{"item": "b", "blocked": null, "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 = 270000000000000000;\n    uint256 constant PHAT_ALPHA_RETAIL = 60000000000000000;\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[3] = WAD; \n        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n        slots[15] = 400000000000000000 | (uint256(2000000000000000) << 160); slots[13] = 902500000000; slots[14] = slots[5]; \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 = uint64(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        uint256 sigmaForFast = sigmaHat;\n        uint256 fastHat = slots[14];\n        uint256 uncertainty = slots[13];\n        uint256 silent = trade.timestamp > lastTs ? trade.timestamp - lastTs : 0;\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            // Process variance is propagated inside the censored update.\n            if (uncertainty > 100000000000000) uncertainty = 100000000000000;\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        // S: infer a no-trade interval center from the last post-trade spot.\n        uint256 silenceScale = WAD;\n        if (firstInStep && silent > 1) {\n            uint256 g = silent - 1;\n            if (g > 1) g = 1;\n            uint256 w = WAD - _powWad(800000000000000000, g);\n            uint256 s = uint128(slots[2] >> 64);\n            if (s == 0) s = pHat;\n            uint256 c = (wmul(s, WAD - prevBidFee) + wdiv(s, WAD - prevAskFee)) / 2;\n            if (c >= pHat) pHat += wmul(w, c - pHat);\n            else pHat -= wmul(w, pHat - c);\n            silenceScale = WAD - wmul(300000000000000000, w);\n        }\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[12] = pImplied >= pHat ? 1 : 2; }\n            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n            alpha = wmul(alpha, silenceScale);\n            adaptiveGate = wmul(adaptiveGate, silenceScale);\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        // Censored assumed-density posterior. No external or future inputs.\n        uint256 arbProbability;\n        (fastHat, uncertainty, arbProbability) = _posterior(PosteriorInput(\n            fastHat, uncertainty, pImplied, spot, uint128(slots[2] >> 64),\n            prevBidFee, prevAskFee, firstInStep, silent, trade.isBuy,\n            trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0\n        ));\n        slots[13] = uncertainty;\n        slots[14] = fastHat;\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 originalLambda = lambdaHat; uint256 originalSize = sizeHat;\n\n        if (241859945937197184 > 0) {\n            uint256 packedFlow = slots[15];\n            uint256 rate = uint80(packedFlow);\n            uint256 count = uint80(packedFlow >> 80);\n            uint256 meanSize = uint80(packedFlow >> 160);\n            if (rate == 0) rate = 400000000000000000;\n            if (meanSize == 0) meanSize = 2000000000000000;\n            if (isNewStep) {\n                uint256 inst = count / silent;\n                if (inst > 3 * WAD) inst = 3 * WAD;\n                uint256 retention = _powWad(999000000000000000, silent > 64 ? 64 : silent);\n                rate = wmul(rate, retention) + wmul(inst, WAD-retention);\n                count = 0;\n            }\n            uint256 weight = firstInStep ? WAD-arbProbability : WAD;\n            uint256 correctedWeight = weight;\n            if (2 == 2) {\n                uint256 missing = wmul(feeUsed, 196030880396139429888);\n                if (missing > 333333333333333376) missing = 333333333333333376;\n                correctedWeight = wdiv(weight, WAD-missing);\n            }\n            count += correctedWeight;\n            uint256 learning = wmul(WAD-999000000000000000, weight);\n            meanSize = _blend(meanSize, tradeRatio, learning);\n            slots[15]=rate | (count << 80) | (meanSize << 160);\n            uint256 retailRate = wmul(rate, 366383424913407168);\n            uint256 retailSize = 2 == 0 ? sizeHat : wmul(meanSize,1837966741671826944);\n            lambdaHat = _blend(lambdaHat,retailRate,241859945937197184);\n            sizeHat = _blend(sizeHat,retailSize,241859945937197184);\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 fMidAsk = fMid;\n        {\n            uint256 sh = slots[2] >> 192;\n            sh = sh == 0 ? WAD / 2 : sh - 1;\n            uint256 sw = firstInStep ? WAD - arbProbability : WAD;\n            sh = _blend(sh, trade.isBuy ? 