paper (Messinis et al., Optics Express 2021). Lemma rebuilds the microscope lens in Optiland and the wafer targets in Tidy3D.
Now add the near field with Tidy3D (my Flexcompute key is set; cap the cloud spend at 10 FlexCredits, and say the estimate before each submit). Take the structures from the paper: (1) the nano-scatterers used for the aberration calibration, and (2) the overlay grating targets. …
Reproduce a paper's figures live, next to the original.
Ask how superconductivity can come from repulsion. Lemma reads the literature, writes a short, visual, interactive lesson and checks its physics.
superconductivity in hubbard models
A short, visual, interactive lesson at your level.
Lemma finds, reads and compares the key papers on a topic, in an interactive notebook.
Graphene and 2D-material photodetectors: how does responsivity trade off against speed across detection mechanisms (photoconductive gain, photogating, photovoltaic, photothermoelectric, bolometric, waveguide-integrated)? Map every device on one log-log chart of responsivity vs bandwidth, coloured by mechanism.
Find, read and compare the key papers on a topic.
Lemma digitises a plot into an interactive notebook, then optionally fits a model.
Fig. 1a
Digitise a plot, then optionally fit a model.
Open a ready-made twisted-bilayer-graphene notebook, then ask for something similar: bilayer graphene on hBN.
can you show something similar for bilayer graphene aligned on hbn? make a new notebook
also make sure to show the band structure
Open a working notebook, play with the physics, then make it your own.
Attach a screenshot of a hard problem. Lemma solves it, checks the result numerically and builds a notebook you can play with to understand why.
Solve problem 3 from my problem set and turn it into an interactive notebook that teaches it step by step: the derivation, the effective potential with sliders for a and Ω, and an animation of the pendulum that checks the stability threshold.
Attach a screenshot of a hard problem. Here: Kapitza's pendulum, a pendulum that balances upside down on a vibrating pivot.