# Dyck-1 independent replication protocol

Locked before training at **2026-07-21T14:32:51+04:00**.

## Motivation

The discovery cohort (seeds 0–14) found a large far-OOD exact-match gain for
`p=.5` over `p=0`, but the primary paired test was marginal (`t=2.247`,
two-sided threshold `2.145`) and its balanced-accuracy sensitivity check did not
clear the same threshold (`t=2.127`). Because the decision to collect more seeds
followed that result, a pooled 30-seed test would inherit optional-stopping bias.
Seeds 15–29 are therefore a separate confirmatory replication cohort.

## Frozen experiment

- Task: Dyck-1.
- Arms: `p=0` and `p=.5`.
- Training seeds: 15–29, paired across arms; no overlap with discovery seeds.
- Six isolated five-seed jobs: seed starts 15, 20, and 25 for each arm.
- Configuration: exactly `scripts/dyck1_seedscale.py::job_config` — two physical
  LoopDeepNorm blocks, `R=8`, recall-add, fixed schedule, `n_ref=max`, batch 128,
  AdamW LR `3e-4`, Muon LR `.01`, 2,500 maximum steps, curriculum enabled,
  truncated-BPTT window `k=8`, and MPS/bfloat16.
- Checkpoint selection: best ID validation accuracy using seed 4242, unchanged
  from Stage 1a.
- Held-out evaluation: 2,048 shared examples per bucket, evaluation seed
  20260721 (bucket-specific offset as implemented), inference `R=8`.
- All 30 runs will be trained and reported regardless of interim outcomes.

## Confirmatory endpoint

The sole confirmatory endpoint is per-seed far-OOD exact-match accuracy on
lengths 62–80. For each seed, compute `p=.5 - p=0`, then apply a paired,
two-sided t-test across replication seeds 15–29 (`n=15`, `df=14`, `alpha=.05`,
critical `|t|=2.1447867`). Replication succeeds only if the mean difference is
positive and `t > 2.1447867`.

The replication means, mean paired difference, paired t-statistic, and decision
will be reported regardless of direction. No task, bucket, metric, seed, or
checkpoint will be excluded after training except a documented technical failure
that prevents a checkpoint from being produced.

## Secondary and descriptive analyses

- Far-OOD balanced exact match on the same replication cohort.
- Near-OOD (22–40), mid-OOD (42–60), and ID (2–20) exact match.
- Discovery (seeds 0–14) and replication (seeds 15–29) results side by side.
- Pooled 30-seed mean differences and 95% confidence intervals as descriptive
  estimates only; no pooled confirmatory p-value.

Any analysis not listed above is exploratory and will be labeled as such.