0 : WAD, wmul(WAD - 999900000000000000, sw));\n            slots[2] = ((sh + 1) << 192) | uint192(slots[2]);\n            uint256 lamA = _sideLam(lambdaHat, 2 * sh, 2257346805976610816, 239162152072287296, true);\n            uint256 lamB = _sideLam(lambdaHat, 2 * (WAD - sh), 2257346805976610816, 239162152072287296, true);\n            fMid = _sideFee(fMid, lambdaHat, lamB, sizeHat);\n            fMidAsk = _sideFee(fMidAsk, lambdaHat, lamA, sizeHat);\n        }\n        lambdaHat = originalLambda; sizeHat = originalSize;\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 = fMidAsk > skew ? fMidAsk - skew : 0;\n        } else {\n            askFee = fMidAsk + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;\n        }\n\n        {\n            uint256 staleHat = wmul(pHat, 700000000000000000) + wmul(fastHat, 300000000000000000);\n            uint256 staleTox = wdiv(absDiff(spot, staleHat), staleHat);\n            if (staleTox > TOX_CAP) staleTox = TOX_CAP;\n            uint256 staleShift = wmul(STALE_DIR_COEF, staleTox);\n            uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);\n            if (spot >= staleHat) {\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 (!firstInStep && tradeBoost > 16 * BPS) tradeBoost = 16 * BPS;\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        if (firstInStep) {\n            if (askFee > bidFee && bidFee > 30 * BPS) bidFee = 30 * BPS;\n            else if (bidFee > askFee && askFee > 30 * BPS) askFee = 30 * BPS;\n        }\n\n        if (bidFee > askFee && askFee > 36 * BPS) askFee = 36 * BPS;\n        else if (askFee > bidFee && bidFee > 36 * BPS) bidFee = 36 * BPS;\n\n        slots[0] = bidFee; slots[1] = askFee; slots[2] = ((slots[2] >> 192) << 192) | (spot << 64) | 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\n    struct PosteriorInput {\n        uint256 mu; uint256 v; uint256 obs; uint256 spot; uint256 preSpot;\n        uint256 bid; uint256 ask; bool first; uint256 silent; bool buy; uint256 size;\n    }\n    function _posterior(PosteriorInput memory x) internal pure returns (uint256, uint256, uint256) {\n        if (x.mu == 0) x.mu = x.spot;\n        if (x.v < 10000000000) x.v = 10000000000;\n        uint256 lo = wmul(x.preSpot, WAD-x.bid);\n        uint256 hi = wdiv(x.preSpot, WAD-x.ask);\n        if (x.first) {\n            if (x.silent>1 && x.preSpot>0) {\n                uint256 elapsed=x.silent>8?8:x.silent;\n                x.v += 902500000000*(elapsed-1);\n                (x.mu,x.v)=_band(x.mu,x.v,lo,hi);\n            }\n            x.v+=902500000000;\n        }\n        uint256 mRetail = x.mu;\n        uint256 vRetail = x.v;\n        // A missing own-pool trade is a censored price observation.\n        if (x.first && x.preSpot > 0) {\n            (mRetail, vRetail) = _band(x.mu, x.v, lo, hi);\n        }\n        if (!x.first) {\n            // A later print is retail. Only an interior route is an observation\n            // of the other pool, with explicit observation uncertainty.\n            uint256 fee = x.buy ? x.bid : x.ask;\n            if (fee > 30 * BPS) {\n                uint256 normal = x.buy ? wdiv(wmul(x.spot, WAD-fee), WAD-30*BPS)\n                    : wdiv(wmul(x.spot, WAD-30*BPS), WAD-fee);\n                uint256 residual = wdiv(absDiff(normal, x.mu),x.mu);\n                uint256 noise = 9000000000000 + wmul(residual,residual);\n                uint256 k = wdiv(x.v,x.v+noise);\n                return (_blend(x.mu,normal,k),wmul(x.v,WAD-k),0);\n            }\n            return (x.mu,x.v,0);\n        }\n        uint256 e = wdiv(absDiff(x.obs,x.mu),x.mu);\n        uint256 totalV = x.v + 22500000000;\n        uint256 z = wdiv(wmul(e,e),totalV);\n        uint256 density = _powWad(wdiv(WAD,WAD+z/8),4);\n        uint256 odds = wmul(density,wdiv(4000000000000000,_isqrt(totalV*WAD)));\n        if (x.size > 3000000000000000) odds = wmul(odds,4*WAD/10);\n        if (x.silent > 1) odds = wmul(odds,8*WAD/10);\n        uint256 sd = _isqrt(x.v*WAD);\n        uint256 width = wdiv(hi-lo,x.mu);\n        uint256 distance = x.mu<lo?lo-x.mu:(x.mu>hi?x.mu-hi:0);\n        uint256 zBand = wdiv(wdiv(distance,x.mu),sd);\n        uint256 mass = wmul(wdiv(width,width+2*sd),wdiv(WAD,WAD+wmul(zBand,zBand)));\n        if (mass < WAD/100) mass = WAD/100;\n        odds = wdiv(odds,mass);\n        uint256 prob = wdiv(odds,WAD+odds);\n        uint256 kArb = wdiv(x.v,totalV);\n        uint256 mArb = _blend(x.mu,x.obs,kArb);\n        uint256 mean = _blend(mRetail,mArb,prob);\n        uint256 between = wdiv(absDiff(mArb,mRetail),x.mu);\n        uint256 variance = wmul(prob,wmul(x.v,WAD-kArb)) + wmul(WAD-prob,vRetail)\n            + wmul(wmul(prob,WAD-prob),wmul(between,between));\n        if (variance > 100000000000000) variance = 100000000000000;\n        return (mean,variance,prob);\n    }\n    function _sideLam(uint256 lam, uint256 f, uint256 cap, uint256 m, bool neg) internal pure returns (uint256) {\n        if (f > cap) f = cap;\n        uint256 target = wmul(lam, f);\n        if (!neg) return _blend(lam, target, m);\n        // negative side_mix: move away from the target by |m|\n        if (target >= lam) { uint256 d = wmul(target - lam, m); return lam > d ? lam - d : 0; }\n        return lam + wmul(lam - target, m);\n    }\n    function _sideFee(uint256 f, uint256 lam, uint256 lamSide, uint256 size) internal pure returns (uint256) {\n        uint256 d;\n        if (lamSide >= lam) { d = lamSide - lam; return f + wmul(LAMBDA_COEF, d) + wmul(FLOW_SIZE_COEF, wmul(d, size)); }\n        d = lam - lamSide; uint256 dec = wmul(LAMBDA_COEF, d) + wmul(FLOW_SIZE_COEF, wmul(d, size));\n        return f > dec ? f - dec : 0;\n    }\n    function _blend(uint256 a,uint256 b,uint256 w) internal pure returns(uint256) {\n        return b>=a ? a+wmul(b-a,w) : a-wmul(a-b,w);\n    }\n    function _band(uint256 mu,uint256 v,uint256 lo,uint256 hi) internal pure returns(uint256,uint256) {\n        // Soft interval likelihood avoids discontinuities at quadrature nodes.\n        uint256 sd=wmul(mu,_isqrt(v*WAD));\n        uint256[3] memory acc;\n        for(uint256 j=0;j<7;j++) {\n            uint256 p=j<3 ? (mu>(3-j)*sd?mu-(3-j)*sd:1) : mu+(j-3)*sd;\n            uint256 w=j==3?72:(j==2||j==4?45:(j==1||j==5?10:1));\n            uint256 distance=p<lo?lo-p:(p>hi?p-hi:0);\n            uint256 z=sd>0?wdiv(distance,sd):0;\n            uint256 likelihood=wdiv(WAD,WAD+4*wmul(z,z));\n            w=wmul(w*WAD,likelihood);\n            acc[0]+=w;acc[1]+=wmul(w,p);\n            uint256 d=wdiv(absDiff(p,mu),mu);\n            acc[2]+=wmul(w,wmul(d,d));\n        }\n        uint256 m=wdiv(acc[1],acc[0]);\n        uint256 d=wdiv(absDiff(m,mu),mu);\n        uint256 second=wdiv(acc[2],acc[0]);\n        return(m,second>wmul(d,d)?second-wmul(d,d):10000000000);\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    // Floor square root: bit-length seed and seven Newton steps (all uint256).\n    function _isqrt(uint256 x) internal pure returns (uint256 r) {\n        if (x == 0) return 0;\n        unchecked {\n            uint256 y = x;\n            r = 1;\n            if (y >> 128 != 0) { y >>= 128; r <<= 64; }\n            if (y >> 64 != 0) { y >>= 64; r <<= 32; }\n            if (y >> 32 != 0) { y >>= 32; r <<= 16; }\n            if (y >> 16 != 0) { y >>= 16; r <<= 8; }\n            if (y >> 8 != 0) { y >>= 8; r <<= 4; }\n            if (y >> 4 != 0) { y >>= 4; r <<= 2; }\n            if (y >> 2 != 0) { r <<= 1; }\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            uint256 t = x / r;\n            return r < t ? r : t;\n        }\n    }\n\n    function getName() external pure override returns (string memory) { return \"censored_10\"; }\n}\n", "sha256": "01c941bf542ed9e279009e509299295010e4e9e24f78c852db1db50c2284f76a", "params": {"side_mix": -0.2391621520722873, "side_retention": 