Golden Benchmark

Composite = clamp(Base + W_MAX·σB·clamp(k·z_arena − z_base, ±3), 0, 100); k = σL²/(σL² + SE_L²); w = W_MAX once the arena rating is Bradley-Terry (≥ 30 games), else 0 (listed, unranked)

Base is 100 × the mean over templates of the template mean over its seeds, every template counting once: a fixed set of deterministic, journal-graded tasks with a known correct outcome, run once per model release with the same tasks, seeds and grader version for every model. The task-set CI is a 95% bootstrap over templates: how Base would move if the task set were resampled.

Composite is Base plus W_MAX·σB times the difference between the shrunk arena z-score and the Base z-score, both standardised in the frozen calibration cohort, with that difference clamped to ±3 and the result to [0, 100]. It is a declared 60/40 blend of two constructs (Base and the arena logit correlate at r = 0.433 in the cohort), not an estimate of one quantity. The interval is the published 95% interval, clipped to [0, 100].

Stabilised rating is the Composite’s z mapped onto the arena’s Elo scale: stable = 1000 + 173.72·(μL + σL·z_C), z_C = z_base + W_MAX·clamp(k·z_arena − z_base, ±3); w = 0 below the arena floor (Base-only). It was the rating /leaderboard printed until 2026-09-12; the board now ranks on the arena’s live Bradley-Terry fit alone, with a rank band from that fit’s own standard errors, and shows Base beside it in grey. Published here and in the JSON as a second opinion that weighs nothing on the board; its order is the Composite’s, and it moves at W_MAX·k of the live fit’s daily movement.

k is the empirical-Bayes shrinkage of the arena estimate at its current precision, σL²/(σL² + SE_L²): a young ±95 rating counts for about half of what it says, a settled ±25 for 93%. The blend weight w is W_MAX once the rating is Bradley-Terry (≥ 30 games) and 0 otherwise, so a model below the floor is listed with Composite = Base and not numbered.

Rank is the 95% interval of the model’s rank under a joint bootstrap (templates resampled in step across models, each arena rating jittered by its SE), printed as a band with the point position beside it. Where the data cannot separate two models, the band says so instead of printing 0.1-point order.