{
  "approach": "Closed-form one-step edge surrogate: truncated-lognormal moments of the router split give fees plus second-order CP impact; Gaussian positive-part-square gives arb loss. Its maximisers form a calibrated five-bin table. EWMA implied-price innovations, non-arb counts per timestamp and bounded fill sizes supply volatility/flow risk. Fee-band reconstruction uses gains 1/4 and 1/20; shrunk spot/fair displacement sets asymmetric fees. Tuning:0..1999; frozen confirmation:300000..301999. Classification, censoring and the uniform normalizer-band prior remain approximations.",
  "tried": [
    {
      "variant": "v18",
      "description": "80% router table; 0.80 fair-price skew.",
      "code_sha256": "8e7a5b19cc810867b977bafa79621e482a1c930246e13035d0ec325aded6f178",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 516.3245872795829,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 147.52016666189732,
        "se": 0.8331572826573839,
        "worst": [
          {
            "seed": 922,
            "diff": 73.57378086593917
          },
          {
            "seed": 907,
            "diff": 74.03029171486924
          },
          {
            "seed": 1994,
            "diff": 74.53676636958244
          },
          {
            "seed": 1459,
            "diff": 76.26496816451686
          },
          {
            "seed": 526,
            "diff": 76.44899293747613
          }
        ]
      },
      "tuning_rank": 1,
      "promotion_rank": 1,
      "model": {
        "engine_commit": "6b6921f8d463314aa7c96234e1be25a25245f704",
        "paired_protocol": "For each seed i, numpy default_rng(i) draws mean size U[19,21], retail rate U[0.6,1.0], then sigma U[0.000882,0.001008]; Rust price seed i, retail seed i+1; 10000 steps; candidate and starter each face fixed 30 bps normalizer in separate runs with identical seeds. run_batch uses four workers. SE uses sample standard deviation (ddof=1)/sqrt(n). Worst are the five smallest candidate-minus-reference differences.",
        "normalization": "Own x=y=p=1; normalizer invariant equals ours and spot offset n is uniform on [-0.003,0.003].",
        "router": "g=1-f; g2=0.997; r=sqrt(g/g2); h=g+r*g2; k=r*g2/h; d=(r*sqrt(1+n)-1)/h; own fill Q=clip(kY+d,0,Y).",
        "tail_moments": "For lognormal Y with mean mu and tau=1.2: M_j(L)=mu^j exp((j*j-j)*tau*tau/2) Phi((ln(mu/L)+(j-0.5)*tau*tau)/tau).",
        "fill_moments": "If d<0, L=-d/k: E[Q]=k*M1+d*M0, E[Q^2]=k*k*M2+2*k*d*M1+d*d*M0. If d>=0, L=d/(1-k): E[Q]=mu+(k-1)*M1+d*M0, E[Q^2]=mu*mu*exp(tau*tau)+(k*k-1)*M2+2*k*d*M1+d*d*M0.",
        "objective": "lambda/2*(f*E[Q]+g*g*E[Q^2])-sigma*sigma/4*((1+z*z)*Phi(-z)-z*phi(z)), z=f/sigma; average over the normalizer-band prior.",
        "nominal_table": {
          "mean_size_to_reserve": [
            0.001,
            0.0015,
            0.002,
            0.0025,
            0.003
          ],
          "fee_bps": [
            29,
            30,
            33,
            35,
            38
          ],
          "sigma": 0.001,
          "lambda": 0.8,
          "search_step_bps": 1
        },
        "runtime_approximation": "Coarse size bins and tuning multiplier; additive EWMA innovation proxy/[10*(observed_nonarb_rate+0.2)]. This is a calibrated approximation to reoptimisation, not an exact conditional optimum. Flow estimates are selection-biased; the size proxy is twice our fill, winsorized to the known 19..21 prior. First-in-timestamp arb classification is probabilistic and imperfect.",
        "timing": "seconds_per_simulation is measured wall time divided by simulation count with four workers; excludes compilation.",
        "runtime_checks": {
          "callbacks": 5000,
          "gas_limit_each": 250000,
          "all_succeeded": true
        },
        "promotion": "Only this candidate is promoted, after the independent confirmation against the previous best (50 bps starter). The other rows are tuning trials, not promotions.",
        "starter_code_sha256": "8f2cea337f6736105f58c6758da6c3ebf002951d34492bcd5b7101bef2d1e7f3",
        "starter_tuning_score": {
          "n": 2000,
          "mean_edge": 368.80442061768565
        }
      }
    },
    {
      "variant": "v20",
      "description": "60% router table; 0.80 fair-price skew.",
      "code_sha256": "0e46d40b0a9b6e460e196f3e723b60bb13d8f1906bd4343bcbbcd5fd4a4c6bf2",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 513.1956659114359,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 144.39124529375013,
        "se": 0.8074038062815768,
        "worst": [
          {
            "seed": 922,
            "diff": 73.4516948982677
          },
          {
            "seed": 1994,
            "diff": 74.05758328606174
          },
          {
            "seed": 445,
            "diff": 74.30903488657924
          },
          {
            "seed": 907,
            "diff": 74.72679171342185
          },
          {
            "seed": 1459,
            "diff": 75.9562541630898
          }
        ]
      },
      "tuning_rank": 2
    },
    {
      "variant": "v17",
      "description": "100% router table; 0.80 fair-price skew.",
      "code_sha256": "56f9f8d8ce623553383d434dfb70101b3330ef2ec47575f344ae44fcd0d18035",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 511.51987142065445,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 142.71545080296875,
