{"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 _anchorSigma(uint256 current, uint256 packed) internal pure returns (uint256) {\n        uint256 mean = uint80(packed >> 80);\n        if (uint32(packed >> 160) == 0) mean = current;\n        return wmul(1047182309813441000, _blend(current, mean, 682794863439784300));\n    }\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 packedSigma = slots[6]; uint256 sigmaHat = uint80(packedSigma); 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 = 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(_anchorSigma(sigmaHat, packedSigma), 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                if (682794863439784300 > 0) {\n                    uint256 count = uint32(packedSigma >> 160);\n                    uint256 mean = uint80(packedSigma >> 80);\n                    if (count < 5377) count++;\n                    if (sigmaHat >= mean) mean += (sigmaHat - mean) / count;\n                    else mean -= (mean - sigmaHat) / count;\n                    packedSigma = (mean << 80) | (count << 160);\n                }\n\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, 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 (342406799193418304 > 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,1883296158119298304);\n            lambdaHat = _blend(lambdaHat,retailRate,342406799193418304);\n            sizeHat = _blend(sizeHat,retailSize,342406799193418304);\n        }\n        uint256 flowSize = wmul(lambdaHat, sizeHat);\n        uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, _anchorSigma(sigmaHat, packedSigma)) + 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(_anchorSigma(sigmaHat, packedSigma), toxSignal));\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 = fMid > skew ? fMid - skew : 0;\n        } else {\n            askFee = fMid + 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] = (spot << 64) | trade.timestamp;\n        slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n        slots[6] = sigmaHat | (682794863439784300 > 0 ? (packedSigma & ~uint256(type(uint80).max)) : 0); 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 _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\"; 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candidate in its 256-seed recheck and 512-seed held-out; oog includes all roles in these arms.","recorded_arms_scope":"Recorded search-candidate, recheck, held-out and parity counters. Search RS2 counters were checked per evaluation and all valid; calibration and smoke pilots reported separately or excluded.","search_candidates":{"max_ok":204249,"init_max_ok":243121,"oog":0,"other_halts":0},"recorded_arms":{"max_ok":204249,"init_max_ok":243121,"oog":0,"other_halts":0},"held_rs2":{"max_ok":198893,"init_max_ok":243099,"oog":0,"other_halts":0}},"parity":{"seeds":[919600,919631],"params":[0,1,5377],"vs_rs2":{"n":32,"mean_diff":0.0,"se":0.0,"worst":[{"seed":919600,"d":0.0},{"seed":919601,"d":0.0},{"seed":919602,"d":0.0},{"seed":919603,"d":0.0},{"seed":919604,"d":0.0}]},"trajectory_equal_by_seed":{"919600":true,"919601":true,"919602":true,"919603":true,"919604":true,"919605":true,"919606":true,"919607":true,"919608":true,"919609":true,"919610":true,"919611":true,"919612":true,"919613":true,"919614":true,"919615":true,"919616":true,"919617":true,"919618":true,"919619":true,"919620":true,"919621":true,"919622":true,"919623":true,"919624":true,"919625":true,"919626":true,"919627":true,"919628":true,"919629":true,"919630":true,"919631":true},"all_equal":true,"candidate_gas":{"max_ok":198768,"init_max_ok":243118,"oog":0,"other_halts":0},"rs2_gas":{"max_ok":197634,"init_max_ok":243099,"oog":0,"other_halts":0},"trajectory_hash_input":"For each chronological step, network-order binary doubles: submission spot, bid fee, ask fee. Edge and decomposition also compared per seed."