About

One place to learn a mechanism, test it, and see where it stops being understood.

Continuous Function is a mathematical atlas, a notebook, and a small research lab that share the same objects. A concept you read about in the Atlas is the same object you predict against in the Lab and the same object a research program cites when it runs out of certainty.

Maintained by: One person
Accounts: None
Your data: Stays in this browser
Cost: Free

The three surfaces

They are not three products. They are three things you can do with one set of objects, and the site is arranged so that moving between them never means starting over.

The Atlas — what is knownReadingConcept notebooks with intuition, mathematics, code, and an interactive figure, plus the mathematical foundations underneath them. Read-only, and the largest part of the site.The Lab — what you can testDoingInvestigations that take your prediction before showing the calculation. Eight transformer systems stations, guided paths, and single-sitting checks.Research — what is not yet knownOpenPrograms published by claim boundary and evidence state rather than by progress. Currently one deep program, Atlas-64, and one methods track.

The loop, concretely

Every investigation starts with a question you answer before any result appears. Your answer is locked in first, so the calculation has something honest to compare against. There is no score, and wrong guesses are the useful ones. After the comparison you change one input and watch the calculation respond.

Every result shown is calculated in your browser from the settings displayed. None of them is a measurement taken from a production model or a server. Where a page cites a paper or a course, the source is linked next to the claim it supports.

What is recorded

Your predictions and saved comparisons stay in this browser. No account is created, no score is kept, and nothing you enter leaves the browser. Clearing this site’s browser data removes the record completely.

What does not exist yet

Not built

There is no AI assistant answering on this site, no account system, and no community features. Concept pages carry an Object Companion panel, but it is a copy-only prompt tool: it composes a prompt from the page and your selections for you to paste into an AI tool you already use, and it sends nothing anywhere itself.

The research programs are published at proposal stage and say so. Atlas-64 has verified sources, frozen protocols, and an audited evaluator, and it has not loaded a model. When any of this changes — an assistant, an account, a model result — it will be described here before it appears anywhere else on the site.

Where this is going

The near-term work is a single verified experiment: removing the artificial routing signal from the one Atlas-64 result that still stands, and reporting whatever comes back. A negative result is a publishable outcome here and would be reported as one.

The most useful thing a reader can do right now is disagree with something specific. The Atlas-64 report ends with four claims worth attacking. The contact link in the footer reaches the person who wrote them.