0.9999, "side_cap": 2.257346805976611, "mix": 0.24185994593719717, "size_scale": 1.837966741671827, "other_rs2_params_exact": {"structure": 2, "retention_per_step": 0.999, "rate_scale": 0.36638342491340714, "quote_correction_slope": 196.03088039613942, "correction_cap": 1.5}}, "mechanism": "Per-side retail state on RS2 (built on V10). A decayed, posterior-weighted share sh of own fills that were retail buys (trader buys X, i.e. trade.isBuy==false, ask side) is kept in the free top 64 bits of slots[2] (stored as sh+1; 0 = uninitialised = 1/2), so afterInitialize is untouched (no new SSTORE in init). Per fill: weight = firstInStep ? 1-arbProbability : 1 (V10 posterior); sh = blend(sh, isRetailBuy?1:0, (1-side_retention)*weight). After RS2's blended lambdaHat is formed, the ask side's lambda input moves by side_mix toward min(2*sh,side_cap)*lambdaHat and the bid side's toward min(2*(1-sh),side_cap)*lambdaHat (negative side_mix moves away from the target); each side's fMid is recomputed from its own lambda via LAMBDA_COEF and FLOW_SIZE_COEF*lambda*sizeHat, then RS2's skew/stale/tail logic is applied unchanged. side_mix=0 returns RS2's exact source (sha256 f24b6ca1...eaf2, verified).", "log": [{"params": {"side_mix": 0.3637, "side_retention": 0.9999, "side_cap": 1.99, "mix": 0.4599, "size_scale": 1.402}, "sha256": "d2e6a4fdf5890ea90857c834c84c490a208e747a26c25334c89566c76a3abe76", "block": [870000, 870063], "n": 64, "gen": 0, "mean_diff": -0.4286, "se": 0.1018, "max_ok": 201226, "oog": 0}, {"params": {"side_mix": -0.7318, "side_retention": 0.9999, "side_cap": 2.191, "mix": 0.0, "size_scale": 1.1}, "sha256": "0b9ce55cad1ef229ffbfd26fe77bf4bf66603401ac6e154732f47074c9bea4cd", "block": [870000, 870063], "n": 64, 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870383], "n": 64, "gen": 5, "mean_diff": -0.5153, "se": 0.1093, "max_ok": 199997, "oog": 0}, {"params": {"side_mix": 0.7949, "side_retention": 0.9999, "side_cap": 3.0, "mix": 0.0, "size_scale": 1.086}, "sha256": "8c037ea665d08299e443c1d7f6371479dae5c20234ffae3935ebea21e7919a1a", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.01235, "se": 0.008008, "max_ok": 193334, "oog": 0}, {"params": {"side_mix": 0.5005, "side_retention": 0.9943, "side_cap": 3.0, "mix": 0.2028, "size_scale": 1.54}, "sha256": "589bbf93f12a9495d4415c240fbbf991f47b2710c2ea46ed313f516d6f9570ec", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.1898, "se": 0.05795, "max_ok": 199905, "oog": 0}, {"params": {"side_mix": 1.0, "side_retention": 0.9999, "side_cap": 2.447, "mix": 0.4528, "size_scale": 1.817}, "sha256": "92e6e2912efe3dd886d68648daa474f003cc05d79b64014d20b708c979c7359e", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.1304, "se": 0.07578, "max_ok": 199899, "oog": 0}, {"params": {"side_mix": 0.6496, "side_retention": 0.9999, "side_cap": 2.507, "mix": 0.1991, "size_scale": 1.147}, "sha256": "cb1e9e51dc43d1886394eb8a38195c940d3a8aaa5572248fd9404793d694be62", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.08372, "se": 0.06622, "max_ok": 199905, "oog": 0}, {"params": {"side_mix": 0.4302, "side_retention": 0.9967, "side_cap": 3.0, "mix": 0.09188, "size_scale": 1.389}, "sha256": "585ab1e774c216e3aeadd8095fdd1ab201649c686aa3340b4e9d4b2eba5a3e89", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.1597, "se": 0.04469, "max_ok": 199905, "oog": 0}, {"params": {"side_mix": 0.3307, "side_retention": 0.9743, "side_cap": 2.203, "mix": 0.03348, "size_scale": 1.009}, "sha256": "2a2f1ff100bbd92ae75569fc64c35cd733685349f34a6edbab91be7cf2fa9fbe", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.06442, "se": 0.04046, "max_ok": 199915, "oog": 0}, {"params": {"side_mix": 0.2654, "side_retention": 0.9971, "side_cap": 2.539, "mix": 0.2821, "size_scale": 2.068}, "sha256": "f4bf52c40659b5a4b08b27afa257a123e615256214c352e7950365de8991166b", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.1955, "se": 0.05749, "max_ok": 199905, "oog": 0}, {"params": {"side_mix": 1.0, "side_retention": 0.9966, "side_cap": 2.591, "mix": 0.2431, "size_scale": 