# qb2: qm-2 on fresh real-engine seeds 9614592..9614847, paired vs trim-1, t03, IB

Policy credit: Taylor (gtmcknight) solved the game by dynamic programming (github.com/gtmcknight/amm-sim @ 4812a638, research/solved). qm-2 ports Taylor's Gaussian filter + qm tables (qm-spline compressed); trim-1 ports Taylor's Gaussian filter + plain tables. The qm-2 and trim-1 contract headers credit Taylor.

## Summary

- On all 256 seeds, **qm-2 beats every other arm**: +0.887 ± 0.040 (se) vs trim-1 (231/256 wins), +2.122 ± 0.082 vs t03 (247/256), +2.963 ± 0.088 vs IB (255/256).
- **Gas: qm-2 had 1 OutOfGas** in afterSwap. It was in chunk 9614816..9614847, out of 2,768,247 calls; gas_stats is per chunk, so the seed is not known. qm-2's engine-reported afterSwap peak per chunk was above 245,000 in 5 of 8 chunks (highest 249,885). That means qm-2 does **not** meet the goal's "0 OutOfGas" limit on this run. trim-1, t03 and IB had 0 OutOfGas and peaks ≤ 237,473. The upstream qm-2 artifact already said its engine peak (245,140) was above the nominal 245,000 with all calls succeeding. It also said the engine's reported gas is on a different scale from the cap and the margin is thin. This run reached the limit.
- All four arm sources were saved byte-exact; each sha256 matched the brief. All four passed `amm-match validate`. Runtime sizes for qm-2 (19,346 B) and trim-1 (16,077 B) match the brief.

## Method

- Platform: Linux x86_64. amm-challenge was cloned at 6b6921f8d463314aa7c96234e1be25a25245f704 inside the workspace. The 8-line `### setup.sh` block of artifact e8c967d6… ran once from the checkout root. All steps succeeded, including the wheel sha256 check and `amm-match validate contracts/src/StarterStrategy.sol`.
- Arms:
  - qm-2: the ```solidity block under `## Strategy.sol` of artifact e50ab7b9….
  - trim-1: the ```solidity block of artifact fce772b9….
  - t03 and IB: zlib-decompressed base64 `code_zb64` of artifacts 2333ecf2… and afd5183e….
  - Each was saved and checked against the brief's sha256.
- Engine: `amm_sim_rs.run_batch(creation_bytecode, VanillaStrategy bytecode, configs, 8)`.
  - Configs follow `MatchRunner._build_configs`: `np.random.default_rng(seed=seed)` draws retail_mean_size, retail_arrival_rate and gbm_sigma, in that order, from BASELINE_VARIANCE. All other fields come from `build_base_config`, with sim seed = seed.
  - Score = `edges['submission']`.
  - Runs used 8 chunks of 32 seeds per arm, one process per chunk (each under 25 s). `gas_stats_reset()` ran before each chunk and `gas_stats()` after. Every seed ran exactly once per arm, in arm order qm-2, trim-1, t03, IB. No seed was rerun.
- se = sample sd / sqrt(n). diff = qm-2 edge − other arm edge on the same seed.
- Gas "peak" is `max_ok_gas` and "mean" is `sum_ok_gas / ok`, both as reported by `amm_sim_rs.gas_stats()` for role Submission, callback afterSwap. For scale: the 30 bps Vanilla baseline's afterSwap reads ~22,592 on the same counter.

### Arms

| arm | name (getName) | sha256 of saved source | runtime bytes | amm-match validate |
|---|---|---|---|---|
| qm-2 | TaylorGaussianQmSpline | `50a741b97a7ed79237ecbd34a4bc20b5c70b7872d8916f31dc3fe3f72b4fe859` | 19,346 | pass |
| trim-1 | TaylorGaussianPlainNet2 | `d849c5f15d69499560b5c3ea08f55ad27153b393eba7abb7dd186f451ad46a24` | 16,077 | pass |
| t03 | censored_10 | `cb6d945511e1e10af78baa64c2a6cb25806f0998403ce6440654bfc3c70092d9` | 14,654 | pass |
| IB | inputs_b | `301941829a44bb60977bb28181a5e4bfa6544f3696763f987054789b2611d686` | 14,528 | pass |

### Paired differences (score = edges['submission'], each arm alone vs 30 bps VanillaStrategy)

Means over the 256 seeds: qm-2 526.567232, trim-1 525.679788, t03 524.444849, IB 523.604610.

