Evidence
How do you know?
An idea, an example, a computation, a computation someone has checked, a result published in the literature, an open conjecture, a claim that turned out to be wrong — these are not the same thing, even when they sound similar. An answer is interesting. Knowing why you should believe it is part of the mathematics.
From idea to public claim
Every mathematical statement on this site follows the same path before it can be stated publicly.
- Computation. A program or a researcher produces a result — an example, a search outcome, a candidate proof step.
- Verification. The result is checked independently: reproduced, compared against a published source, or validated against a deterministic rule.
- Claim ledger. What may actually be stated publicly is recorded in one place, with its evidence status and where it came from.
- Public presentation. Wording on this site is never allowed to say more than the ledger entry it comes from.
Four evidence states
Every entry in the claim ledger carries exactly one of four statuses. None of them mean “true” on their own — they say how a claim was checked.
- Primary
- Checked directly against the original source — the published paper, its LaTeX, or a source-code archive.
- Computed
- Verified computationally inside this project. Not checked against an external source.
- Indirect
- Consistent with a known result, but the primary source has not yet been checked directly.
- Rejected
- Previously proposed, then found to be false or unsupported. Kept on record so it is not proposed again.
These four statuses, and their meanings, are set by
MATH_CLAIMS.md itself — the wording above is a
plain-English translation, not a redefinition.
Finite is not infinite
A computation can map an enormous finite region exactly. It still does not tell us, by itself, what must happen forever. “A long example was checked and found clean” and “an infinite example exists” are different kinds of claim — not a weaker and a stronger version of the same one. This project keeps them labelled as what they are, wherever they appear.
The public claim ledger
MATH_CLAIMS.md is the project's sole authority for what
it asserts mathematically. Every public mathematical statement traces
back to a row in it.
Each row records a claim, exactly where it came from, and one of the four statuses above. It is a plain text file, kept in the open alongside the code, so anyone can read the same entry this site is summarising.
The ledger currently contains some Finnish-language internal descriptions, migrated to English gradually rather than all at once. Its status fields, sources, and the figures this site is allowed to quote all remain inspectable regardless.
Computation and verification
Depending on the claim, verification here can mean exact string equality, a deterministic checksum, an independent re-run, an exhaustive search over every case in a stated range, a direct character-by-character comparison against a published source, an automated regression test, or a deliberate attempt to break a safety check by feeding it something it should reject.
Not every claim uses every method — the ledger records which ones were actually used for each row. Verified computation answers the finite question it was built to check. It does not, on its own, answer a stronger infinite one.
What happens when something fails
A failed approach, an incorrect conjecture, or a claim that turned out to be wrong is not deleted here. It is kept visible, with the reason it failed, in a dedicated public record. Dead ends are useful research evidence: they save the next person from spending a week rediscovering the same wall.
Open means showing not only what worked, but also what did not.
Inspect it yourself
Open collaboration, same evidence standard
Participation here is open — researchers, developers, students, educators, and independent contributors are all welcome, and no institutional affiliation is required. Contributions can be mathematics, computation, verification, software, documentation, explanations, testing, or research tools.
Being open does not mean claims go unreviewed. Anything accepted as a public claim still passes through the same evidence and review process described above, whoever it comes from.