For the sceptical reader

This library is written by AI, and it is built for readers who treat that as a reason for caution. This page lists what a careful reader can check.

The failure mode

Generative AI earned its reputation for slop honestly: bulk output, unstated sources, no checking, and nobody answerable when it is wrong. Each part of that has a mechanism aimed at it here. Every statement and every proof carries a provenance label naming where it came from. Every proof is parsed by a mechanical checker, read by two judges from different model families working to break it rather than approve it, and audited by a human before publication. Every item carries a Report an issue control, and reports reach us directly; a confirmed error is corrected on the record, and the declared dependency graph lists exactly what rested on it, so a correction stays bounded.

These mechanisms make errors rare. They cannot make them impossible; the About page states the limits.

Where the statements come from

The mathematics here is overwhelmingly human in origin; the pipeline’s work is faithful restatement, organisation and proof, with every departure labelled. Of the 5,333 items published today, 2,596 state a result exactly as an identified published treatment gives it and 2,413 adapt one. 260 statements were formulated by AI, and 64 predate the two-label scheme and are intentionally unclassified.

The AI-formulated statements are labelled as such, and they are barred from being load-bearing: nothing in the library is allowed to depend on one. An undetected defect in a generated claim therefore stays where it is instead of propagating through the corpus.

Phase-stratified proofs

Every proof is written as numbered steps in labelled phases, each step ending in a bracketed note naming exactly what it follows from: an earlier step, a stated hypothesis, or a result the library has already established. The strictness does mathematical work. A model writing in this format cannot wave its hands, because a step with no named justification does not parse. A judge reading it checks one bounded inference at a time instead of holding a page of prose in its head, which is where machine verification is most reliable. And a wrong proof is wrong at a specific numbered step, which is where you will find it.

Your part

Working through a proof step by step is how the mathematics becomes yours, and the format makes that checking cheap: every claim names its origin, every step its justification, and every prerequisite is a page or two away with a proof of its own. Sceptical reading is welcome and encouraged, it’s the only path to true understanding.

Against the alternatives

Wikipedia is a fine encyclopaedia and a hard place to learn a subject: articles assume different backgrounds, notation shifts between pages, and proofs are sketched or absent, so study becomes link-chasing. Here the corpus is one acyclic dependency graph in one notation; every result names its exact prerequisites, each carries a dependency level, and a reader can enter at their own level and climb.

A chatbot answers fluently, cites nothing, and its answer is gone when the window closes. Every claim here is published at a stable address, carries its sources, its provenance labels and its verification record, and is accountable: when one is wrong, it can be reported, corrected on the record, and traced through everything that depended on it.

The pipeline behind all of this is animated in how a level is built, and a single proof is followed from draft through rejection and repair in authoring a proof.