        "se": 0.8506104051347997,
        "worst": [
          {
            "seed": 907,
            "diff": 65.81604147784168
          },
          {
            "seed": 922,
            "diff": 67.40414007848187
          },
          {
            "seed": 526,
            "diff": 68.59114337577995
          },
          {
            "seed": 1994,
            "diff": 69.57495471700992
          },
          {
            "seed": 445,
            "diff": 69.93360142925889
          }
        ]
      },
      "tuning_rank": 3
    },
    {
      "variant": "v15",
      "description": "100% router table; 0.70 fair-price skew.",
      "code_sha256": "e58413be6364c6e6e48a016d55bc8544c2f1199d2ad62e6edd96c8321ef0c92a",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 509.8303660643444,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 141.02594544665877,
        "se": 0.8053915535758107,
        "worst": [
          {
            "seed": 907,
            "diff": 69.69894223691523
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          {
            "seed": 922,
            "diff": 70.14130939454003
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          {
            "seed": 1994,
            "diff": 70.52223799656002
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          {
            "seed": 445,
            "diff": 71.4040430748517
          },
          {
            "seed": 1459,
            "diff": 72.71764972564876
          }
        ]
      },
      "tuning_rank": 4
    },
    {
      "variant": "v19",
      "description": "100% router table; 0.85 fair-price skew.",
      "code_sha256": "6da754c903efc572d1c75d2d16104f37ab28e9c6704f742cbbcc530d694bebf0",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 507.7104766082561,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 138.9060559905704,
        "se": 0.8637775747969431,
        "worst": [
          {
            "seed": 907,
            "diff": 58.66621854423079
          },
          {
            "seed": 922,
            "diff": 62.55653165011449
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          {
            "seed": 113,
            "diff": 62.87755159746149
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          {
            "seed": 526,
            "diff": 64.36859369135988
          },
          {
            "seed": 445,
            "diff": 66.00055659508575
          }
        ]
      },
      "tuning_rank": 5
    },
    {
      "variant": "v14",
      "description": "100% router table; 0.65 fair-price skew.",
      "code_sha256": "59005bd03f2c77dffd4fdb17ea84bed750127adafbc59d8e21b9a65e0b40ef31",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 505.98824684840986,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 137.18382623072424,
        "se": 0.7773427903340961,
        "worst": [
          {
            "seed": 907,
            "diff": 69.25673567620453
          },
          {
            "seed": 1994,
            "diff": 69.26948429875819
          },
          {
            "seed": 922,
            "diff": 69.56847075097721
          },
          {
            "seed": 445,
            "diff": 70.22034281139679
          },
          {
            "seed": 1459,
            "diff": 71.24071360430719
          }
        ]
      },
      "tuning_rank": 6
    },
    {
      "variant": "v16",
      "description": "80% router table; 0.60 fair-price skew.",
      "code_sha256": "0502e545b2ffa047b9447bfe142f799fc6d83e53f4a07bca41845633d62bb23f",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 501.0340761617735,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 132.22965554408782,
        "se": 0.7155119154690396,
        "worst": [
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            "seed": 922,
            "diff": 70.36492581479644
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          {
            "seed": 1459,
            "diff": 70.80835183546549
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          {
            "seed": 1994,
            "diff": 71.1685370951592
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          {
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            "diff": 72.38706802520124
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          {
            "seed": 445,
            "diff": 72.42278078288541
          }
        ]
      },
      "tuning_rank": 7
    },
    {
      "variant": "v12",
      "description": "100% router table; 0.60 fair-price skew.",
      "code_sha256": "456c2cd1edbb8dbdea917588dbbcec118c4d467e806ecd77bdd0ce6a2f11ecb6",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 500.5232532154063,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 131.71883259772068,
        "se": 0.7450472492117137,
        "worst": [
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            "seed": 1994,
            "diff": 66.6714270026394
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            "diff": 67.39760542684297
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            "diff": 68.10263035054356
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          {
