❓ How to use this site
Inversion height two in the free field of the free group: strict hierarchies and a non-membership criterion — the paper, statement by statement. Each piece below can be shown on the page: «Show me».
The blueprint of the paper
Every statement of the paper, how they depend on each other, and what was checked besides the proofs. This short tour shows the pieces, one at a time.
Two ways to read
📄 Paper shows the statements and proofs as in the paper. 🔍 Explore adds explanations, figures and labs.
Show meThe sections
The sections of the paper. Click one to read it; every statement has its own link.
Show meA statement
Each statement carries its number in the paper. Its proof is right below, and you can fold it.
Show meThe paper at this statement
📕 opens the paper (PDF) at the page of this statement — in English or in Español.
Show meWhere it sits
📍 shows this statement on the map of the whole paper, highlighted; from there you come back.
Show meCite it, or tell the author
❝ gives the citation of this statement, ready to copy. ⚠ writes to the author about it.
Show meChecked by a computer
Point at a statement like this one: L∃∀N shows the parts checked by the Lean proof assistant, with the code.
Show meTry it yourself
🧪 A lab runs the paper's own computations in your browser, with values you choose. Nothing to install.
Show meFigures in motion
The figures of the paper, drawn live: drag to turn a 3D figure, press ▶ to animate. The paper's static figure is one click away.
Show meThe whole paper on one page
🗺️ Map: the main results, the tools they use and what they serve, on one page.
Show meThat is all
❓ Tour repeats this tour; «How to use» explains each piece. Enjoy the paper.
Your browser can translate these pages (the formulas stay as they are); the paper itself has its translations in the 📕 PDF view.