},"generator_source":"from decimal import Decimal\n\ndef generate(base,p):\n    w,g,N=p; w=int(Decimal(str(w))*10**18);g=int(Decimal(str(g))*10**18);N=int(round(N))\n    s=base.replace('uint256 sigmaHat = slots[6];','uint256 packedSigma = slots[6]; uint256 sigmaHat = uint80(packedSigma);')\n    s=s.replace('wmul(sigmaHat, GATE_SIGMA_MULT)','wmul(_anchorSigma(sigmaHat, packedSigma), GATE_SIGMA_MULT)')\n    needle='sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);'\n    s=s.replace(needle,needle+f'''\n                if ({w} > 0) {{\n                    uint256 count = uint32(packedSigma >> 160);\n                    uint256 mean = uint80(packedSigma >> 80);\n                    if (count < {N}) count++;\n                    if (sigmaHat >= mean) mean += (sigmaHat - mean) / count;\n                    else mean -= (mean - sigmaHat) / count;\n                    packedSigma = (mean << 80) | (count << 160);\n                }}\n''')\n    s=s.replace('wmul(SIGMA_COEF, sigmaHat)','wmul(SIGMA_COEF, _anchorSigma(sigmaHat, packedSigma))')\n    s=s.replace('wmul(sigmaHat, toxSignal)','wmul(_anchorSigma(sigmaHat, packedSigma), toxSignal)')\n    s=s.replace('slots[6] = sigmaHat;',f'slots[6] = sigmaHat | ({w} > 0 ? (packedSigma & ~uint256(type(uint80).max)) : 0);')\n    pos=s.index('    function afterInitialize')\n    s=s[:pos]+f'''    function _anchorSigma(uint256 current, uint256 packed) internal pure returns (uint256) {{\n        uint256 mean = uint80(packed >> 80);\n        if (uint32(packed >> 160) == 0) mean = current;\n        return wmul({g}, _blend(current, mean, {w}));\n    }}\n\n'''+s[pos:]\n    return s\n","harness_source":"\"\"\"Run from the pinned amm-challenge checkout, with the brief's environment active.\npython harness.py --start 5000000 --n 2000 --out measured.json candidate.sol STACK.sol\nDo not use confirmation seeds to choose or change a strategy.\n\"\"\"\nimport argparse,hashlib,json,math,struct\nfrom pathlib import Path\nimport numpy as np\nimport amm_sim_rs as sim\nfrom amm_competition.evm.compiler import SolidityCompiler\n\n\ndef configs(start,n):\n    configs=[]\n    for seed in range(start,start+n):\n        rng=np.random.default_rng(seed)\n        size=rng.uniform(19.,21.)\n        rate=rng.uniform(.6,1.)\n        sigma=rng.uniform(.000882,.001008)\n        configs.append(sim.SimulationConfig(n_steps=10000,initial_price=100.,\n            initial_x=100.,initial_y=10000.,gbm_mu=0.,gbm_sigma=sigma,gbm_dt=1.,\n            retail_arrival_rate=rate,retail_mean_size=size,retail_size_sigma=1.2,\n            retail_buy_prob=.5,seed=seed))\n    return configs\n\n\ndef decomposition(r,initial_fee=.0004):\n    # Fees are outside reserves, so k stays fixed up to floating-point roundoff.\n    # The arb acts before retail, using the preceding step's final spot and fees.