{
 "item": "r04",
 "batch": "ep8-sweep-f22",
 "np2_check": {
  "seeds": "0..999",
  "n": 1000,
  "mean_edge": 526.115572,
  "se": 2.7896,
  "expected": 526.1156,
  "match": true,
  "sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0",
  "construction": "TWO code (artifact 528a6da7...) with NP code (artifact da313379...) from '// Interior retail routing' to (excl.) 'uint256 tradeRatio =' inserted before TWO's 'uint256 tradeRatio ='",
  "np2_constants": {
   "PHAT_ALPHA": 270000000000000000,
   "PHAT_ALPHA_RETAIL": 60000000000000000,
   "PHAT_ALPHA_SAME": 120000000000000000
  }
 },
 "np2_mean_10000_11999": 523.801274,
 "np2_se_10000_11999": 2.035626,
 "cells": [
  {
   "retail": 0.04,
   "same": 0.09,
   "first": 0.22,
   "n": 2000,
   "mean_diff": -0.255223,
   "se": 0.017297,
   "worst": [
    {
     "seed": 10870,
     "diff": -12.231866
    },
    {
     "seed": 10846,
     "diff": -5.39458
    },
    {
     "seed": 10014,
     "diff": -5.180539
    },
    {
     "seed": 10609,
     "diff": -3.88708
    },
    {
     "seed": 10227,
     "diff": -2.817456
    }
   ],
   "sha256": "ca3c9c976197566cd68e2bd830c2040838bf3b36c8ec725fa19c2f0ea359ad64",
   "cand_mean_10000_11999": 523.546051,
   "wads": {
    "PHAT_ALPHA": 220000000000000000,
    "PHAT_ALPHA_RETAIL": 40000000000000000,
    "PHAT_ALPHA_SAME": 90000000000000000
   }
  },
  {
   "retail": 0.04,
   "same": 0.12,
   "first": 0.22,
   "n": 2000,
   "mean_diff": -0.132219,
   "se": 0.016004,
   "worst": [
    {
     "seed": 10870,
     "diff": -12.077202
    },
    {
     "seed": 10846,
     "diff": -5.051632
    },
    {
     "seed": 10014,
     "diff": -4.253669
    },
    {
     "seed": 10609,
     "diff": -3.540871
    },
    {
     "seed": 10463,
     "diff": -2.598558
    }
   ],
   "sha256": "5330c1902556c92d9e17da6192103a2fab8a0ffdccebd2f022176de56a92992e",
   "cand_mean_10000_11999": 523.669055,
   "wads": {
    "PHAT_ALPHA": 220000000000000000,
    "PHAT_ALPHA_RETAIL": 40000000000000000,
    "PHAT_ALPHA_SAME": 120000000000000000
   }
  },
  {
   "retail": 0.04,
   "same": 0.16,
   "first": 0.22,
   "n": 2000,
   "mean_diff": -0.167956,
   "se": 0.015573,
   "worst": [
    {
     "seed": 10870,
     "diff": -11.832351
    },
    {
     "seed": 10846,
     "diff": -5.850871
    },
    {
     "seed": 10014,
     "diff": -4.635607
    },
    {
     "seed": 10227,
     "diff": -4.428049
    },
    {
     "seed": 10609,
     "diff": -3.025069
    }
   ],
   "sha256": "1f72066d89fb73aaaafa1d2957c60784444f00fcc756793334c7e870d0d59312",
   "cand_mean_10000_11999": 523.633318,
   "wads": {
    "PHAT_ALPHA": 220000000000000000,
    "PHAT_ALPHA_RETAIL": 40000000000000000,
    "PHAT_ALPHA_SAME": 160000000000000000
   }
  }
 ],
 "best_cell": {
  "retail": 0.04,
  "same": 0.12,
  "first": 0.22,
  "mean_diff": -0.132219,
  "se": 0.016004,
  "sha256": "5330c1902556c92d9e17da6192103a2fab8a0ffdccebd2f022176de56a92992e",
  "note": "best of the three only in the sense of least negative; every cell is below NP2 by >8 se, so none should be stacked"
 },
 "code": "// SPDX-License-Identifier: MIT\npragma solidity ^0.8.24;\n\nimport {AMMStrategyBase} from \"./AMMStrategyBase.sol\";\nimport {TradeInfo} from \"./IAMMStrategy.sol\";\n\ncontract Strategy is AMMStrategyBase {\n    uint256 constant ELAPSED_CAP = 8;\n    uint256 constant SIGNAL_THRESHOLD = WAD / 650;\n    uint256 constant DIR_DECAY = 750000000000000000;\n    uint256 constant ACT_DECAY = 530000000000000000;\n    uint256 constant SIZE_DECAY = 530000000000000000;\n    uint256 constant TOX_DECAY = 910000000000000000;\n    uint256 constant SIGMA_DECAY = 690000000000000000;\n    uint256 constant LAMBDA_DECAY = 990000000000000000;\n    uint256 constant SIZE_BLEND_DECAY = 828000000000000000;\n    uint256 constant TOX_BLEND_DECAY = 51000000000000000;\n    