# Merge 01, batch r6-base-f: candidate 5d1bd527… vs comparator bf0d179f… on finalist seeds 900000–901999

Sources: `.imd/reads/artifacts/item-base-f1..f4` (item result JSONs; file SHA-256 listed below). All numbers below are copied from or recomputed from those files; recomputed values are recomputed from each file's `per_seed` list (seed, spread, d).

Candidate SHA-256 `5d1bd5272884f513b19f0e66a7c235f6c188a08e4f7787ac9346f1614dda3ed3`; comparator SHA-256 `bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae` (identical in all four items). The items do not name the candidate/comparator; d = candidate − comparator.

## 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-f1 | 900000–900499 | 500 | True | 0 | 0 | 4/4 passed (310000–310003) | 522.8821 | 31870.057 | 1.0458 | 0.3543 | 93.9591 | 95.0048 | -0.4353 | 1.4811 |
| base-f2 | 900500–900999 | 500 | True | 0 | 0 | 4/4 passed (310000–310003) | 605.6686 | 20388.656 | 1.2113 | 0.2807 | 101.5092 | 102.7205 | -0.2739 | 1.4852 |
| base-f3 | 901000–901499 | 500 | True | 0 | 0 | 4/4 passed (310000–310003) | 632.3302 | 32559.477 | 1.2647 | 0.3568 | 114.6106 | 115.8753 | -0.2059 | 1.4705 |
| base-f4 | 901500–901999 | 500 | True | 0 | 0 | 4/4 passed (310000–310003) | 279.8036 | 28128.201 | 0.5596 | 0.3348 | 101.4877 | 102.0473 | -0.7860 | 1.3456 |

Item file SHA-256: item-base-f1 `639ed8986a8161dc6e96292dc31ccf1fcce02a7915fae9bae816a9e922ffb13c`; item-base-f2 `77516a9c100859dcf2aca6d92c1ab63f7286385ddcab734e22d6f5c6a51e4797`; item-base-f3 `df3aa395aa5742f96b39d34194c04c397ba799d6704ef9a5ea0ac42838418a69`; item-base-f4 `3f3aab5c3300c8ea2f9ccfa1711f75faef9fd4d231d94c5afdd33cdcea320689`

### By spread (per item)

| key | spread | n | sum_d | sum_d2 | mean_diff | se | retail_diff | arb_diff | worst 3 seeds (seed: d, recomputed from per_seed) |
|---|---|---|---|---|---|---|---|---|---|
| base-f1 | 1 | 126 | 131.4429 | 25924.584 | 1.0432 | 1.2796 | -0.5758 | 1.6190 | 900146: -98.549, 900120: -24.450, 900039: -13.060 |
| base-f1 | 2 | 136 | 257.5450 | 4315.357 | 1.8937 | 0.4566 | -0.4707 | 2.3644 | 900268: -32.156, 900138: -13.082, 900383: -4.769 |
| base-f1 | 3 | 104 | 57.1797 | 1162.830 | 0.5498 | 0.3250 | -0.5307 | 1.0805 | 900425: -14.950, 900414: -7.094, 900384: -6.886 |
| base-f1 | 4 | 134 | 76.7144 | 467.286 | 0.5725 | 0.1541 | -0.1933 | 0.7658 | 900300: -4.646, 900201: -4.278, 900172: -3.832 |
| base-f2 | 1 | 109 | 169.7591 | 4354.276 | 1.5574 | 0.5894 | -0.3135 | 1.8709 | 900545: -8.918, 900887: -3.166, 900941: -2.474 |
| base-f2 | 2 | 128 | 292.9309 | 14754.679 | 2.2885 | 0.9308 | -0.4723 | 2.7608 | 900902: -27.378, 900507: -21.015, 900763: -14.539 |
| base-f2 | 3 | 125 | 89.7992 | 709.332 | 0.7184 | 0.2040 | -0.2086 | 0.9270 | 900942: -5.293, 900782: -4.735, 900806: -3.065 |
| base-f2 | 4 | 138 | 53.1794 | 570.369 | 0.3854 | 0.1705 | -0.1177 | 0.5030 | 900835: -16.102, 900570: -4.645, 900813: -4.151 |
| base-f3 | 1 | 132 | 137.1564 | 20326.053 | 1.0391 | 1.0804 | 0.0218 | 1.0172 | 901021: -62.495, 901194: -32.477, 901132: -21.150 |
| base-f3 | 2 | 143 | 347.9839 | 10333.680 | 2.4335 | 0.6835 | -0.1999 | 2.6333 | 901239: -31.410, 901042: -20.614, 901321: -14.294 |
| base-f3 | 3 | 103 | 111.7929 | 1463.108 | 1.0854 | 0.3574 | -0.3003 | 1.3856 | 901350: -10.532, 901120: -4.792, 901162: -1.912 |
| base-f3 | 4 | 122 | 35.3970 | 436.635 | 0.2901 | 0.1699 | -0.3795 | 0.6697 | 901072: -5.707, 901354: -4.629, 901441: -4.452 |
| base-f4 | 1 | 120 | 50.4398 | 19311.127 | 0.4203 | 1.1623 | -1.5126 | 1.9330 | 901696: -93.949, 901640: -33.681, 901547: -23.468 |
| base-f4 | 2 | 104 | 154.8732 | 4559.095 | 1.4892 | 0.6357 | -0.6821 | 2.1713 | 901967: -26.720, 901586: -26.710, 901643: -23.913 |
| base-f4 | 3 | 137 | 21.0011 | 2968.270 | 0.1533 | 0.3989 | -0.7103 | 0.8636 | 901672: -34.977, 901539: -16.442, 901933: -15.413 |
| base-f4 | 4 | 139 | 53.4894 | 1289.709 | 0.3848 | 0.2572 | -0.3110 | 0.6958 | 901606: -24.693, 901511: -8.775, 901645: -6.486 |