\n    steps=r.steps\n    fair=np.array([s.fair_price for s in steps])\n    spots=np.array([r.initial_fair_price]+[s.spot_prices['submission'] for s in steps[:-1]])\n    bids=np.array([initial_fee]+[s.fees['submission'][0] for s in steps[:-1]])\n    asks=np.array([initial_fee]+[s.fees['submission'][1] for s in steps[:-1]])\n    x0,y0=r.initial_reserves['submission'];k=x0*y0\n    x=np.sqrt(k/spots);y=np.sqrt(k*spots)\n    ga=1-asks;gb=1-bids\n    out=np.minimum(np.maximum(x-np.sqrt(k/(ga*fair)),0),.99*x)\n    paid=(k/(x-out)-y)/ga\n    buyprofit=np.where(out>0,np.maximum(out*fair-paid,0),0)\n    gross=np.maximum((np.sqrt(k*gb/fair)-x)/gb,0)\n    received=y-k/(x+gb*gross)\n    sellprofit=np.where(gross>0,np.maximum(received-gross*fair,0),0)\n    arb=-float(np.sum(np.where(spots<fair,buyprofit,sellprofit)))\n    return arb,r.edges['submission']-arb\n\n\ndef aggregate(chunks):\n    out={}\n    for chunk in chunks:\n        for row in chunk['raw']:\n            key=(row['role'],row['callback'])\n            dest=out.setdefault(key,{'role':row['role'],'callback':row['callback']})\n            for k,v in row.items():\n                if k in ['role','callback']:continue\n                dest[k]=max(dest.get(k,0),v) if k=='max_ok_gas' else dest.get(k,0)+v\n    return list(out.values())\n\n\ndef run(source,start,n,vanilla,compiler,capture=False):\n    compiled=compiler.compile(source)\n    assert compiled.success,compiled.errors\n    rows=[];chunks=[]\n    for first in range(start,start+n,20):\n        count=min(20,start+n-first)\n        sim.gas_stats_reset()\n        batch=sim.run_batch(list(compiled.bytecode),list(vanilla),configs(first,count),8)\n        results=batch.results\n        assert sorted(r.seed for r in results)==list(range(first,first+count))\n        for r in results:\n            arb,retail=decomposition(r)\n            rows.append({'seed':r.seed,'edge':r.edges['submission'],'arb':arb,'retail':retail})\n            if capture:\n                digest=hashlib.sha256()\n                for step in r.steps:\n                    digest.update(struct.pack('!ddd',step.spot_prices['submission'],*step.fees['submission']))\n                rows[-1]['trajectory_sha256']=digest.hexdigest()\n        chunks.append({'start':first,'raw':sim.gas_stats()})\n        del results,batch\n        if n >= 256 and ((first-start+count) % 100 == 0 or first+count == start+n):\n            print('progress',hashlib.sha256(source.encode()).hexdigest()[:12],start,first-start+count,'/',n,flush=True)\n    return {'sha256':hashlib.sha256(source.encode()).hexdigest(),'rows':rows,\n            'raw_counters':aggregate(chunks),'chunks':chunks}\n\n\ndef stats(d):\n    d=np.asarray(d,dtype=float)\n    return {'mean':float(d.mean()),'se':float(d.std(ddof=1)/np.sqrt(len(d)))}\n\n\ndef compare(candidate,stack):\n    a={r['seed']:r for r in candidate['rows']};b={r['seed']:r for r in stack['rows']}\n    assert a.keys()==b.keys()\n    seeds=sorted(a)\n    d=np.array([a[s]['edge']-b[s]['edge'] for s in seeds])\n    arb=np.array([a[s]['arb']-b[s]['arb'] for s in seeds])\n    retail=np.array([a[s]['retail']-b[s]['retail'] for s in seeds])\n    assert np.max(np.abs(d-arb-retail))<1e-8\n    summary=stats(d)\n    return {'paired':{'n':len(d),'mean_diff':summary['mean'],'se':summary['se'],\n                'worst':[{'seed':seeds[i],'d':float(d[i])} for i in np.argsort(d)[:5]]},\n            'retail_edge_delta':stats(retail),'arb_edge_delta':stats(arb),\n            'reconciliation_max_abs':float(np.max(np.abs(d-arb-retail)))}\n\n\nif __name__=='__main__':\n    p=argparse.ArgumentParser()\n    p.add_argument('--start',type=int,required=True);p.add_argument('--n',type=int,required=True)\n    p.add_argument('--out',required=True);p.add_argument('candidate');p.add_argument('stack')\n    