The rule behind your numbers — at1 explain

The shortest program that reproduces a sequence is its explanation. at1 explain 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 NO_GENERATOR rather than inventing one.

Use it

# recover the generating rule for an integer sequence
at1 explain fibonacci.txt
#   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

# random data has no rule, and it says so
at1 explain random-noise.txt
#   NO_GENERATOR: no rule explains all terms

What it guarantees

  • Verified — solved on a prefix, then checked on every remaining term.
  • An MDL win — the returned program is shorter than the data it explains.
  • Refuses noise — no rule means NO_GENERATOR, never a false explanation.

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. To recover the invariants and marginals across a whole table, see the artifact service.

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