**Merge 2: retreat-cancel on m-plus-b — positive observed gain; measurement incomplete.**

CANDIDATE beats BASE by more than twice its standard error **among the 4,787 reported paired seeds**: mean CANDIDATE minus BASE = **+0.400306**, SE = **0.040331**, and 2 × SE = **0.080662**. The mean is 9.93 SE above zero; mean ± 2 SE is [0.319643, 0.480968]. These are recomputed from the supplied moments, with equal weight for every reported seed. [Sources B01–B10](#sources), `overall`.

**This is not a completed 5,000-seed result.** B01–B09 each report 500 successful pairs; B10 reports only 287, sets `complete=false`, and attributes the shortfall to its time budget. Coverage is 4,787/5,000 (95.74%), with 213 seeds missing. No input artifact is missing or empty. B10’s empty `failures` list does not establish completion. The full planned mean, SE, per-spread results, and extremes remain unknown. [B10](#source-b10), `n`, `complete`, `failures`, `notes`, `per_seed`; [coverage checks](#coverage-checks).

The nine complete blocks alone give mean **+0.419027**, SE **0.037308**, n = 4,500, also exceeding 2 SE. That supports the direction of the observed improvement, but neither this sensitivity check nor the partial pool substitutes for the missing seeds. These inputs cover only m-plus-b: they cannot select between m-plus-a and m-plus-b, identify which was swarm #1042, or establish a new leaderboard score. [Sources B01–B09](#sources), `overall`; assignment scope.

**Strategy identity and measurement definition.** All ten inputs identify BASE as `m-plus-b`, BASE code SHA-256 `4f9167dddd457f394e988bf9c9e2576dd6120834bfb8d93573ce9451fd587598`, and CANDIDATE code SHA-256 `02696ea6fd0922f64167a1153748f6a38bf2fd5d87c7a4ac6cb974bb9482f57c`. These identifiers agree across the supplied files. They report CANDIDATE as `BASE + RC[len(N):]`, after checking that RC begins with N exactly. These are source reports of code verification; this merge verifies the input JSON hashes, not the original strategy code or new simulations. [Sources B01–B10](#sources), strategy fields and `notes`.

B08 identifies N code SHA-256 as `bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae` and RC code SHA-256 as `3c07bdcd221ac25729c3ebc92b21ac9e2014510ecb85816c4391ed81e933291f`. [B08](#source-b08), `notes[1]`.

Each reported d is `CANDIDATE.total_edge - BASE.total_edge` on the same seed and sampled configuration. Inputs describe fresh strategy instances/factories, BASE followed by CANDIDATE, and the unmodified simulator at commit `b244530ee2a6247b5f930830eeca9dd950da0e7e` (B10 abbreviates it to `b244530`). Spread denotes `cfg.competitor.spread_ticks`. [B01](#source-b01), [B02](#source-b02), [B06](#source-b06), [B10](#source-b10), `notes`.

**Pooling method.** For each pool, add the reported `n`, `sum_d` and `sum_d2`: N = Σ n, S = Σ sum_d, Q = Σ sum_d2. Then mean = S/N and SE = sqrt((Q − S²/N)/(N(N − 1))), the sample standard deviation of paired differences divided by sqrt(N). Apply the same calculation separately within each spread. Do not average block SEs, and do not give B10’s 287 seeds the weight of a complete block. The uncertainty calculation follows the sources’ sample-SE convention; a ±2 SE interval is a descriptive normal approximation, not a guarantee about missing seeds or extreme losses. [B02](#source-b02), `notes[3]`; [B07](#source-b07), `notes`.

<a id="pooled-moments"></a>

**Pooled reported seeds, overall and by spread.** The following table is calculated from the ten inputs’ `overall`/`by_spread` moments. [Sources B01–B10](#sources). Moments are shown to 12 decimals; mean and SE to 6.

| Pool | N | Σ d | Σ d² | Mean d | SE | 2 SE | Mean > 2 SE? |
| --- | --- | --- | --- | --- | --- | --- | --- |
| overall | 4787 | 1916.263021919699 | 38033.665121068031 | 0.400306 | 0.040331 | 0.080662 | Yes |
| 1 | 1149 | 0.000000000000 | 0.000000000000 | 0.000000 | 0.000000 | 0.000000 | No; zero effect |
| 2 | 1226 | 1047.063225796299 | 24581.725090390423 | 0.854048 | 0.125587 | 0.251175 | Yes |
| 3 | 1179 | 869.199796123400 | 13451.940029677608 | 0.737235 | 0.096043 | 0.192085 | Yes |
| 4 | 1233 | 0.000000000000 | 0.000000000000 | 0.000000 | 0.000000 | 0.000000 | No; zero effect |

The observed gains occur at spreads 2 and 3. Every reported spread-1 and spread-4 difference is zero; neither satisfies the strict “greater than 2 SE” test. This is an observation about the supplied seeds, not a finding about the unmeasured ones. [Sources B01–B10](#sources), `by_spread` and `per_seed`.