args=p.parse_args()\n    compiler=SolidityCompiler()\n    vanilla=compiler.compile(Path('contracts/src/VanillaStrategy.sol').read_text(),'VanillaStrategy')\n    assert vanilla.success,vanilla.errors\n    candidate=run(Path(args.candidate).read_text(),args.start,args.n,vanilla.bytecode,compiler)\n    stack=run(Path(args.stack).read_text(),args.start,args.n,vanilla.bytecode,compiler)\n    out=compare(candidate,stack);out.update(candidate=candidate,stack=stack)\n    errors=['oog','revert','other_halt','tx_error','bad_return']\n    out['valid']=all(not any(row.get(e,0) for e in errors)\n        for arm in [candidate,stack] for row in arm['raw_counters'])\n    Path(args.out).write_text(json.dumps(out,allow_nan=False))\n    print(json.dumps({k:v for k,v in out.items() if k not in ['candidate','stack']}))\n","search_source":"import sys,json,time,math\nfrom pathlib import Path\nsys.path.insert(0,'scratch')\nimport harness as h\nfrom anchor import generate\nimport cma\nbase=Path('scratch/rs2_code.txt').read_text()\nc=h.SolidityCompiler(); v=c.compile(Path('contracts/src/VanillaStrategy.sol').read_text(),'VanillaStrategy').bytecode\n\ndef valid(r):\n return all(not any(row.get(e,0) for e in ['oog','revert','other_halt','tx_error','bad_return']) for row in r['raw_counters']) and all(row.get('max_ok_gas',0)<(245000 if row['callback']=='afterInitialize' else 235000) for row in r['raw_counters'] if row['role']=='Submission' and row['callback'] in ['afterSwap','afterInitialize'])\n\ndef params(x):return [float(x[0]),float(.5+1.5*x[1]),int(round(10**(2+2*x[2])))]\nes=cma.CMAEvolutionStrategy([.65,1/3,.5],.28,{'seed':42,'bounds':[0,1],'popsize':6,'verbose':-9})\nstarted=time.monotonic(); logs=[];idx=0\nwhile idx<46 and time.monotonic()-started<1450:\n xs=es.ask();fits=[]\n for x in xs:\n  if idx>=46 or time.monotonic()-started + max([z['seconds'] for z in logs],default=160) > 1480:break\n  p=params(x);start=915000+idx*64\n  t=time.monotonic();b=h.run(base,start,64,v,c);a=h.run(generate(base,p),start,64,v,c)\n  comp=h.compare(a,b); good=valid(a) and valid(b)\n  entry={'params':p,'n':64,'start':start,'mean_diff':comp['paired']['mean_diff'],'se':comp['paired']['se'],'valid':good,'fitness':comp['paired']['mean_diff'] if good else -1000,'seconds':time.monotonic()-t,'gas':a['raw_counters']}\n  logs.append(entry);fits.append(-entry['fitness']);Path('scratch/search_log.json').write_text(json.dumps(logs));print(json.dumps(entry),flush=True);idx+=1\n if len(fits)!=len(xs):break\n es.tell(xs,fits)\nPath('scratch/search_done.json').write_text(json.dumps({'elapsed_seconds':time.monotonic()-started,'evaluations':idx,'log':logs}))\n","confirmation_source":"import sys,json,hashlib,time\nfrom pathlib import Path\nsys.path.insert(0,'scratch')\nimport harness as h\nfrom anchor import generate\nbase=Path('scratch/rs2_code.txt').read_text();c=h.SolidityCompiler()\nv=c.compile(Path('contracts/src/VanillaStrategy.sol').read_text(),'VanillaStrategy').bytecode\nlogs=json.load(open('scratch/search_done.json'))['log']\ntop=sorted([x for x in logs if x['valid']],key=lambda x:x['mean_diff'],reverse=True)[:3]\ndef save(name,x):Path('scratch/'+name+'.json').write_text(json.dumps(x))\nb=h.run(base,918000,256,v,c);save('recheck_base',b)\nrecheck=[]\nfor i,row in enumerate(top):\n p=row['params'];a=h.run(generate(base,p),918000,256,v,c);save('recheck_'+str(i),a)\n