            "seed": 1104,
            "diff": 68.40183437896849
          }
        ]
      },
      "tuning_rank": 8
    },
    {
      "variant": "v21",
      "description": "40% router table; 0.80 fair-price skew.",
      "code_sha256": "6ff580047ce9139b17175b9d20b6f01322feeb517a6cb46d7dc0c768547ea72d",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 499.1313083931927,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 130.326887775507,
        "se": 0.7778834697877761,
        "worst": [
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            "seed": 922,
            "diff": 62.45356392813403
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          {
            "seed": 1994,
            "diff": 62.71627868591412
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          {
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            "diff": 64.94362414438825
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          {
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            "diff": 66.09150022786326
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          {
            "seed": 526,
            "diff": 66.26099896750219
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        ]
      },
      "tuning_rank": 9
    },
    {
      "variant": "v11",
      "description": "150% router table; 0.70 fair-price skew.",
      "code_sha256": "7d89e2b251c88ff070e1ca4b59e8cb5ba2502217ce0a0b17ef9987c811512d63",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 496.35199924678665,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 127.54757862910097,
        "se": 0.8363178505722263,
        "worst": [
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            "diff": 55.322990918000244
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            "diff": 55.48809829812046
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            "diff": 55.84031868864139
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        ]
      },
      "tuning_rank": 10
    },
    {
      "variant": "v13",
      "description": "125% router table; 0.60 fair-price skew.",
      "code_sha256": "8129f5de9b92e1bf01276553030c5d2831ff72c901bc759ac716583f338d33c9",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 496.0918346299521,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 127.28741401226638,
        "se": 0.7682746912174466,
        "worst": [
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            "diff": 60.29539856271953
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            "diff": 60.75204308134062
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            "diff": 61.59046081497462
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          {
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            "diff": 62.49265883284562
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        ]
      },
      "tuning_rank": 11
    },
    {
      "variant": "v10",
      "description": "150% router table; 0.50 fair-price skew.",
      "code_sha256": "17b85438bbb6fb80e6daed1743e3492641871a4bb8431486565ecb773e66218e",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 478.22171635370887,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 109.41729573602316,
        "se": 0.717301074722605,
        "worst": [
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            "diff": 49.534593573603104
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            "diff": 49.8703729916092
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        ]
      },
      "tuning_rank": 12
    },
    {
      "variant": "v3",
      "description": "40% fee table; full skew; clipped first-trade filter; no within-step updates.",
      "code_sha256": "0ac950a71afc80cdcac7646f3cd99da81d74a43f2ee7e96ad3b430fd042a41c4",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 446.9187185745998,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 78.11429795691406,
        "se": 0.9052416281249893,
        "worst": [
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            "seed": 1949,
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          {
            "seed": 1919,
            "diff": -86.30418999244887
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          {
            "seed": 1904,
            "diff": -77.94657802959875
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        ]
      },
      "tuning_rank": 13
    },
    {
      "variant": "v8",
      "description": "100% router table; 0.30 fair-price skew.",
      "code_sha256": "37cf4fbb422516e0f0aec4ac33f28ecee78d7863f2b92cfb1c89fb26f8b5fa74",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 443.8640413202162,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 75.05962070253052,
        "se": 0.4525775267845305,
        "worst": [
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          {
            "seed": 1104,
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        ]
      },
      "tuning_rank": 14
    },
    {
      "variant": "v6",
      "description": "65% router table; full skew; first/later gains 1/4 and 1/20.",
      "code_sha256": "b355a1ad24ac590abd126ea6d7234d8a4f923668f343b0a694aae1e20c6b8c46",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 439.7023691468205,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 70.89794852913482,