**qm-2 minus trim-1**: n=256, mean_diff=0.887444, se=0.040107 (sample sd 0.641708), wins=231/256 (ties 0)  
worst5: (9614759, -1.107829), (9614771, -0.904445), (9614660, -0.730634), (9614760, -0.651627), (9614630, -0.593939)  
best5: (9614808, 2.445114), (9614711, 2.388288), (9614826, 2.232997), (9614730, 2.114943), (9614693, 2.098085)

**qm-2 minus t03**: n=256, mean_diff=2.122383, se=0.082415 (sample sd 1.318634), wins=247/256 (ties 0)  
worst5: (9614831, -1.593833), (9614809, -1.330061), (9614768, -0.916535), (9614843, -0.590108), (9614817, -0.551999)  
best5: (9614808, 5.647306), (9614606, 5.546051), (9614755, 5.338741), (9614841, 5.292944), (9614682, 5.186336)

**qm-2 minus IB**: n=256, mean_diff=2.962622, se=0.087940 (sample sd 1.407046), wins=255/256 (ties 0)  
worst5: (9614598, -0.196556), (9614817, 0.010097), (9614843, 0.076954), (9614608, 0.107824), (9614831, 0.170145)  
best5: (9614726, 6.778259), (9614808, 6.630811), (9614794, 6.431179), (9614750, 6.308604), (9614700, 6.232255)

### Gas: Submission afterSwap (amm_sim_rs.gas_stats(), reset before each 32-seed chunk)

| arm | calls | ok | OutOfGas | reverts | other halts/tx errors/bad returns | peak (max_ok_gas) | mean (sum_ok_gas/ok) |
|---|---|---|---|---|---|---|---|
| qm-2 | 2,768,247 | 2,768,246 | 1 | 0 | 0 | 249,885 | 155307.5 |
| trim-1 | 2,741,373 | 2,741,373 | 0 | 0 | 0 | 233,101 | 131589.4 |
| t03 | 2,750,236 | 2,750,236 | 0 | 0 | 0 | 237,473 | 135731.7 |
| IB | 2,730,070 | 2,730,070 | 0 | 0 | 0 | 236,928 | 135393.5 |

Per chunk (start seed; calls / peak / OutOfGas):

| chunk start | qm-2 | trim-1 | t03 | IB |
|---|---|---|---|---|
| 9614592 | 334,131 / 247,240 / 0 | 330,465 / 221,683 / 0 | 333,077 / 237,473 / 0 | 331,154 / 236,928 / 0 |
| 9614624 | 360,893 / 248,387 / 0 | 357,827 / 220,356 / 0 | 356,916 / 211,904 / 0 | 353,646 / 211,389 / 0 |
| 9614656 | 334,310 / 243,450 / 0 | 330,743 / 221,142 / 0 | 333,420 / 232,450 / 0 | 331,375 / 231,820 / 0 |
| 9614688 | 340,041 / 243,217 / 0 | 336,375 / 220,596 / 0 | 338,592 / 232,608 / 0 | 336,241 / 231,938 / 0 |
| 9614720 | 349,958 / 248,371 / 0 | 346,413 / 228,291 / 0 | 346,765 / 232,627 / 0 | 343,948 / 232,015 / 0 |
| 9614752 | 354,113 / 242,913 / 0 | 350,904 / 223,909 / 0 | 351,283 / 232,518 / 0 | 348,534 / 231,906 / 0 |
| 9614784 | 346,054 / 240,469 / 0 | 343,107 / 233,101 / 0 | 344,031 / 235,503 / 0 | 341,699 / 234,934 / 0 |
| 9614816 | 348,747 / 249,885 / 1 | 345,539 / 224,947 / 0 | 346,152 / 235,291 / 0 | 343,473 / 234,724 / 0 |

### Timing

Seconds per seed (run_batch wall time / seeds, 8 workers on a 6-core x86_64 Linux machine): qm-2 0.562, trim-1 0.363, t03 0.356, IB 0.330.

