# Merge 02, batch r6-base-f: candidate MA vs comparator N on finalist seeds 902000–903999

Sources: `.imd/reads/artifacts/item-base-f5..f8` (item results, read as data; SHA-256 as given in the task, verified by `sha256sum`). Every number below is either copied from an item or recomputed from its `n`, `sum_d`, `sum_d2`. d = candidate − comparator total edge per seed.

Candidate sha256 (all four items): `5d1bd5272884f513b19f0e66a7c235f6c188a08e4f7787ac9346f1614dda3ed3`  
Comparator sha256 (all four items): `bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae`

## Rows

| key | seeds | n | complete | missing | failures | check values | sum_d | sum_d2 | mean_diff | se | comparator_mean | candidate_mean | retail_diff | arb_diff |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| base-f5 | 902000–902499 | 500 | True | 0 | 0 | 310000–310003 all match | 807.684470 | 42910.0464 | 1.615369 | 0.408356 | 110.324676 | 111.940045 | -0.257345 | 1.872714 |
| base-f6 | 902500–902999 | 500 | True | 0 | 0 | 310000–310003 all match | 380.941753 | 9281.2528 | 0.761884 | 0.189832 | 100.188486 | 100.950369 | -0.338135 | 1.100019 |
| base-f7 | 903000–903499 | 500 | True | 0 | 0 | 310000–310003 all match | 490.070516 | 12070.4747 | 0.980141 | 0.215531 | 100.104156 | 101.084297 | -0.551356 | 1.531497 |
| base-f8 | 903500–903999 | 500 | True | 0 | 0 | 310000–310003 all match | 1312.817853 | 845576.4383 | 2.625636 | 1.837190 | 110.932334 | 113.557970 | -0.630290 | 3.255925 |

### Per spread, per row

| key | spread | n | sum_d | sum_d2 | mean_diff | se | retail_diff | arb_diff | worst seeds (seed: d) |
|---|---|---|---|---|---|---|---|---|---|
| base-f5 | 1 | 127 | 287.698108 | 8605.1224 | 2.265339 | 0.705000 | 0.636885 | 1.628454 | — |
| base-f5 | 2 | 125 | 339.151664 | 31824.1760 | 2.713213 | 1.412022 | -0.810126 | 3.523339 | 902138: -67.388, 902379: -35.083, 902088: -16.505 |
| base-f5 | 3 | 123 | 94.432483 | 1633.8090 | 0.767744 | 0.322561 | -0.545312 | 1.313056 | 902463: -22.736 |
| base-f5 | 4 | 125 | 86.402215 | 846.9390 | 0.691218 | 0.225362 | -0.329742 | 1.020960 | 902152: -9.844 |
| base-f6 | 1 | 131 | 34.744774 | 3215.7779 | 0.265227 | 0.433923 | -0.791821 | 1.057049 | 902960: -47.020 |
| base-f6 | 2 | 123 | 148.236522 | 2710.7833 | 1.205175 | 0.410781 | -0.383759 | 1.588934 | 902719: -26.414, 902828: -19.207, 902878: -9.276 |
| base-f6 | 3 | 119 | 72.467301 | 2358.1000 | 0.608969 | 0.405942 | -0.146145 | 0.755114 | 902513: -29.985 |
| base-f6 | 4 | 127 | 125.493156 | 996.5917 | 0.988135 | 0.233516 | -0.005870 | 0.994005 | — |
| base-f7 | 1 | 125 | 99.481351 | 5511.3238 | 0.795851 | 0.591998 | -0.865615 | 1.661466 | 903203: -27.042, 903450: -21.263, 903214: -18.565 |
| base-f7 | 2 | 127 | 299.654214 | 4823.3958 | 2.359482 | 0.507189 | -0.449764 | 2.809246 | 903422: -17.871 |
| base-f7 | 3 | 123 | 21.575642 | 1304.6489 | 0.175412 | 0.294431 | -0.699859 | 0.875270 | 903049: -24.619 |
| base-f7 | 4 | 125 | 69.359309 | 431.1061 | 0.554874 | 0.159155 | -0.194189 | 0.749063 | — |
| base-f8 | 1 | 121 | 225.617930 | 6713.4043 | 1.864611 | 0.658318 | 0.286537 | 1.578074 | — |
| base-f8 | 2 | 131 | 990.401816 | 835226.2376 | 7.560319 | 6.971709 | -2.290340 | 9.850659 | 903809: -81.345, 903673: -75.687, 903693: -31.475 |
| base-f8 | 3 | 127 | 77.658267 | 1224.6744 | 0.611482 | 0.271229 | -0.157382 | 0.768864 | — |
| base-f8 | 4 | 121 | 19.139840 | 2412.1221 | 0.158180 | 0.407327 | -0.246229 | 0.404410 | 903973: -43.769, 903715: -15.438 |

Worst seeds are the five most negative d per item overall (from each item's `worst_seeds`), placed under their spread; items did not report per-spread worst lists.