        "se": 1.1185836898354575,
        "worst": [
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        ]
      },
      "tuning_rank": 15
    },
    {
      "variant": "v4",
      "description": "60% fee table; full skew; clipped first-trade filter; no within-step updates.",
      "code_sha256": "46809ebc0a2497192731b3087ca3c4ccf52f90cfd9ab43b3fa0333ee58c35cf1",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 430.7757429700288,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 61.971322352343115,
        "se": 0.9318892465327816,
        "worst": [
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          {
            "seed": 1949,
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        ]
      },
      "tuning_rank": 16
    },
    {
      "variant": "v7",
      "description": "65% router table; 0.30 fair-price skew.",
      "code_sha256": "d3b41356d37a57f54d394dc947bbcde8cc89fe448a1552ba1c2abb9aa82c373f",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 418.4035552095998,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 49.59913459191409,
        "se": 0.38323830248659924,
        "worst": [
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            "seed": 587,
            "diff": 24.61263905553676
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        ]
      },
      "tuning_rank": 17
    },
    {
      "variant": "v5",
      "description": "Router retail-edge/GBM-loss table; full skew; first/later gains 1/4 and 1/20.",
      "code_sha256": "f434c17cb87d5bb931a8157914bc19349a329b266ae5359fb7b0bc74cfc38cb3",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 413.16474342665674,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": 44.36032280897108,
        "se": 1.1551835601237863,
        "worst": [
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            "seed": 281,
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          {
            "seed": 208,
            "diff": -164.3004379558717
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        ]
      },
      "tuning_rank": 18
    },
    {
      "variant": "control30",
      "description": "Fixed 30 bps control.",
      "code_sha256": "9bf61770e9049d495ea17cc8051f3c21ec3d04140734aa509edc8987b23e89f9",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 342.94218249497794,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": -25.862238122707726,
        "se": 0.19765280872841595,
        "worst": [
          {
            "seed": 1849,
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          {
            "seed": 118,
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          {
            "seed": 1503,
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          {
            "seed": 1588,
            "diff": -52.96637616291895
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        ]
      },
      "tuning_rank": 19
    },
    {
      "variant": "v2",
      "description": "60% fee table; full skew; rejection filter; size estimate constrained to known prior.",
      "code_sha256": "5b1a29a49cb7a3186c97e8f3972f42c257181397b480fe8cf54fc41cf4675946",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 232.69525770762766,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": -136.10916291005802,
        "se": 1.9676546353021218,
        "worst": [
          {
            "seed": 901,
            "diff": -342.91653606230045
          },
          {
            "seed": 531,
            "diff": -334.14993065178857
          },
          {
            "seed": 330,
            "diff": -332.62255889684326
          },
          {
            "seed": 229,
            "diff": -327.76154825379695
          },
          {
            "seed": 1069,
            "diff": -326.7746926390648
          }
        ]
      },
      "tuning_rank": 20
    },
    {
      "variant": "v1",
      "description": "Fee-only table; full skew; rejection filter; uncorrected fill-size estimate.",
      "code_sha256": "1e0f170a7d9bef229d6cc97c7cffca2cb509053ab6522801e9c8497f8b774598",
      "n": 2000,
      "reference": "StarterStrategy.sol (50 bps)",
      "mean_edge": 198.67128309996602,
      "paired": {
        "n": 2000,
        "seed_start": 0,
        "mean_diff": -170.1331375177197,
        "se": 1.558626177270299,
        "worst": [
          {
            "seed": 901,
            "diff": -344.1254107809781
          },
          {
            "seed": 531,
            "diff": -339.4390126662996
          },
          {
            "seed": 330,
            "diff": -332.0779469774325
          },
          {
            "seed": 229,
            "diff": -328.3504595482484
          },
          {
            "seed": 1067,
            "diff": -327.72962617042174
          }
        ]
      },
      "tuning_rank": 21
    }
  ],
  "next": [
    "Model normalizer displacement conditionally instead of using a uniform band prior.",
    "Correct censored retail fills and distinguish fair-price estimation error from GBM volatility.",
    "Use exact multiplicative fee conversion; compare it and the batch winner on new paired seeds, since this confirmation is only versus the starter."