1.992}, "sha256": "f287647ebb107f1989ad5c56a7d4519d4074ae3f69805a65ca403d75507e44ca", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.1425, "se": 0.05423, "max_ok": 199899, "oog": 0}, {"params": {"side_mix": 0.02211, "side_retention": 0.9915, "side_cap": 2.271, "mix": 0.1987, "size_scale": 1.562}, "sha256": "45f2cf58354cdaa514e87cb1163955586668f36baa5ffe922c7559c5da6cb468", "block": [870320, 870383], "n": 64, "gen": 5, "mean_diff": 0.2027, "se": 0.05352, "max_ok": 199905, "oog": 0}, {"params": {"side_mix": 0.2147, "side_retention": 0.9986, "side_cap": 2.922, "mix": 0.2391, "size_scale": 2.083}, "sha256": "5530fbc285d401ad2516e4bfd5c9c7005fb36c7ee4018042a9b5f6b1c0e8c583", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.1992, "se": 0.04455, "max_ok": 199917, "oog": 0}, {"params": {"side_mix": 0.09351, "side_retention": 0.9878, "side_cap": 2.153, "mix": 0.2892, "size_scale": 0.8097}, "sha256": "3c2cbea19c727f6a7cb18790265ffe717bcc957ca8e145b783af8bbe4610f14f", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": -0.2242, "se": 0.1061, "max_ok": 199927, "oog": 0}, {"params": {"side_mix": -0.2392, "side_retention": 0.9999, "side_cap": 2.257, "mix": 0.2419, "size_scale": 1.838}, "sha256": "01c941bf542ed9e279009e509299295010e4e9e24f78c852db1db50c2284f76a", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.2128, "se": 0.05043, "max_ok": 199999, "oog": 0}, {"params": {"side_mix": -0.1942, "side_retention": 0.9836, "side_cap": 3.0, "mix": 0.295, "size_scale": 1.651}, "sha256": "e24d7fdcc5ded4bcfd5217276cf6c3bcd7e8190af480f2ba6e7fc65de051ddee", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.1662, "se": 0.07325, "max_ok": 199999, "oog": 0}, {"params": {"side_mix": 0.1903, "side_retention": 0.9951, "side_cap": 2.339, "mix": 0.1438, "size_scale": 1.211}, "sha256": "a69acbd1d038505dc77e525b1c26013be3f01100033c39e1d9fd4ca46466b759", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.04744, "se": 0.05282, "max_ok": 199917, "oog": 0}, {"params": {"side_mix": -0.3497, "side_retention": 0.9999, "side_cap": 2.391, "mix": 0.0, "size_scale": 1.248}, "sha256": "1b80b4fefa2cc9f56b2651fb20f1ab71205f4622d17cf1d6f108826c7eaa1614", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": -0.009718, "se": 0.008704, "max_ok": 193428, "oog": 0}, {"params": {"side_mix": 0.3692, "side_retention": 0.9905, "side_cap": 2.32, "mix": 0.5448, "size_scale": 1.809}, "sha256": "11c84a82be9218d0c7d903775016f0b158abe691e4cc5d2818984b196924caba", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": -0.1027, "se": 0.1554, "max_ok": 199917, "oog": 0}, {"params": {"side_mix": -0.1114, "side_retention": 0.9999, "side_cap": 3.0, "mix": 0.4194, "size_scale": 1.458}, "sha256": "75bb9ab60ac346368b9fab22a26471d352484fc6ab04cfcd2814f976735f443d", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": -0.1008, "se": 0.1055, "max_ok": 199999, "oog": 0}, {"params": {"side_mix": 0.004669, "side_retention": 0.9818, "side_cap": 2.502, "mix": 0.14, "size_scale": 2.336}, "sha256": "1740d2df3ead9613e0e3762903ceeeabad4c97f7524da80780876684cc505b0c", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.1838, "se": 0.1031, "max_ok": 199917, "oog": 0}, {"params": {"side_mix": -0.3948, "side_retention": 0.9631, "side_cap": 3.0, "mix": 0.1129, "size_scale": 1.901}, "sha256": "dbb6a4b1aeb7f1d1c9b5cabc15f22c9c16fb9060abd3c9887ad2e2428bf74a5c", "block": [870384, 870447], "n": 64, "gen": 6, "mean_diff": 0.01824, "se": 0.04661, "max_ok": 199999, "oog": 0}, {"params": {"side_mix": 0.2607, "side_retention": 0.9894, "side_cap": 2.853, "mix": 0.2322, "size_scale": 1.65}, "sha256": "ed1814a650a1ca8358e882141e80d7479536cfa926a3ce31348d03b7dfccf9aa", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.1659, "se": 0.05269, "max_ok": 202825, "oog": 0}, {"params": {"side_mix": -0.5118, "side_retention": 0.9999, "side_cap": 2.172, "mix": 0.3392, "size_scale": 2.248}, "sha256": "a9708c67e59af393c72d77ba6e4c02c110560442c108ad3d3af39187c3792188", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.1325, "se": 0.0487, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": -0.444, "side_retention": 