For the nine complete blocks, the pooled moments are N = 4,500, S = 1885.62149721039910, Q = 28969.2302898629828. Per spread, the complete-block sensitivity check is: [Sources B01–B09](#sources), `by_spread`.

| Spread | N | Σ d | Σ d² | Mean d | SE |
| --- | --- | --- | --- | --- | --- |
| 1 | 1075 | 0.000000000000 | 0.000000000000 | 0.000000 | 0.000000 |
| 2 | 1156 | 1072.521339425399 | 15768.529463304937 | 0.927787 | 0.105189 |
| 3 | 1115 | 813.100157785000 | 13200.700825558046 | 0.729238 | 0.100749 |
| 4 | 1154 | 0.000000000000 | 0.000000000000 | 0.000000 | 0.000000 |

**Block coverage and overall moments.** Values of S and Q below preserve the numeric precision supplied in each input; block means and SEs are recomputed from those moments. Every `failures` list is empty. [Sources B01–B10](#sources), `seeds`, `n`, `complete`, `overall`, `failures`.

| Source | Assigned seeds (inclusive) | N | Complete | Σ d | Σ d² | Mean d | SE |
| --- | --- | --- | --- | --- | --- | --- | --- |
| [B01](#source-b01) | 705000–705499 | 500 | true | 172.36631633249988 | 3755.214411047988 | 0.344733 | 0.121708 |
| [B02](#source-b02) | 705500–705999 | 500 | true | 259.7378386063998 | 3212.7581181084824 | 0.519476 | 0.111068 |
| [B03](#source-b03) | 706000–706499 | 500 | true | 249.16658360510007 | 2348.8520433410376 | 0.498333 | 0.094428 |
| [B04](#source-b04) | 706500–706999 | 500 | true | 198.4722540859997 | 3236.7663891201023 | 0.396945 | 0.112504 |
| [B05](#source-b05) | 707000–707499 | 500 | true | 163.414003 | 2308.010095 | 0.326828 | 0.095060 |
| [B06](#source-b06) | 707500–707999 | 500 | true | 123.82999728129995 | 3185.8582235815725 | 0.247660 | 0.112455 |
| [B07](#source-b07) | 708000–708499 | 500 | true | 242.351745 | 2316.898419 | 0.484703 | 0.093890 |
| [B08](#source-b08) | 708500–708999 | 500 | true | 226.4097781189995 | 6370.224758354377 | 0.452820 | 0.158496 |
| [B09](#source-b09) | 709000–709499 | 500 | true | 249.8729811801002 | 2234.647832309423 | 0.499746 | 0.091957 |
| [B10](#source-b10) | 709500–709999 | 287 | false | 30.64152470929997 | 9064.434831205048 | 0.106765 | 0.332252 |

<a id="coverage-checks"></a>

B01–B09 cover every seed from 705000 through 709499 exactly once. B10 reports these four inclusive completed ranges: `709500–709507`, `709563–709829`, `709878–709883`, `709941–709946`. The missing ranges are **`709508–709562` (55), `709830–709877` (48), `709884–709940` (57), `709947–709999` (53)**. There are no duplicate seed IDs across the ten inputs. These coverage findings are computed from `per_seed`, not inferred from the assigned `seeds` endpoints. [Sources B01–B10](#sources), especially [B10](#source-b10).

**Five worst and five best reported single runs.** Rank by paired d, not by either strategy’s absolute edge. Sorting all 4,787 `per_seed` rows produces the same top/bottom seed IDs as sorting the union of the inputs’ five-best/five-worst lists. Differences are displayed to six decimals. These rankings include the partial tenth block and can change when missing seeds are measured. [Sources B01–B10](#sources), `per_seed`, `worst`, `best`.

| Worst rank | Seed | Spread | CANDIDATE − BASE | Source |
| --- | --- | --- | --- | --- |
| 1 | 709790 | 2 | -90.875201 | [B10](#source-b10) |
| 2 | 708875 | 3 | -55.473471 | [B08](#source-b08) |
| 3 | 707780 | 3 | -38.644767 | [B06](#source-b06) |
| 4 | 705337 | 3 | -27.088252 | [B01](#source-b01) |
| 5 | 705899 | 3 | -20.236248 | [B02](#source-b02) |

| Best rank | Seed | Spread | CANDIDATE − BASE | Source |
| --- | --- | --- | --- | --- |
| 1 | 705380 | 2 | 28.662815 | [B01](#source-b01) |
| 2 | 705532 | 2 | 27.834418 | [B02](#source-b02) |
| 3 | 709318 | 2 | 25.827115 | [B09](#source-b09) |
| 4 | 708779 | 2 | 25.770270 | [B08](#source-b08) |
| 5 | 706624 | 2 | 23.293348 | [B04](#source-b04) |

The worst reported loss is **−90.875201**, seed 709790, spread 2, in the incomplete block; a positive pooled mean therefore coexists with substantial single-run downside. [B10](#source-b10), `worst[0]` and matching `per_seed` row. No absolute BASE/CANDIDATE total edges for these extreme seeds are supplied, so their absolute outcomes cannot be recovered here.