  ],
  "code": "pragma solidity ^0.8.24;\nimport {AMMStrategyBase} from \"./AMMStrategyBase.sol\";\nimport {TradeInfo} from \"./IAMMStrategy.sol\";\ncontract Strategy is AMMStrategyBase {\nfunction afterInitialize(uint256 x,uint256 y) external override returns(uint256,uint256){slots[0]=y*WAD/x;slots[2]=50*BPS;slots[3]=50*BPS;slots[4]=10*BPS;slots[5]=8e17;slots[6]=20e18;return(50*BPS,50*BPS);}\nfunction afterSwap(TradeInfo calldata t) external override returns(uint256 b,uint256 a){\nuint256 s=t.reserveY*WAD/t.reserveX;uint256 p=slots[0];uint256 dt=t.timestamp+1-slots[1];\nuint256 f=t.isBuy?slots[2]:slots[3];uint256 q=t.isBuy?s*(WAD-f)/WAD:s*WAD/(WAD-f);\nbool arb;\nif(dt>0){uint256 d=absDiff(q,p)*WAD/p;uint256 g=clamp(slots[4]*(dt>8?8:dt)*3,30*BPS,300*BPS);\nif(d<g){arb=true;slots[4]=(slots[4]*63+clamp(d/(dt>1?2:1),4*BPS,20*BPS))/64;}uint256 h=p*g/WAD;if(q>p)p+=((q-p)>h?h:q-p)/4;else p-=((p-q)>h?h:p-q)/4;\nslots[5]=(slots[5]*64+slots[7]*WAD)/(64+dt);slots[7]=0;slots[1]=t.timestamp+1;}\nif(dt==0)p=(p*19+q)/20;\nif(!arb){slots[7]++;uint256 v=t.amountY*2;slots[6]=(slots[6]*63+clamp(v,19e18,21e18))/64;}\nslots[0]=p;uint256 u=slots[6]*10000/t.reserveY;\nuint256 c=u<15?29:u<20?30:u<25?33:u<30?35:38;\nc=c*80/100;uint256 risk=slots[4]*10e17/(slots[5]+2e17);c=c*BPS+risk/10;\nint256 m=(int256(s)-int256(p))*int256(WAD)/int256(p)*8/10;\nb=uint256(clampi(int256(c)+m));a=uint256(clampi(int256(c)-m));slots[2]=b;slots[3]=a;return(b,a);}\nfunction clampi(int256 x) internal pure returns(int256){return x<0?int256(0):x>int256(MAX_FEE)?int256(MAX_FEE):x;}\nfunction getName() external pure override returns(string memory){return \"EdgeMax\";}\n}\n",
  "code_sha256": "8e7a5b19cc810867b977bafa79621e482a1c930246e13035d0ec325aded6f178",
  "score": {
    "n": 1000,
    "mean_edge": 517.5319553867561
  },
  "paired": {
    "n": 2000,
    "seed_start": 300000,
    "mean_diff": 147.19419277642743,
    "se": 0.8435187956431697,
    "worst": [
      {
        "seed": 301522,
        "diff": 70.94522868401401
      },
      {
        "seed": 300592,
        "diff": 71.78002605617479
      },
      {
        "seed": 300886,
        "diff": 73.04208647364584
      },
      {
        "seed": 301201,
        "diff": 74.93770432675595
      },
      {
        "seed": 300076,
        "diff": 75.67849773513035
      }
    ]
  },
  "starter_mean_edge": 368.71392872072875,
  "seconds_per_simulation": 0.11146851978101767,
  "validate": "pass"
}