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Algorithm 1: Meta-Research with a Learned Search Controller

Inputs:
    Task T
    Search budget B
    Seed prompt p0 initialized from the task description
    Controller model M
    Proposal model G (GPT-5)
    Number of proposals per round N

Initialize:
    best_score ← -∞
    frontier ← ∅
    prompt ← p0
    history ← ∅

for t = 1, 2, ..., B do
    1. Prompt mutation:
        prompt' ← M.mutate_prompt(prompt, history, frontier)

    2. Candidate generation:
        C = {c1, c2, ..., cN} ← G.generate_solutions(prompt')

    3. Candidate scoring / selection:
        a_t ← M.select_candidate(C, history, frontier)

    4. Evaluation:
        score_t, feedback_t ← Evaluate(a_t, T)

    5. Frontier update:
        if score_t > best_score then
            best_score ← score_t
            frontier ← frontier ∪ {a_t}
        end if

    6. Store experience:
        history ← history ∪ {(prompt', C, a_t, score_t, feedback_t)}

    7. Learning signal:
        reward_t ← FrontierImprovement(score_t, best_score before evaluation)

    8. Controller update (during training only):
        M ← Update(M, history, reward_t)

    9. Prepare next round:
        prompt ← prompt'
end for

Return:
    Best solution found within budget B