**Other retained findings and data limitations.** Across the reported rows there are 1,800 positive differences, 605 negative differences, and 2,382 zeros. Seed-weighted `retail_diff` is approximately −0.167528 and `arb_diff` +0.567833. Seed-weighted BASE and CANDIDATE means are approximately 102.177278 and 102.577584, respectively; these are this seed set’s edge means, not leaderboard scores. The components and means are aggregated from the supplied block means, so their last digits reflect source rounding. [Sources B01–B10](#sources), `per_seed` and `overall`.

The merge checked all ten JSON files against the assignment’s SHA-256 values; checked row counts, seed ranges, uniqueness, spread counts and extreme rankings; and checked reported moments and SEs against the rounded per-seed data within rounding bounds. B05 and B07 explicitly round aggregate statistics to six decimals, while other inputs generally retain more digits. Consequently the reported moments are the pooling authority; recomputing from six-decimal `per_seed` differences would lose precision. B07’s spread-specific `sum_d2` values add to 2316.898418, whereas its overall `sum_d2` is 2316.898419, a 0.000001 rounding discrepancy. Each pool uses its own supplied moments; there is no adjustment or concealed reconciliation. [B05](#source-b05), [B07](#source-b07), `overall`, `by_spread`, `notes`; [sources B01–B10](#sources), `per_seed`.

Execution provenance varies: B02 reports Python 3.13.5, B09 3.12.16, and several others 3.12.3. B07 describes eight concurrent processes, serial execution within each seed pair, and resumption after a timeout; B10 also describes contention. The other detailed notes generally describe serial in-process execution. Timing fields use different inclusion rules, so no common speed estimate is inferred from them. These facts do not change the supplied paired arithmetic, but the merge does not independently certify simulator execution or cross-version equivalence. [B02](#source-b02), [B07](#source-b07), [B09](#source-b09), [B10](#source-b10), `notes`; [B01](#source-b01), [B06](#source-b06), [B08](#source-b08), timing notes.

**Per-block spread moments retained for audit.** For spreads 1 and 4 all supplied S and Q are zero; their counts are retained in the first table. The second table retains each spread-2/spread-3 contribution, at source precision. This makes all pooled sufficient statistics above recoverable from this report. [Sources B01–B10](#sources), `by_spread`.

| Source | Spread 1 N (S=Q=0) | Spread 4 N (S=Q=0) |
| --- | --- | --- |
| [B01](#source-b01) | 107 | 119 |
| [B02](#source-b02) | 130 | 132 |
| [B03](#source-b03) | 118 | 120 |
| [B04](#source-b04) | 132 | 132 |
| [B05](#source-b05) | 114 | 124 |
| [B06](#source-b06) | 115 | 135 |
| [B07](#source-b07) | 124 | 151 |
| [B08](#source-b08) | 114 | 124 |
| [B09](#source-b09) | 121 | 117 |
| [B10](#source-b10) | 74 | 79 |

| Source | Spread | N | Σ d | Σ d² |
| --- | --- | --- | --- | --- |
| [B01](#source-b01) | 2 | 156 | 113.7225606776 | 2400.6029178949216 |
| [B01](#source-b01) | 3 | 118 | 58.64375565489986 | 1354.6114931530662 |
| [B02](#source-b02) | 2 | 116 | 116.84028784409992 | 1466.3427506874266 |
| [B02](#source-b02) | 3 | 122 | 142.8975507622999 | 1746.4153674210559 |
| [B03](#source-b03) | 2 | 138 | 112.22064211119987 | 1283.6008955592563 |
| [B03](#source-b03) | 3 | 124 | 136.94594149390022 | 1065.2511477817814 |
| [B04](#source-b04) | 2 | 108 | 102.36362926869998 | 2570.093089802711 |
| [B04](#source-b04) | 3 | 128 | 96.10862481729973 | 666.673299317391 |
| [B05](#source-b05) | 2 | 122 | 60.801665 | 1586.219651 |
| [B05](#source-b05) | 3 | 140 | 102.612338 | 721.790444 |
| [B06](#source-b06) | 2 | 135 | 65.21008440229991 | 811.5558581458773 |
| [B06](#source-b06) | 3 | 115 | 58.61991287900004 | 2374.3023654356953 |
| [B07](#source-b07) | 2 | 127 | 151.767979 | 1357.765617 |
| [B07](#source-b07) | 3 | 98 | 90.583766 | 959.132801 |
| [B08](#source-b08) | 2 | 131 | 176.5985354129996 | 2671.117318403342 |
| [B08](#source-b08) | 3 | 131 | 49.81124270599988 | 3699.107439951035 |
| [B09](#source-b09) | 2 | 123 | 172.99595570850013 | 1621.2313648114023 |
| [B09](#source-b09) | 3 | 139 | 76.87702547160006 | 613.4164674980207 |
| [B10](#source-b10) | 2 | 70 | -25.45811362910003 | 8813.195627085486 |
| [B10](#source-b10) | 3 | 64 | 56.0996383384 | 251.2392041195622 |