Seeds not run: none (every seed 9614592..9614847 ran exactly once per arm).

### Per-seed edges (9 decimals)

```csv
seed,qm2,trim1,t03,IB
9614592,579.657011088,578.598305980,576.526446492,575.816830065
9614593,477.607046324,476.789621604,475.610247305,475.746936846
9614594,537.435117513,537.271830280,535.872142410,536.055754808
9614595,453.527997993,452.680135800,449.889328693,449.347033391
9614596,482.321649808,481.219353716,481.237486207,479.920111512
9614597,672.113238752,671.408758020,668.390518456,666.976218381
9614598,414.428058406,412.505021367,414.869566644,414.624613980
9614599,388.374461640,387.255906494,387.149611848,386.518307910
9614600,449.480593036,448.310533471,448.317443297,448.253328173
9614601,637.679245290,637.852696128,634.842990147,634.500297663
9614602,633.428433920,633.800938003,631.358244759,629.949602991
9614603,491.025374124,490.235494680,489.902239016,489.238085890
9614604,721.210537268,721.273420275,718.584354640,718.552417072
9614605,615.226764120,614.495659129,612.255635379,610.647736447
9614606,621.980444908,620.486640498,616.434393591,616.057656166
9614607,569.287156165,568.631087629,567.523237520,566.200951257
9614608,386.876568935,385.718399154,386.629698498,386.768744924
9614609,463.470977653,461.822593818,462.556833511,462.183379809
9614610,465.289975407,464.491262587,464.111202262,463.449886028
9614611,391.611773523,391.128920823,389.689337351,389.539109071
9614612,452.591140243,450.874969386,449.625905322,449.051748489
9614613,472.537598959,471.988715978,470.703468402,469.337947062
9614614,484.101402983,482.947549398,481.584290238,481.300347048
9614615,361.545798504,359.726867472,360.585128683,359.843385027
9614616,529.476063014,529.051788056,527.538446647,525.997066170
9614617,575.464376095,574.144217887,574.403560103,573.665128702
9614618,432.239275652,431.173138010,430.695325288,428.666633221
9614619,575.916586224,575.717015202,574.219254471,573.498446007
9614620,573.066088086,571.720224174,568.950656110,568.876380601
9614621,503.172957532,502.106540689,502.039410784,500.296024826
9614622,535.669049521,533.675966802,533.743046696,533.842897013
9614623,473.352248267,472.143443133,470.578681062,469.879475909
9614624,456.431363754,454.467467915,453.659108896,452.178517787
9614625,450.721677793,450.228904438,448.398763781,446.856267173
9614626,680.558512906,679.496769026,678.293199611,677.066065866
9614627,554.903393771,553.068101292,553.042629392,551.937610928
9614628,414.734930169,414.399311878,414.682932289,413.362036807
9614629,630.983708215,631.198378043,626.513277617,626.461897828
9614630,586.449051246,587.042989876,583.255910253,582.016438212
9614631,729.693160414,728.718378169,727.334898518,725.841211317
9614632,555.527437814,554.314399490,554.111040298,552.241381943
9614633,514.098970407,513.593824042,512.605994206,512.100909460
9614634,634.579037569,633.008657859,632.017798153,632.093926803
9614635,605.581038236,604.296291037,601.794439818,601.847695038
9614636,667.593147974,666.274988789,667.432224351,666.341639088
9614637,748.071455925,747.243798467,744.853354894,743.678568473
9614638,716.729296966,716.922383212,713.366199266,712.064501159
9614639,486.163914016,485.461609767,484.461043757,484.213725449
9614640,486.671751815,485.426095207,485.658308718,485.018622488
9614641,484.314060593,483.103615712,482.127435034,480.950818368
9614642,572.986489660,571.740235967,571.485189730,570.912535200
9614643,443.631895826,442.949302333,441.215852091,439.323410465
9614644,715.708497373,715.405959318,714.635556792,714.018581744
9614645,471.843497223,471.516020461,469.165572237,467.962335096
9614646,607.715569680,607.773100219,605.855144308,606.524091344
9614647,597.276127156,596.073673921,593.405710724,591.615698807
