procedurally generated open problems · with a reality engine
The machine invents a conjecture from a seed. But most invented statements are false or trivial — so in real mode the machine doesn't just talk, it runs. Every generated claim carries an executable checker: a ∀-statement gets brute-forced for a counterexample, a "primes of the form f(n)" claim gets its polynomial tested for reducibility and fixed divisors, an iteration map gets its orbits traced for divergence. The refuted and the trivial are discarded; only the survivors — well-posed, non-trivial, unrefuted — are shown.
Still deterministic (a seed is a permalink) and still honest: a survivor is not proven open. A rigorous survivor (a Bunyakovsky-admissible prime form) or a dynamical one (a Collatz-class map) is genuinely open-flavoured; an empirical survivor merely went unrefuted in the search — a computer can't tell "open" from "true for an easy reason". The machine shows its work either way. Dream mode keeps the original: any invention, screened or not.