<a id="sources"></a>

**Source manifest.** The inputs are supplied local measurement artifacts, not independently published results. Each source label below identifies `.imd/reads/artifacts/item-rc-on-b-NN`, whose declared original output is `artifacts/goal/items/rc-on-b-NN/result.json`. The SHA-256 is of the input JSON bytes, distinct from the strategy code hashes. All ten hashes were checked during this merge. Retained statistics and missing ranges above allow the pooling arithmetic to be reviewed even when the input files are not distributed with the merge; the full per-seed records remain in these identified source artifacts.

| Label | Supplied input | SHA-256 of input JSON |
| --- | --- | --- |
| <a id="source-b01"></a>B01 | [item-rc-on-b-01](../../../../.imd/reads/artifacts/item-rc-on-b-01) | `1fb3f6456c9118ecceb6a66eafdd0fbbcf3b3e53b7f2e12e25724752ceef4a22` |
| <a id="source-b02"></a>B02 | [item-rc-on-b-02](../../../../.imd/reads/artifacts/item-rc-on-b-02) | `6933986c635778830f6579341c839867ff53a1037a0e0ba9bc22fd8dc3b7b12f` |
| <a id="source-b03"></a>B03 | [item-rc-on-b-03](../../../../.imd/reads/artifacts/item-rc-on-b-03) | `3c599834ca300a92963465d462cfbafd320e2bc9f072003e282094463c07dcf5` |
| <a id="source-b04"></a>B04 | [item-rc-on-b-04](../../../../.imd/reads/artifacts/item-rc-on-b-04) | `4e0e3a4e05a9549ac20768bec49fcb3b4019f8e5cae426a2efaa154937ebc8ed` |
| <a id="source-b05"></a>B05 | [item-rc-on-b-05](../../../../.imd/reads/artifacts/item-rc-on-b-05) | `ad8b48d0549c780285910d62aded1161e483e19476c83bb79c6241176a45663b` |
| <a id="source-b06"></a>B06 | [item-rc-on-b-06](../../../../.imd/reads/artifacts/item-rc-on-b-06) | `b277dafb95843e7357b4f20bfe94fbe5d9f9b3ae8f27ef3fc39adc423eff3c5e` |
| <a id="source-b07"></a>B07 | [item-rc-on-b-07](../../../../.imd/reads/artifacts/item-rc-on-b-07) | `3e3cfc0f4c04b23af7cd9f733fc9af83ad7ed42c419ef3e074cbd9b8b25dd9e3` |
| <a id="source-b08"></a>B08 | [item-rc-on-b-08](../../../../.imd/reads/artifacts/item-rc-on-b-08) | `fe607b701c06e502ee0c166ab61bb64f012f200ddce209e76d2b73eb59e7040a` |
| <a id="source-b09"></a>B09 | [item-rc-on-b-09](../../../../.imd/reads/artifacts/item-rc-on-b-09) | `241739e7ad50c5baa17c8f85050bf24ecfb6f58ec379554a344bb40a3afffef6` |
| <a id="source-b10"></a>B10 | [item-rc-on-b-10](../../../../.imd/reads/artifacts/item-rc-on-b-10) | `516d5cf7baf748ffd1f544312606942ee035f0ba65eba8d0951d39f86c36506c` |

**Decision supported by this merge:** retreat-cancel has a positive paired mean exceeding 2 SE on the reported m-plus-b seeds, including on the nine complete blocks alone. Finish the 213 missing m-plus-b seeds before treating the planned ten-block experiment as complete, and use the separate m-plus-a results before choosing a file for submission. The submission decision cannot be settled from these ten artifacts alone. [Sources B01–B10](#sources), coverage and pooled moments above; assignment scope.