Expected results

Every value below is what a correct replication reproduces. The synthetic
ciphertext sizes are byte-deterministic (a mismatch is a real regression); the
real-genome headline numbers are deterministic given the committed sample and
variant selection rules.

Contents

• Synthetic BFV exactness taxonomy (Section 10)
• E5 — allele-frequency panel
• E6 — cross-population differentiation
• E7 — release-policy differencing
• E8 — linkage-disequilibrium window

Synthetic BFV exactness taxonomy (paper Section 10)

At N=20, L=10, 128-bit security, seed 42. max_error must be 0 for every row.

The four additive applications share an identical ciphertext size; the payload
premium of one multiplicative level is 5× (variance) and 10× (covariance).

E5 — allele-frequency panel

• Source: IGSR/1000 Genomes Phase 3 20130502, region 22:16050000-17000000.
• 10 public samples, 12 complete-call biallelic SNPs.
• Encrypted first moment (allele_frequency_count) and first+second moments
  (allele_frequency_with_variance) match the cleartext oracle exactly.
• Mean absolute AF deviation vs IGSR global: 0.0609.
• Mean heterozygote rate: 0.3083. Mean dosage variance: 0.2542.

E6 — cross-population differentiation

• Region 22:16050000-17000000; 50 samples (10 per super-population), 24 SNPs.
• Exact moments vs oracle.
• Maximum F_ST-like value 0.1363 at 22:16067208:C:G (EAS 0.90 vs AMR 0.45).
• Panel mean F_ST-like 0.0611; mean absolute AF deviation vs IGSR global
  0.0311; 624 small-cell group rows suppressed (n < 10).
• The F_ST-like statistic is a simplified equal-weight heterozygosity contrast over
  a small selected panel — not a population-genetics estimate.

E7 — release-policy differencing

• Region 22:16050000-17250000; N=25 vs adjacent N=24, 40 SNPs; the held-out
  sample carries a nonzero alt dosage at 6 of the 40 positions.
• Both encrypted aggregates match the cleartext counts; the exact-count difference
  recovers the held-out sample’s dosage vector exactly.
• Recovery rate by policy:

• Query-budget curve is linear: recovery = (positions the budget allows) / 40
  (budget 1 → 0.025, 5 → 0.125, 10 → 0.250, 20 → 0.500, 40 → 1.000).

E8 — linkage-disequilibrium window (draft genotype_pair_ld)

• Region 22:16050000-16900000; 25 samples, 11 adjacent variant pairs.
• All five product-moment vectors (sum_a, sum_b, sum_a2, sum_b2, sum_ab) match
  the cleartext oracle exactly.
• Maximum r2 = 1.0000 (pair 4) — a small-count artifact: both variants carry
  only 3 alternate alleles across 25 samples and perfectly co-occur. This is
  expected spurious LD, not a population signal.
• E8 ran below the application’s declared floor of 30 contributors, so it is a
  compute-path correctness check, not a governed release.