9614648,430.353558202,429.809970223,428.360538264,426.678401576
9614649,555.415368364,554.114285751,553.168434118,552.007221924
9614650,534.868365309,534.804317604,533.290912130,531.563831761
9614651,618.895076668,618.659770540,614.203883057,616.208481347
9614652,476.864074743,475.130511196,474.891523346,473.607788719
9614653,759.445301760,758.874552991,756.611940384,753.980512212
9614654,447.258524357,446.632095666,445.587497644,444.989416870
9614655,515.299352839,514.496259923,512.428912496,512.136737768
9614656,617.498746000,617.822929001,616.324925642,615.078530171
9614657,591.551061689,590.412163944,589.241890566,588.729505492
9614658,420.229613014,419.024558875,420.168516773,418.963980613
9614659,446.229148661,445.423109066,444.957186303,444.256846021
9614660,504.531501526,505.262135689,503.711773490,503.239637099
9614661,593.665540179,592.263557865,591.319938487,591.375430824
9614662,469.111734029,467.551322395,467.833533741,466.319344016
9614663,486.997552492,486.116674679,485.886966796,484.583640962
9614664,443.182106434,442.230875836,441.426964355,440.982312843
9614665,393.690885501,391.929055113,393.532387219,392.165367641
9614666,441.357055401,440.137255533,439.712411684,437.975747453
9614667,627.832161805,627.163314431,625.218905823,623.547660110
9614668,478.355316519,477.767489273,476.848790483,475.718016162
9614669,551.518835306,551.581547178,547.665646256,546.951512294
9614670,590.253903374,589.792736535,585.369498381,584.754247872
9614671,471.036117207,469.560338041,469.325702233,467.945829072
9614672,440.296747604,439.583089215,440.330413618,439.767008418
9614673,589.409160954,588.030949753,585.304705165,585.961724032
9614674,403.550366690,401.853530774,400.907947838,400.365786954
9614675,521.043667477,520.685316785,520.204254502,518.417180067
9614676,357.433308721,356.948576364,357.278094969,355.715692941
9614677,534.400149383,533.808124895,532.890931250,532.387641786
9614678,432.896731266,432.803434768,430.638214289,429.946215888
9614679,432.925665429,433.038390371,431.453013354,430.526962558
9614680,481.805267104,481.587450711,480.927103697,480.306493357
9614681,410.708408833,409.494743308,409.456136229,408.535153434
9614682,547.523426676,545.982992018,542.337090707,543.293193719
9614683,391.398340476,390.489487646,390.831941972,390.066109536
9614684,329.973488262,329.374458669,329.197879490,328.045531711
9614685,672.695154128,672.031921557,669.321225315,668.565296754
9614686,642.676017741,641.724910110,638.478850508,637.331553465
9614687,428.612407317,427.514707995,427.470112927,426.622893832
9614688,617.919918182,616.297460560,616.180239457,613.982993270
9614689,363.549446435,361.746189808,362.926096049,362.246843611
9614690,485.892427008,484.388713120,483.016239706,481.770729501
9614691,373.523684810,372.723712566,372.074549921,371.597614467
9614692,653.612111469,652.294530995,649.016254104,647.727511246
9614693,377.846341123,375.748256530,375.488974049,372.893008973
9614694,416.045004597,415.755469304,413.484101984,413.893683501
9614695,618.938372349,618.148920261,614.860598854,614.453032807
9614696,560.400254014,560.900779232,560.559326436,559.295704688
9614697,521.580074775,521.003762374,519.491563184,518.561731353
9614698,568.318093516,566.740381370,564.777692143,564.661555337
9614699,674.066953657,673.987877550,671.758403517,671.923515686
9614700,640.650167645,640.344245269,636.997967819,634.417912971
9614701,407.994104728,406.670559219,406.371404512,405.084846447
9614702,428.284666849,427.432229708,426.878464228,426.235250124
9614703,466.845678811,465.509897564,462.566228932,461.714326126
9614704,463.004769566,461.962513456,461.345594514,460.570692699
9614705,461.361813504,460.019889857,458.977848329,459.226824906