uint256 constant ACT_BLEND_DECAY = 985000000000000000;\n    uint256 constant PHAT_ALPHA = 220000000000000000;\n    uint256 constant PHAT_ALPHA_RETAIL = 40000000000000000;\n    uint256 constant PHAT_ALPHA_SAME = 120000000000000000;\n    uint256 constant REVERT_U = 0;\n    uint256 constant DIR_IMPACT_MULT = 4;\n    uint256 constant GATE_SIGMA_MULT = 7200000000000000000;\n    uint256 constant MIN_GATE = 30000000000000000;\n    uint256 constant TRADE_TOX_BOOST = 3500 * BPS;\n    uint256 constant STALE_ATTRACT_FRAC = 1050000000000000000;\n    uint256 constant RET_CAP = WAD / 35;\n    uint256 constant TOX_CAP = WAD / 5;\n    uint256 constant TRADE_RATIO_CAP = WAD / 5;\n    uint256 constant LAMBDA_CAP = 1820000000000000000;\n    uint256 constant STEP_COUNT_CAP = 64;\n    uint256 constant BASE_FEE = 4 * BPS;\n    uint256 constant SIGMA_COEF = 200000000000000000;\n    uint256 constant LAMBDA_COEF = 12 * BPS;\n    uint256 constant FLOW_SIZE_COEF = 4842 * BPS;\n    uint256 constant TOX_COEF = 300 * BPS;\n    uint256 constant TOX_QUAD_COEF = 15000 * BPS;\n    uint256 constant ACT_COEF = 91843 * BPS;\n    uint256 constant DIR_COEF = 20 * BPS;\n    uint256 constant DIR_TOX_COEF = 100 * BPS;\n    uint256 constant STALE_DIR_COEF = 6850 * BPS;\n    uint256 constant SIGMA_TOX_COEF = 500 * BPS;\n    uint256 constant TAIL_KNEE = 600 * BPS;\n    uint256 constant TAIL_SLOPE_PROTECT = 930000000000000000;\n    uint256 constant TAIL_SLOPE_ATTRACT = 850000000000000000;\n\n    function afterInitialize(uint256 initialX, uint256 initialY) external override returns (uint256, uint256) {\n        slots[0] = BASE_FEE; slots[1] = BASE_FEE; slots[2] = 0; slots[3] = WAD; slots[4] = 0;\n        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n        slots[9] = 0; slots[10] = 0; slots[11] = 0; slots[12] = 0;\n        return (BASE_FEE, BASE_FEE);\n    }\n\n    function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {\n        uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = slots[2];\n        uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];\n        uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n        uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10];\n\n        bool isNewStep = trade.timestamp > lastTs;\n        if (isNewStep) {\n            uint256 elapsedRaw = trade.timestamp - lastTs;\n            uint256 elapsed = elapsedRaw > ELAPSED_CAP ? ELAPSED_CAP : elapsedRaw;\n            dirState = _decayCentered(dirState, DIR_DECAY, elapsed);\n            actEma = wmul(actEma, _powWad(ACT_DECAY, elapsed));\n            sizeHat = wmul(sizeHat, _powWad(SIZE_DECAY, elapsed));\n            toxEma = wmul(toxEma, _powWad(TOX_DECAY, elapsed));\n            if (stepTradeCount > 0 && elapsedRaw > 0) {\n                uint256 lambdaInst = (stepTradeCount * WAD) / elapsedRaw;\n                if (lambdaInst > LAMBDA_CAP) lambdaInst = LAMBDA_CAP;\n                lambdaHat = wmul(lambdaHat, LAMBDA_DECAY) + wmul(lambdaInst, WAD - LAMBDA_DECAY);\n            }\n            stepTradeCount = 0;\n        }\n\n        bool firstInStep = stepTradeCount == 0;\n        uint256 spot = trade.reserveX > 0 ? wdiv(trade.reserveY, trade.reserveX) : pHat;\n        if (pHat == 0) pHat = spot;\n\n        uint256 feeUsed = trade.isBuy ? prevBidFee : prevAskFee;\n        uint256 gamma = feeUsed < WAD ? WAD - feeUsed : 0;\n        uint256 pImplied;\n        if (gamma == 0) { pImplied = spot; }\n        else { pImplied = trade.isBuy ? wmul(spot, gamma) : wdiv(spot, gamma); }\n\n        {\n            uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;\n            uint256 alpha = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;\n            uint256 prePhat = pHat;\n            bool secondPrint = !firstInStep && stepTradeCount == 1;\n            bool sameDir = false; bool oppDir = false;\n            if (secondPrint) {\n                bool up2 = pImplied >= pHat;\n                uint256 d1 = slots[12];\n                if (d1 != 0) { sameDir = (d1 == 1) == up2; oppDir = !sameDir; }\n                if (sameDir) alpha = PHAT_ALPHA_SAME;\n            }\n            if (firstInStep) { slots[11] = pHat; slots[12] = pImplied >= pHat ? 