GB-002 · Controlled Goldbach selection
Which structural rules actually help?
All seven policies receive the same allocation within each band of 100 even integers. Three intervals, three budgets, and four family removals test whether the full priority policy earns its complexity.
- Reference
- 3,000 even integers in three fixed intervals
- Budgets
- 20, 50, or 100 evaluations per interval
- Primary analysis
- Exact rational expected recall and variance
- Simulation check
- 2,048 seeds × 7 policies × 3 intervals
The target is the lowest 5% of partition-count ratios within each band, including ties. Uniform ordering inside a policy's priority groups makes expected recall exactly calculable. Simulation intervals measure Monte Carlo error on these fixed inputs; they do not estimate performance on larger integers.
Full policy and every ablation
Loading the controlled study…
| Policy | Expected recall | Exact fraction | Simulation mean | Priority minus policy (percentage points) | Monte Carlo interval (percentage points) |
|---|
Primary result
What the study found
The full priority policy has higher expected recall than uniform and ascending selection in all nine interval/budget combinations. At budget 100, its expected recall is 12.90%, 20.64%, and 20.68%, compared with uniform's 10% in each interval.
The twice-prime rule hurts this objective. Removing it raises expected recall to 33.04%, 34.46%, and 28.71% at budget 100, and improves every tested combination. Removing the modulo-6 rule changes no selections because earlier groups already fill the quotas. An inactive ablation says nothing about that rule outside this ordering and budget.
This revised policy is different from GB-001's generator. Narrow bands match size allocation but leave possible within-band size effects. The study measures reference-query selection quality, not runtime, mathematical progress, or generalization. Selecting a better policy from these results requires a new prospective study on other domains.
How the evidence is checked
The verifier recounts every reference and replays every seed. A separate implementation enumerates prime pairs using trial division and checks exact moments through inclusion-indicator covariances. All 54 simultaneous Monte Carlo intervals contain the exact contrasts. Source snapshots, environment versions, all 43,008 policy-replicate records, and all 30 stratum thresholds are in the bundle. Checksums identify files; they do not authenticate authorship or establish peer review. The protocol was committed before outcomes, without an external preregistration service.
Reproduce from a fresh checkout
python -m venv .venv
# Activate .venv, then install the lightweight study package:
pip install .
python -m codebase.experiments reproduce GB-002 results/gb002 --bundle src/experiments/gb-002/bundle.zipThe command checks the pinned archive, verifies it, reruns the study, and compares scientific artifacts. Omitting --bundle downloads the registered public bundle. Other research engines use the research installation extra.