## Pooled over the 4 complete rows (seeds 900000–901999)

se = sqrt((sum_d2 − sum_d²/n)/(n−1)/n); retail/arb/means weighted by n.

| scope | n | sum_d | sum_d2 | mean | se | mean/se | retail_diff | arb_diff | comparator_mean | candidate_mean |
|---|---|---|---|---|---|---|---|---|---|---|
| overall | 2000 | 2040.6845 | 112946.391 | 1.0203 | 0.1665 | 6.13 | -0.4253 | 1.4456 | 102.8916 | 103.9120 |
| spread 1 | 487 | 488.7984 | 69916.039 | 1.0037 | 0.5416 | 1.85 | -0.5859 | 1.5896 | 48.5655 | 49.5692 |
| spread 2 | 511 | 1053.3330 | 33962.811 | 2.0613 | 0.3493 | 5.90 | -0.4383 | 2.4997 | 83.8472 | 85.9085 |
| spread 3 | 469 | 279.7729 | 6303.540 | 0.5965 | 0.1672 | 3.57 | -0.4467 | 1.0432 | 134.8381 | 135.4347 |
| spread 4 | 533 | 218.7802 | 2764.000 | 0.4105 | 0.0971 | 4.23 | -0.2470 | 0.6575 | 142.6771 | 143.0875 |

Pooled reading: mean paired gain 1.0203 with se 0.1665; gain exceeds 2×se (0.3330). All four items show positive mean_diff; the gain comes from arbitrage (arb_diff positive in every item and spread) partly offset by retail loss (retail_diff negative in every item except f3 spread 1, +0.0218). This merge covers 2000 of the 4000 finalist seeds (900000–901999); 902000–903999 are not in these inputs.

## Notes

- All four rows complete: 500/500 seeds, no missing seeds, no failures, check values for seeds 310000–310003 matched in every item (reported in differing formats: list with passed flags in f1/f3, dict with `matched`/`all_match` true in f2/f4).
- Items report per-seed d to 6 decimals in per_seed; recomputing sums from per_seed agreed with reported sums within rounding.
- Items disagree only on seconds_per_simulation (f1 0.338, f2 0.739, f3 0.748, f4 0.706), which does not affect results. Item f4 has the smallest gain (0.5596, se 0.3348); between-item spread of means is consistent with their SEs.