1 : 2; }\n            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n            if (ret <= adaptiveGate) { pHat = wmul(pHat, WAD - alpha) + wmul(pImplied, alpha); }\n            if (oppDir && REVERT_U > 0) {\n                uint256 pre = slots[11];\n                if (pre > pHat) pHat = pHat + wmul(pre - pHat, REVERT_U);\n                else pHat = pHat - wmul(pHat - pre, REVERT_U);\n            }\n            if (firstInStep) {\n                if (ret > RET_CAP) ret = RET_CAP;\n                sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);\n            }\n        }\n\n        // Interior retail routing equalizes fee-adjusted marginal prices.\n        // Subsequent trades in a step cannot be the initial arbitrage trade.\n        if (!firstInStep && feeUsed > 30 * BPS && gamma > 0) {\n            uint256 normalSpot = trade.isBuy\n                ? wdiv(wmul(spot, gamma), WAD - 30 * BPS)\n                : wdiv(wmul(spot, WAD - 30 * BPS), gamma);\n            pHat = wmul(pHat, 90 * WAD / 100) + wmul(normalSpot, 10 * WAD / 100);\n        }\n\n        uint256 tradeRatio = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n        if (tradeRatio > TRADE_RATIO_CAP) tradeRatio = TRADE_RATIO_CAP;\n\n        if (tradeRatio > SIGNAL_THRESHOLD) {\n            uint256 push = tradeRatio * DIR_IMPACT_MULT;\n            if (push > WAD / 4) push = WAD / 4;\n            if (trade.isBuy) {\n                dirState = dirState + push;\n                if (dirState > 2 * WAD) dirState = 2 * WAD;\n            } else {\n                dirState = dirState > push ? dirState - push : 0;\n            }\n            actEma = wmul(actEma, ACT_BLEND_DECAY) + wmul(tradeRatio, WAD - ACT_BLEND_DECAY);\n            sizeHat = wmul(sizeHat, SIZE_BLEND_DECAY) + wmul(tradeRatio, WAD - SIZE_BLEND_DECAY);\n            if (sizeHat > WAD) sizeHat = WAD;\n        }\n\n        uint256 tox = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n        if (tox > TOX_CAP) tox = TOX_CAP;\n        toxEma = wmul(toxEma, TOX_BLEND_DECAY) + wmul(tox, WAD - TOX_BLEND_DECAY);\n        uint256 toxSignal = toxEma;\n\n        stepTradeCount = stepTradeCount + 1;\n        if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;\n\n        uint256 flowSize = wmul(lambdaHat, sizeHat);\n        uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n        uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);\n        fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));\n\n        uint256 dirDev; bool sellPressure;\n        if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }\n        else { dirDev = WAD - dirState; sellPressure = false; }\n\n        uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));\n        uint256 bidFee; uint256 askFee;\n        if (sellPressure) {\n            bidFee = fMid + skew;\n            askFee = fMid > skew ? fMid - skew : 0;\n        } else {\n            askFee = fMid + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;\n        }\n\n        {\n            uint256 staleShift = wmul(STALE_DIR_COEF, toxSignal);\n            uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);\n            if (spot >= pHat) {\n                bidFee = bidFee + staleShift;\n                askFee = askFee > attractShift ? askFee - attractShift : 0;\n            } else {\n                askFee = askFee + staleShift;\n                bidFee = bidFee > attractShift ? bidFee - attractShift : 