Baseline

When a round opens, the gate computes the head’s ability θ_h (the MAP of the head’s own pass/fail on gate-pool tasks: its winning candidate run and its head runs, under the fitted model) and sets each task’s inclusion probability:

w_i is the task’s share weight (size shares: each environment counts by its size, so every task has the same w_i). Probabilities are capped at cap and any excess is spread over the uncapped tasks. Each task is then included independently with probability π_i, using a commit-reveal seed fixed by a future block hash:

The knobs, with the live values:

• floor = 0.10 — the uniform share of the draw. A higher floor flattens the curve; at 1 the draw would be uniform.
• √ — the Neyman choice: drawing in proportion to the square root of the information (a standard deviation, not a variance) minimizes the variance of the estimate for a given sample size.
• a′ — the discrimination as the draw uses it: many tasks have little data, so a is pulled halfway (log scale) toward the pool median and clipped to [0.5, 2]× median; no task can get extreme weight from a noisy a.
• θh — recomputed when each round opens, so the draw follows the head: as it improves, the weight moves to tasks that are still hard for it. a, b are refit daily. Per-task a, b, θ_h and π_i stay private.
• N = 500 — the expected draw size. It scales the whole curve (Σ π_i = N).
• cap = 0.10 — the most any task can get; the excess is spread over the others. It binds under the information weighting: about 260 tasks sit at the cap.
• previous — from E497 to Nov 2 (prior-v1) the draw used √v_i, v_i = E[p(1 − p)] under Beta(s_i + 1, n_i − s_i + 1) from the prior table (s/n = the head’s solved/sampled counts), same N, floor, cap: the dashed curves.

The gain is a Hájek (inverse-probability ratio) estimate per environment, so the non-uniform draw does not bias it. Every drawn task i is weighted by 1 / π_i, with d_i = candidate minus head pass rate:

Live since Nov 2, 2026: IRT information weighting. The 2PL model: P_i(θ) = 1 / (1 + e^{−a_i(θ − b_i)}), with θ a checkpoint’s ability, b_i the task’s difficulty and a_i its discrimination (how sharply it separates slightly stronger from slightly weaker checkpoints), fitted (MAP) on every recorded checkpoint×task pass/fail (first fit: 365 checkpoints, 3.06M rollouts; refit daily, last fit —). I_i = a_i² P_i(1 − P_i) is the information a task carries about a small change of θ at the head, so the draw spends its ~500 tasks where a better candidate shows most. The checkpoints mostly come from one training chain, so a is weakly determined for many tasks; the shrinkage and clip above, the 10% floor and the cap bound what any one task can get. The estimate stays unbiased whatever the weights (Hájek, 1/π). Code: priors/baseline_v1.py (irt_score, theta_map) and priors/irt/.