# Pre-registration — Study 1 confirmatory replicate (equal-vote design) — 2026-07-02

Filed before the replicate run, per Amendment 1 to the 2026-06-25 registration.
This replicate exists to (a) confirm, on fresh items and as a *registered*
prediction, the debate-inflation finding that the Study 1 correction reported
exploratorily, and (b) turn the vote-count-granularity diagnosis from a
re-analysis argument into a designed result.

## 1. Design — four arms, one temperature, equal votes

All arms: `claude-haiku-4-5-20251001`, temperature **0.7 everywhere** (the
temperature asymmetry of the first run is removed), prompts byte-identical to
the Study 1 run (`instrument/swarm/debate.py`, `instrument/baseline.py`),
external scoring only, answers never in agent context.

| Arm | What it is | Votes | Calls/item |
|-----|-----------|-------|------------|
| A3 | 3-agent debate swarm, 2 rounds (round-0 recorded) | 3 | 6 |
| B3 | 3 self-consistency resamples of one agent | 3 | 3 |
| A7 | 7-agent debate swarm, 2 rounds (round-0 recorded) | 7 | 14 |
| B7 | 7 self-consistency resamples of one agent | 7 | 7 |

Compute note (registered up front): this design holds **votes** equal, not
tokens. A debate arm spends roughly 2× the tokens of its resample counterpart
(two rounds). If that extra compute bought accuracy, the comparison would
flatter debate; the prediction below says it will not. The within-swarm primary
contrast (round 0 vs post-debate) is compute-neutral by construction.

## 2. Battery — seeded held-out split, Study 1 items excluded

Pool: `load_gsm8k(60)` + `load_mmlu(180)[:60]` + `load_triviaqa(60)` + the
hand-authored non-code control slice. **Every task id that appeared in the
2026-06-30 Study 1 run is removed from the pool before splitting.** The pool is
then split with `Battery.split(holdout_fraction=0.5, seed=20260702)` and the
**test half** is run, capped at the first 20 items per public source in split
order (cost control, stated here rather than decided after seeing data).
Composition will be reported with the run. Difficulty stratification and the
hard-tail question are **out of scope** (they are Study 2 requirements; the
strata do not exist in the current loaders and will not be improvised).

## 3. Registered predictions (stated so they can fail)

**P1 — PRIMARY, confirmatory (the Amendment 1 registered outcome).** In BOTH
debate arms (A3 and A7), post-debate overconfidence exceeds round-0
overconfidence: the paired item-level bootstrap 95% CI of the delta
(post − round0) excludes 0. Prior exploratory estimate: +0.066
[+0.020, +0.116] at n=66.
*Falsified if* either arm's CI includes 0. If falsified, the site and paper
will report the failed replication with the same prominence as the original.

**P2 — granularity, designed test.** The apparent resolution advantage of the
Study 1 baseline was an artifact of vote count, not architecture. Concretely:
(a) at equal votes, |AUC(A3 post-debate) − AUC(B3)| has a CI including 0; and
(b) more votes buy resolution *within* each architecture: Brier(B7) < Brier(B3)
and Brier(A7 post) < Brier(A3 post), each directionally.
*Falsified if* (a) the equal-vote AUC gap is significant in the baseline's
favour (the architecture, not the vote count, explains discrimination), or
(b) 7-vote arms are not better-resolved than 3-vote arms.

**P3 — secondary, estimation only.** The equal-vote cross-arm confidence gap
(A_k post-debate minus B_k, for k=3 and k=7) is estimated with CIs. Prior
observation: +0.036 [−0.015, +0.086]. Predicted direction: positive. We do
NOT commit to significance at this n; the estimate feeds Study 2 power design.

**Descriptives registered in advance** (reported, no hypothesis): accuracy per
arm; per-source overconfidence; round-0 unanimity rate per debate arm;
diversity by round.

## 4. Analysis conventions (pinned)

10-bin equal-width ECE; tie-corrected Mann-Whitney AUC; paired item-level
percentile bootstrap, B=10,000, seed 20260702 (`instrument/metrics.py`,
unchanged). Analysis script published with the run. No slicing beyond what is
registered above.

## 5. Honesty constraints carried forward

The Anthropic API accepts no seed parameter: runs are not seed-reproducible;
model id, temperature, prompts, item ids, and analysis seed are pinned instead.
Estimated cost ~1,800 calls / ~$5 at Haiku pricing. Mock-validated before any
paid call. Anything in section 6 of the 2026-06-25 registration ("what would
make us NOT report") applies unchanged.