9614706,476.577274904,475.810905348,474.312802720,474.572231780
9614707,586.789413872,586.005839043,584.030205142,583.042978441
9614708,748.443187979,746.922905571,744.902359136,744.017589838
9614709,490.250077736,488.567692875,486.967499492,487.672164294
9614710,457.997319360,456.919348088,457.188690469,456.286746085
9614711,470.996418376,468.608130663,469.841092972,469.374118161
9614712,583.142546488,582.900141372,581.538841434,580.654163720
9614713,498.964276727,497.475211290,497.394368579,496.572411770
9614714,535.851042373,535.156573812,535.106447448,534.450246842
9614715,398.204165218,396.748181493,397.430089919,396.737542251
9614716,683.654422075,683.113920927,680.033745160,679.167568004
9614717,409.166636002,407.829386239,407.147003622,405.309833391
9614718,377.487151776,376.316827753,376.886766680,376.535515735
9614719,479.988433398,479.161009350,480.193765211,479.809380090
9614720,643.210210711,643.231575360,641.104940121,639.233181954
9614721,576.311009370,575.338474735,573.141558443,571.461597145
9614722,549.554425566,549.473854283,546.422741658,546.685528143
9614723,515.199755784,515.067917236,513.458585322,512.994682244
9614724,697.415025533,696.634686153,694.645223972,693.334471927
9614725,605.918335569,604.575987736,604.292413637,602.915099979
9614726,674.983633504,673.475048700,670.210850148,668.205374487
9614727,520.376731407,519.731348939,519.246230141,519.652906177
9614728,471.637453296,470.797844142,468.406757699,467.410447132
9614729,550.123951995,549.113514880,548.259403035,547.941351758
9614730,447.614719196,445.499776087,445.878245430,445.366534907
9614731,421.529667275,420.463825241,420.100049591,419.959019616
9614732,561.647395594,560.839018556,557.608375958,556.986153354
9614733,422.524225697,421.879893726,420.571516874,419.955428903
9614734,430.151161723,429.111208795,428.378606133,427.875507588
9614735,459.222044122,457.957199747,458.033904576,457.137758922
9614736,555.313692296,553.910673649,550.926530399,549.525769293
9614737,700.793559347,699.600903829,699.143766327,698.976672750
9614738,476.282761303,475.590853835,473.823741655,472.119568570
9614739,651.815333702,652.108542840,649.018032982,647.901854330
9614740,684.548269523,683.767805027,681.314864380,680.022658802
9614741,540.744454859,539.837100829,538.293834884,537.177951685
9614742,523.128502393,522.573257144,521.015071451,521.185093621
9614743,574.323606832,572.989682323,570.292279014,569.610788663
9614744,492.392660889,492.128224942,490.668258614,489.386482875
9614745,484.859044289,483.046393389,483.060330333,482.382559683
9614746,585.646877748,583.949015212,581.108159458,581.237662213
9614747,616.111740792,614.733847905,612.556860074,611.571263429
9614748,462.795532549,461.370130572,459.949770235,458.957637770
9614749,639.416097885,638.712285154,634.698772759,634.287836741
9614750,535.525201738,535.197173720,532.265432413,529.216597647
9614751,395.747203204,394.231799391,395.317157253,394.892314254
9614752,533.714251474,532.857763110,529.845389402,528.777610192
9614753,541.557608615,540.667649686,541.260645987,538.613626898
9614754,520.656861242,520.948218483,518.720852340,518.234471860
9614755,681.335455481,679.389924826,675.996714157,676.205942379
9614756,548.217659950,548.210930808,546.856799278,547.074272817
9614757,662.825875415,662.450987544,659.307079134,658.230137352
9614758,512.629687169,511.578555600,510.997684827,510.010777710
9614759,696.262044781,697.369874147,694.335558971,692.958707649
9614760,478.617897234,479.269524187,477.972433861,477.006455789
9614761,633.960045297,632.481386386,631.089918273,630.498038949
9614762,569.346717910,568.168139518,566.698160017,566.025210217
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```