0.992, "side_cap": 2.197, "mix": 0.2541, "size_scale": 2.198}, "sha256": "4d7697e9db158718748afb32919eefd45e4da705aa0b3b7debd0ce1a8095fd13", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.1016, "se": 0.05427, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": 0.3794, "side_retention": 0.9999, "side_cap": 2.412, "mix": 0.2413, "size_scale": 2.71}, "sha256": "d1e8d174c055dcd34f6e30e1529989845651f06ee0d871627a15370814c885a0", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": -0.05806, "se": 0.06142, "max_ok": 202825, "oog": 0}, {"params": {"side_mix": -0.1521, "side_retention": 0.9999, "side_cap": 2.897, "mix": 0.1772, "size_scale": 2.038}, "sha256": "5e30675387a58ac42bec298f190458bc2acac41e802ca3f14498b913c8b0cd75", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.09213, "se": 0.03775, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": -0.2294, "side_retention": 0.9698, "side_cap": 2.294, "mix": 0.1919, "size_scale": 2.185}, "sha256": "ad0e2bffd47c7f64a6399a17f9031721f0f6030d32e1b97e8e78e18510ebdd21", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.106, "se": 0.05365, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": -0.02479, "side_retention": 0.9999, "side_cap": 3.0, "mix": 0.1018, "size_scale": 1.521}, "sha256": "ec3b73bfefd37be3663a59bf9a7d43a1ac8dd5614af61ae8d143a44295ad24d4", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.1087, "se": 0.03456, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": 0.52, "side_retention": 0.968, "side_cap": 2.978, "mix": 0.254, "size_scale": 2.389}, "sha256": "7f1826556a8c718c133e73e5d4f913afff6b3b59a7985b0c6605756b151eb8a4", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.0003117, "se": 0.0629, "max_ok": 202825, "oog": 0}, {"params": {"side_mix": -0.1852, "side_retention": 0.9999, "side_cap": 2.611, "mix": 0.1822, "size_scale": 1.559}, "sha256": "0ac236af2919adf396954d94b8b36c2d96cc1970534964149425189d1f5753aa", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": 0.1728, "se": 0.05053, "max_ok": 202907, "oog": 0}, {"params": {"side_mix": -0.5, "side_retention": 0.9935, "side_cap": 2.292, "mix": 0.3203, "size_scale": 2.637}, "sha256": "d145e8fc998d05c29ca53a4adb46fb7ea0e1337b9321de7646ebe299a5573ea1", "block": [870448, 870511], "n": 64, "gen": 7, "mean_diff": -0.02353, "se": 0.06234, "max_ok": 202907, "oog": 0}], "search": {"method": "numpy CMA-ES (own implementation), default_rng(32), pop 10, mu 5, sigma0 0.2, unit box clipped, 5 dims: side_mix -1..1, side_retention 0.9..0.9999, side_cap 1..3, mix 0..0.9, size_scale 0.3..4; others at RS2 params_exact. Start mean = RS2 values (side_mix 0, retention 0.99, cap 2). Fitness = paired mean vs V10 on fresh 64-seed CRN block 870000+64*gen with V10 run once per block; invalid (any halt, afterSwap>=235000, init>=245000) = -1000 (none occurred).", "generations": 8, "evaluations": 80, "wall_seconds": 1446.9, "seeds_used": [870000, 870511], "stopped": "after generation 7 at 1447 s of measured search time (next generation would exceed 25 min)"}, "recheck": [{"params": {"side_mix": -0.2391621520722873, "side_retention": 0.9999, "side_cap": 2.257346805976611, "mix": 0.24185994593719717, "size_scale": 1.837966741671827}, "sha256": "01c941bf542ed9e279009e509299295010e4e9e24f78c852db1db50c2284f76a", "search_mean_diff": 0.21284368205468596, "seeds": [874000, 874255], "n": 256, "mean_diff": 0.17098558474155978, "se": 0.030330244245658552, "retail": {"mean": 0.9387074643412348, "se": 0.029403624483787215}, "arb": {"mean": -0.7677218795996739, "se": 0.013209601705355145}, "max_ok": 205127, "init_max_ok": 243093, "oog": 0, "other_halts": 0}, {"params": {"side_mix": 0.5798908237892324, "side_retention": 0.9997656146595634, "side_cap": 2.277040506843623, "mix": 0.2382081757393364, "size_scale": 1.9368454822425953}, "sha256": "83b1e5d81a6f47343b9e7d52a9078ef40b125d4b2c29526f88acf16912ea23fc", "search_mean_diff": 0.2037153491531214, "seeds": [874000, 874255], "n": 256, "mean_diff": 0.16711731107976102, "se": 0.028580349508557326, "retail": {"mean": 0.7872717994733534, "se": 0.028362726065157065}, "arb": {"mean": -0.6201544883935888, "se": 