0;\n            }\n        }\n\n        {\n            bool tradeAligned = (trade.isBuy && spot >= pHat) || (!trade.isBuy && spot < pHat);\n            if (tradeAligned) {\n                uint256 tradeBoost = wmul(TRADE_TOX_BOOST, tradeRatio);\n                if (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n                else { askFee = askFee + tradeBoost; }\n            }\n        }\n\n        if (sellPressure) {\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));\n        } else {\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));\n        }\n\n        slots[0] = bidFee; slots[1] = askFee; slots[2] = trade.timestamp;\n        slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n        slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;\n        slots[9] = toxEma; slots[10] = stepTradeCount;\n\n        return (bidFee, askFee);\n    }\n\n    function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {\n        if (fee <= TAIL_KNEE) return fee;\n        return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);\n    }\n\n    function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {\n        result = WAD;\n        while (exp > 0) {\n            if (exp & 1 == 1) result = wmul(result, factor);\n            factor = wmul(factor, factor);\n            exp >>= 1;\n        }\n    }\n\n    function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {\n        uint256 mul = _powWad(decayFactor, elapsed);\n        if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }\n        uint256 below = wmul(WAD - centered, mul);\n        return below < WAD ? WAD - below : 0;\n    }\n\n    function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n",
 "blocked": null,
 "method": {
  "simulator": "github.com/benedictbrady/amm-challenge @ 6b6921f8d463314aa7c96234e1be25a25245f704, built with the item's scratch/setup.sh (uv venv py3.12, maturin develop --release amm_sim_rs), amm-match validate passed for NP2 and all three candidates",
  "configs": "per seed s: g=numpy.random.default_rng(s); retail_mean_size=g.uniform(19,21); retail_arrival_rate=g.uniform(0.6,1.0); gbm_sigma=g.uniform(0.000882,0.001008); build_config(seed=s, gbm_sigma, retail_arrival_rate, retail_mean_size) (same draw order as MatchRunner._build_configs)",
  "runs": "amm_sim_rs.run_batch(candidate, vanilla, cfgs, 8) and run_batch(NP2, vanilla, cfgs, 8) separately, 20 seeds per call, vanilla = get_vanilla_bytecode_and_abi()[0]; d = edges['submission'](cand) - edges['submission'](NP2) per seed; mean_diff = mean(d); se = std(d, ddof=1)/sqrt(n); worst = 5 lowest d with seeds",
  "seeds": "10000..11999 (n=2000) for all cells against one NP2 run on the same seeds; no confirm block (grid-cell measurement, per brief)",
  "wad": "int(round(v*1e18)); candidates differ from NP2 only in the PHAT_ALPHA, PHAT_ALPHA_RETAIL, PHAT_ALPHA_SAME constant lines (the SAME=0.12 cell leaves PHAT_ALPHA_SAME at NP2's value)",
  "seconds_per_2000_seed_run": 251.8
 },
 "next": [
  "Do not stack any of these cells: RETAIL=0.04 together with FIRST=0.22 loses 0.13 to 0.26 vs NP2 at se ~0.016 for every SAME value; FIRST=0.22 is the likely culprit since RETAIL=0.03 alone measured +0.105 (brief).",
  "SAME ordering within the grid: 0.12 (-0.132) > 0.16 (-0.168) > 0.09 (-0.255); the SAME dependence is shallow (~0.1 over 0.09..0.16) compared with the ~-0.2 shift the RETAIL/FIRST pair causes, so measure FIRST alone (0.22 and 0.32 vs 0.27) with RETAIL and SAME at NP2 values to separate the effects.",
  "Seed 10870 loses ~12 edge in all three cells; inspecting that path (likely a large arb step where a slower first-print alpha leaves pHat stale) would tell whether a FIRST decrease is intrinsically harmful.",
  "Constants near NP2 are flat or negative; the objective's call for new mechanisms stands."
 ]
}