Editorial method
Evidence is not proof
Mathomaly treats a successful experiment as evidence. Every exploration states what was calculated, over what range, which result is mathematically established, and which questions remain open.
The seven status labels
Every substantive claim on the site carries exactly one of these, together with its scope and the date the status was last checked.
- Proved
- Established generally by a mathematical argument.
- Exhaustively checked
- Every case in a stated finite range was checked.
- Conjectured
- Precisely stated and believed, but not proved.
- Open problem
- No accepted proof or counterexample is known for the stated question. This describes an unresolved mathematical problem, not an unchecked citation.
- Disproved
- A counterexample or contradiction is known.
- Observed in this run
- Produced by the current configuration only.
- Heuristic
- A model suggests the behaviour without establishing it.
What a computation can and cannot settle
Most of what happens on this site is computed in your browser, as you use it. That makes it evidence about the cases it actually covered, and nothing more - with one important exception.
When a space is finite and every case is checked, exhaustion is a proof. Kaprekar’s four-digit routine has exactly 10,000 states. Checking all of them settles the question completely, and the state-space diagram on that page is not an illustration of the argument - it is the argument.
That page is also a good example of how easily this goes wrong. Because the routine sorts its input, it looks safe to treat the 715 digit multisets as the states and check only those. It is not: 6174 and 4176 share their digits but sit at different distances from the answer, so the shortcut quietly understates how long some starts take. We made exactly that mistake, and the distribution on the page was wrong until an independent brute force disagreed with it.
Checking finitely many examples does not by itself prove a claim about an infinite space. The Collatz map has been verified far past any number you will ever type, and it remains unproved. A result panel that says “checked to 10²⁰” is telling you about 10²⁰ numbers, not about all of them. A single counterexample, however, would disprove the universal claim.
Wherever a number came from a computation, the interface states:
- the exact range covered;
- whether the arithmetic was exact or approximate;
- whether the space was enumerated completely or sampled;
- the version of the algorithm that produced it.
Nothing runs unbounded. Every long computation shows its limit, reports honest progress and can be cancelled - and a cancelled computation produces no claim at all rather than a partial one.
How a laboratory is laid out
Every exploration uses the same arrangement, so it only has to be learned once.
- The figure is on the left, with its views as tabs above it and, beneath it, a key to its marks, how to read it, and what it currently shows.
- The buttons that move the figure are directly under it: step, run, reset, flip, play another game. On a phone that bar stays at the foot of the screen while the figure is in view, so you can press and watch at once.
- Everything you set is in the column beside it, always in this order. First the page asks you to make a prediction: a number, committed before the figure shows it. Then it offers to change the assumption the pattern leans on, one button that breaks it. Then come the laboratory’s own controls, and last the named cases worth seeing. On a wide screen this column stays beside the figure as you scroll; on a phone it follows the figure.
- Your guess goes on the figure. Once a prediction is locked in, the figure is set to the case it was about and carries your number beside the count, so the comparison is made where the answer is.
- Below the laboratory are prompts to try, then your trail: the guesses, cases and questions you have saved, which a link can share.
Rules we hold ourselves to
- An open or conjectured claim cannot publish without at least one source and a verification date. This is enforced by the content schema - a page that breaks it fails the build rather than shipping.
- “Checked to N” must state N, the algorithm, whether the arithmetic was exact, and the assumptions involved.
- Computation performed in your browser is always labelled as local evidence.
- A proof sketch must say which steps it omits, rather than presenting itself as complete.
- AI assistance may help draft prose. It may never set or change a claim’s status, and no explanation is published on its authority.
- Where sources disagree, or a result is recent, the page says so instead of flattening the uncertainty into a confident sentence.
How we check citations
Publication records and mathematical claims need different kinds of evidence.
39 citations on this site still have unresolved bibliographic details. Of 162 citation entries, 123 have a checked publication or database record. Repeated references on different explorations count as separate entries.
A bibliographic check confirms details such as the author, title, date and publication. Each reviewed citation records its date, evidence links, method and limitations. The September 2026 audit was AI-assisted, using source texts, publishers, author records and library catalogues. A catalogue check is not a claim that a person read the paper.
This is separate from mathematical verification. Some results are derived on the page, some are checked over a stated finite range, and others rely on a cited theorem whose proof we do not reproduce. Their claim labels describe those distinctions. An unresolved citation means Mathomaly still needs to confirm its details, not that the mathematics community has left the theorem unproved.