## Pooled over the 4 complete rows

| scope | n | sum_d | sum_d2 | mean | se | mean/se | comparator_mean | candidate_mean | retail_diff | arb_diff |
|---|---|---|---|---|---|---|---|---|---|---|
| overall | 2000 | 2991.514592 | 909838.2123 | 1.495757 | 0.475872 | 3.14 | 105.387413 | 106.883170 | -0.444281 | 1.940039 |
| spread 1 | 504 | 647.542164 | 24045.6284 | 1.284806 | 0.302603 | 4.25 | 50.533262 | 51.818068 | -0.191220 | 1.476026 |
| spread 2 | 506 | 1777.444215 | 874584.5927 | 3.512736 | 1.843420 | 1.91 | 100.071428 | 103.584164 | -0.999254 | 4.511990 |
| spread 3 | 492 | 266.133694 | 6521.2323 | 0.540922 | 0.162478 | 3.33 | 117.102363 | 117.643285 | -0.387266 | 0.928188 |
| spread 4 | 498 | 300.394519 | 4686.7589 | 0.603202 | 0.134922 | 4.47 | 154.730034 | 155.333236 | -0.192833 | 0.796034 |

Formulas: mean = sum_d/n; se = sqrt((sum_d2 − sum_d²/n)/(n−1)/n); comparator/candidate means and retail/arb differences weighted by n.

## Reading
- Pooled over 2000 finalist seeds (902000–903999), MA − N = 1.4958 ± 0.4759 (ratio 3.14). Twice the se is 0.9517, so the promotion rule (gain > 2·se) is met on this pooled block. Note this merge covers 2000 of the 4000 finalist seeds (900000–903999); the other half, if measured, is in another merge and is not seen here.
- The gain is arbitrage loss reduction: arb_diff +1.9400, retail_diff -0.4443 (n-weighted). All four rows have positive mean, ratios 3.96, 4.01, 4.55, 1.43.
- Largest |d| seeds (from per_seed): 903835 (spread 2, base-f8): +904.354; 902495 (spread 2, base-f5): +144.613; 903809 (spread 2, base-f8): -81.345; 903673 (spread 2, base-f8): -75.687; 902138 (spread 2, base-f5): -67.388.
- base-f8 spread 2 is dominated by one outlier (sum_d2 835226 of the row's 845576). Excluding the single largest-|d| seed 903835 (sensitivity check, not a replacement), pooled n=1999, mean 1.0441, se 0.1499 (computed from 6-decimal rounded per_seed values).
- Seeds with d>0: 1092, d<0: 369, d=0: 539.

## Notes on completeness, failures, check values

- All four rows complete (n=500, no missing seeds, no failures). Comparator check values on seeds 310000–310003 (17.116002, 20.017111, 2.390311, 241.484752) matched in all four rows. base-f6 reports check values in a different shape (dict with `match: true`) than the others (list with `passed`); content agrees.
- Python versions differ (f5: 3.13.5; f6–f8: 3.12.3); check values match across them, so no effect is evident.
- Spread label s was taken from the rival's first quotes in each item (per item notes).

### Internal consistency checks

- base-f5: per_seed has 500 rows; sum of rounded per-seed d = 807.6845 (reported sum_d 807.6845); recomputed se from sums = 0.408356 (reported 0.408356); spread n sum = 500; python 3.13.5, 0.617 s/sim.
- base-f6: per_seed has 500 rows; sum of rounded per-seed d = 380.9417 (reported sum_d 380.9418); recomputed se from sums = 0.189832 (reported 0.189832); spread n sum = 500; python 3.12.3, 0.889 s/sim.
- base-f7: per_seed has 500 rows; sum of rounded per-seed d = 490.0705 (reported sum_d 490.0705); recomputed se from sums = 0.215531 (reported 0.215531); spread n sum = 500; python 3.12.3, 1.333 s/sim.
- base-f8: per_seed has 500 rows; sum of rounded per-seed d = 1312.8179 (reported sum_d 1312.8179); recomputed se from sums = 1.837190 (reported 1.837190); spread n sum = 500; python 3.12.3, 1.135 s/sim.