AT-1 Explain

Get the rule behind your numbers, in one readable line

The shortest program that reproduces a sequence isits explanation. AT-1 searches a program space in description-length order and returns the exact generator as a human-readable one-liner — verified on every term, shorter than the data. When no rule fits, it says so, rather than inventing one.

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x[n+2]=…: recovers recurrences, affine, polynomial, periodic rules
verified: solved on a prefix, checked on every remaining term
MDL win: the program is shorter than the data it explains
refuses noise: no rule? it says NO_GENERATOR, no false explanations

at1 explain fibonacci.txt
#   AT-1 Explain: x[n+2] = 1*x[n+1] + 1*x[n], x[0]=0, x[1]=1
#   verified on all 13 terms; program is shorter than the data.
at1 explain random-noise.txt
#   NO_GENERATOR: no rule explains all terms.

Scope. This is the fast, readable answer over integer sequences (constant, affine, quadratic, periodic, linear recurrences). For a byte-exact, self-contained regenerator container over richer generators, use AT-1 Discover.

Billed per explanation, first 5,000/month free. See pricing.

Compression as a way of asking what the rule is

If a sequence was produced by a rule, the shortest way to store it is the rule itself rather than the values. So searching for the smallest program that reproduces a series is the same search as asking what generated it, and a result that compresses far better than the data has any right to is evidence that a rule was found rather than a coincidence fitted.

What comes back is a program you can read, not a model you must trust. You can check it against values it has never seen, which is a stronger test than any goodness of fit statistic, because a wrong rule that happens to match the data you showed it will fail on the next value and say so immediately.

It usually finds nothing, and that is correct

Most real series are not rule governed. Measurement noise, human behaviour and market prices have no short program behind them, and a tool that always returns an explanation is producing fiction on demand. This one returns nothing far more often than it returns something, which is what makes the occasions it does return a rule worth reading.