# 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.

| Application | Tier | Ciphertext bytes / contribution | Premium |
| --- | --- | ---: | ---: |
| `allele_frequency_count` | additive | 262,282 | 1× |
| `carrier_count` | additive | 262,282 | 1× |
| `cohort_histogram` | additive | 262,282 | 1× |
| `polygenic_score_aggregate` | additive | 262,282 | 1× |
| `allele_frequency_with_variance` | mult-supporting | 1,310,882 | 5× |
| `genotype_phenotype_covariance` | mult-supporting | 2,621,791 | 10× |

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:

| Policy | Exact vector recovery |
| --- | ---: |
| No policy / minimum-N = 20 only | 1.000 |
| Minimum-N = 25 blocks adjacent base | 0.000 |
| Cohort freeze (single release) | 0.000 |
| Query budget = 5 | 0.125 |
| Counts rounded to nearest 5 | 0.850 exact-position, 0.000 exact-vector |

- 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.