0.01282317657606047}, "max_ok": 205045, "init_max_ok": 243093, "oog": 0, "other_halts": 0}, {"params": {"side_mix": 0.02210596095167494, "side_retention": 0.9915051626524796, "side_cap": 2.2714960790449323, "mix": 0.1986989161925338, "size_scale": 1.561903284881722}, "sha256": "45f2cf58354cdaa514e87cb1163955586668f36baa5ffe922c7559c5da6cb468", "search_mean_diff": 0.20269971359625583, "seeds": [874000, 874255], "n": 256, "mean_diff": 0.13928596568431573, "se": 0.02945443343071398, "retail": {"mean": 1.0291563099584204, "se": 0.029138717806354582}, "arb": {"mean": -0.8898703442741074, "se": 0.012706020555154032}, "max_ok": 205045, "init_max_ok": 243093, "oog": 0, "other_halts": 0}], "held_out": {"seeds": {"first": 875000, "last": 875511, "n": 512}, "vs_v10": {"n": 512, "mean_diff": 0.1446383911407234, "se": 0.019502819326127126, "worst": [{"seed": 875505, "d": -2.5508431868140633}, {"seed": 875099, "d": -1.1467749617363552}, {"seed": 875436, "d": -1.1149154470175517}, {"seed": 875025, "d": -0.873227778303999}, {"seed": 875333, "d": -0.8275905122152949}], "retail_edge_delta": {"mean": 0.9265212671601475, "se": 0.018820199743846806}, "arb_edge_delta": {"mean": -0.781882876019424, "se": 0.009815983427416682}}, "vs_rs2": {"n": 512, "mean_diff": -0.02535270773484155, "se": 0.013732126587539695, "worst": [{"seed": 875405, "d": -2.235067679955023}, {"seed": 875215, "d": -1.1231627214503987}, {"seed": 875020, "d": -1.0114803262492842}, {"seed": 875443, "d": -0.9900163642682855}, {"seed": 875016, "d": -0.9265714386114041}], "retail_edge_delta": {"mean": -0.5860718567327133, "se": 0.014742041415868058}, "arb_edge_delta": {"mean": 0.5607191489978733, "se": 0.0060735668643783275}}, "rs2_vs_v10": {"n": 512, "mean_diff": 0.16999109887556496, "se": 0.024619995634349058, "worst": [{"seed": 875505, "d": -2.6627983429845017}, {"seed": 875113, "d": -1.534153249876681}, {"seed": 875099, "d": -1.328228560844991}, {"seed": 875025, "d": -1.2586082106878393}, {"seed": 875250, "d": -0.9964951030343627}], "retail_edge_delta": {"mean": 1.5125931238928607, "se": 0.025367575196421327}, "arb_edge_delta": {"mean": -1.3426020250172974, "se": 0.01265427037157619}}, "arm_mean_edge": {"frozen": 531.4726800678692, "rs2": 531.498032775604, "v10": 531.3280416767284}, "arm_gas": {"frozen": {"max_ok": 202931, "init_max_ok": 243093, "oog": 0, "other_halts": 0}, "rs2": {"max_ok": 200268, "init_max_ok": 243099, "oog": 0, "other_halts": 0}, "v10": {"max_ok": 192838, "init_max_ok": 220981, "oog": 0, "other_halts": 0}}}, "gas": {"max_ok": 205127, "init_max_ok": 243093, "oog": 0, "other_halts": 0, "search_max_ok_over_all_evals": 205054, "search_oog_total": 0, "limits_checked": {"afterSwap_max_ok_lt": 235000, "init_lt": 245000}}, "generator_source": "import json,hashlib,sys\n# exec(RS2 artifact generator_source)  -> defines generate, generate7\n# V10 = RS2... V10 artifact `code`\nV10=open('V10.sol').read()  # V10 artifact code, sha256 cd9bdb45...ca245\nPE=[2, 0.3424067991934183, 0.999, 0.36638342491340714, 1.8832961581192982, 196.03088039613942, 1.5]\n\n# generate_side(V10, p): p = RS2 params_exact (7) overridden by mix(p[1]), size_scale(p[4]),\n# plus side_mix, side_retention, side_cap. side_mix==0 -> exactly RS2's generate7 output.\ndef generate_side(base,rs2p,side_mix,side_ret,side_cap):\n    s=generate7(base,rs2p)\n    if side_mix==0: return s\n    M=int(round(abs(side_mix)*1e18)); NEG='true' if side_mix<0 else 'false'\n    R=int(round(side_ret*1e18)); C=int(round(side_cap*1e18))\n    def rep(old,new,cnt=1):\n        nonlocal s\n        assert s.count(old)==cnt,(old,s.count(old)); s=s.replace(old,new)\n    # slots[2] high 64 bits hold share+1 (0 = uninitialised -> 1/2); spot uses bits 64..191\n    rep('slots[2] >> 64','uint128(slots[2] >> 64)',2)\n    rep('        lambdaHat = originalLambda; sizeHat = originalSize;\\n',f'''        uint256 fMidAsk = fMid;\n        {{\n            uint256 sh = slots[2] >> 192;\n            sh = sh == 0 ? WAD / 2 : sh - 1;\n            uint256 sw = firstInStep ? WAD - arbProbability : WAD;\n            sh = _blend(sh, trade.isBuy ? 0 : WAD, wmul(WAD - {R}, sw));\n            slots[2] = ((sh + 1) << 192) | uint192(slots[2]);\n            uint256 lamA = _sideLam(lambdaHat, 2 * sh, {C}, {M}, {NEG});\n            uint256 lamB = _sideLam(lambdaHat, 2 * (WAD - sh), {C}, {M}, {NEG});\n            fMid = _sideFee(fMid, lambdaHat, lamB, sizeHat);\n            fMidAsk = _sideFee(fMidAsk, lambdaHat, lamA, sizeHat);\n        }}\n        lambdaHat = originalLambda; sizeHat = originalSize;\n''')\n    rep('''            bidFee = fMid + skew;\n            askFee = fMid > skew ? fMid - skew : 0;''','''            bidFee = fMid + skew;\n            askFee = fMidAsk > skew ? fMidAsk - skew : 0;''')\n    rep('''            askFee = fMid + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;''','''            askFee = fMidAsk + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;''')\n    rep('slots[2] = (spot << 64) | trade.timestamp;','slots[2] = ((slots[2] >> 192) << 192) | (spot << 64) | trade.timestamp;')\n    rep('    function _blend(',f'''    function _sideLam(uint256 lam, uint256 f, uint256 cap, uint256 m, bool neg) internal pure returns (uint256) {{\n        if (f > cap) f = cap;\n        uint256 target = wmul(lam, f);\n        if (!neg) return _blend(lam, target, m);\n        // negative side_mix: move away from the target by |m|\n        if (target >= lam) {{ uint256 d = wmul(target - lam, m); return lam > d ? lam - d : 0; }}\n        return lam + wmul(lam - target, m);\n    }}\n    function _sideFee(uint256 f, uint256 lam, uint256 lamSide, uint256 size) internal pure returns (uint256) {{\n        uint256 d;\n        if (lamSide >= lam) {{ d = lamSide - lam; return f + wmul(LAMBDA_COEF, d) + wmul(FLOW_SIZE_COEF, wmul(d, size)); }}\n        d = lam - lamSide; uint256 dec = wmul(LAMBDA_COEF, d) + wmul(FLOW_SIZE_COEF, wmul(d, size));\n        return f > dec ? f - dec : 0;\n    }}\n    function _blend(''')\n    return s\n\n# frozen: p=list(PE); p[1]=mix; p[4]=size_scale; generate_side(V10,p,side_mix,side_retention,side_cap)\n", "checks": {"calibration_CH_seeds_0_999_mean_edge": 525.5258821780834, "calibration_exact_match": true, "rs2_rebuild_sha256_match": true, "side_mix_zero_gives_rs2_sha256": true, "v10_sha256_verified": true, "stack_sha256_verified": true, "frozen_amm_match_validate": "passed"}, "notes": ["Negative result. Held-out 875000..875511 (frozen before held-out): frozen vs V10 +0.1446 (se 0.0195); frozen vs RS2 -0.0254 (se 0.0137); RS2 vs V10 on the same seeds +0.170 (se 0.025). The per-side lambda split does not add edge over RS2; the frozen point mainly moved toward a lower RS2 mix (0.242 vs 0.342), which lowers effective fees (retail edge -0.59, arb edge +0.56 vs RS2).", "The search was flat in the side dimensions: side_mix values from -0.5 to +1 all scored within noise (64-seed se ~0.04-0.06) and the leading points had side_mix of mixed sign (-0.24, +0.58, +0.02). side_retention went to the 0.9999 upper bound for most good points; side_cap above 2 is inactive (2*share<=2) and the search sat at 2.2-3, i.e. the cap played no role. Points with mix=0 scored ~0 vs V10 whatever side_mix, so the per-side split on V10's own lambda is worth roughly nothing.", "Top 3 by search score rechecked on 874000..874255 vs V10: +0.171 (0.030), +0.167 (0.029), +0.139 (0.029); the first was frozen.", "Only 8 of a possible ~8 generations ran within the 25-minute cap (about 180 s per generation on this 4-core machine), so CMA-ES did not converge; 80 evaluations.", "This is far below the ~+5 over STACK the goal needs, and it is a V10/RS2-relative result, not a STACK comparison: no fresh >=5000000 STACK confirmation was run (no seeds >=5000000 used). No board claim.", "Method: each arm alone vs VanillaStrategy via amm_sim_rs.run_batch(...,8) in 20-seed chunks with gas_stats_reset/gas_stats per chunk (V10 artifact harness_source), configs per MatchRunner._build_configs; retail/arb split by the V10 harness reconstruction; se = sd(ddof=1)/sqrt(n); no seed dropped. Log params rounded to 4 significant digits; exact frozen params in params."]}