comp=h.compare(a,b);recheck.append({'params':p,**comp,'gas':a['raw_counters']});save('recheck_summary',recheck);print('recheck',i,p,comp,flush=True)\ndef valid(row):\n return all(not any(x.get(e,0) for e in ['oog','revert','other_halt','tx_error','bad_return']) for x in row['gas']) and all(x['max_ok_gas']<(245000 if x['callback']=='afterInitialize' else 235000) for x in row['gas'] if x['role']=='Submission' and x['callback'] in ['afterInitialize','afterSwap'])\nbest=max([r for r in recheck if valid(r)],key=lambda r:r['paired']['mean_diff']);p=best['params'];source=generate(base,p)\nsave('freeze',{'params':p,'sha256':hashlib.sha256(source.encode()).hexdigest(),'selection':'greatest paired mean on 918000..918255 among search top three'})\nPath('scratch/frozen.sol').write_text(source)\na=h.run(source,919000,512,v,c);save('held_candidate',a)\nb=h.run(base,919000,512,v,c);save('held_base',b)\ncomp=h.compare(a,b);save('held_summary',comp);print('held',comp,flush=True)\na=h.run(generate(base,[0,1,p[2]]),919600,32,v,c,capture=True);save('parity_candidate',a)\nb=h.run(base,919600,32,v,c,capture=True);save('parity_base',b)\ncomp=h.compare(a,b); comp['trajectory_equal_by_seed']={str(x['seed']):x['trajectory_sha256']==y['trajectory_sha256'] for x,y in zip(sorted(a['rows'],key=lambda r:r['seed']),sorted(b['rows'],key=lambda r:r['seed']))};save('parity_summary',comp);print('parity',comp,flush=True)\n","calibration":{"strategy":"CH","seeds":[0,999],"n":1000,"mean_edge":525.5258821780834,"expected_mean_edge":525.5258821780834,"abs_error":0.0,"gas":{"max_ok":151647,"init_max_ok":185532,"oog":0,"other_halts":0}},"notes":["Frozen code passed amm-match validate. All numeric performance results are local simulator measurements, not leaderboard claims. No seeds >= 5000000 were used; this item uses only its assigned search, recheck, held-out and parity blocks plus the required CH calibration.","RS2 source sha256 verified as f24b6ca198b744c380842c3a17964a6dc21f311bb04984b26733afa3fee8eaf2. Checkout pinned at 6b6921f8d463314aa7c96234e1be25a25245f704; supplied simulator wheel checksum verified. SolidityCompiler uses solc 0.8.24, optimizer 200, viaIR, paris.","runMean samples the freshly updated sigmaHat once on each firstInStep (the same events that update sigmaHat). n increments up to N; mean moves toward the sample by abs(sample-mean)/n with integer truncation. After reaching N this is a 1/N update.","Packed slots[6]: low 80 bits raw sigmaHat, next 80 bits runMean, next 32 bits n. Initial high bits are zero/unset, and the afterInitialize body is unchanged. Before any sample the overlay uses current sigmaHat as its mean.","The adaptive gate uses the prior stored runMean and current pre-update sigmaHat. SIGMA_COEF and SIGMA_TOX_COEF use the updated runMean and sigmaHat. All three use g * _blend(raw sigmaHat,runMean,w). Raw sigmaHat is stored separately in the low bits; no compounding of g or w into its EMA.","Price, stale-shift and posterior code are unchanged apart from the explicitly requested adaptive-gate sigma substitution. Overlay-off parity is w=0,g=1.","CMA parameters are normalized to [0,1]^3: w=x0, g=0.5+1.5*x1, N=round(10**(2+2*x2)); initial normalized mean [0.65,1/3,0.5], step size 0.28, population 6, seed 42. Each evaluation uses a disjoint 64-seed block starting at 915000+64*i. Fitness is paired mean vs RS2; halts or gas-limit violations receive -1000. Search wall time seconds: 1444.5381647390313.","Before CMA, a two-seed unselected overlay smoke test [w=0.5,g=1,N=1000] and RS2 ran on 919600..919601. These measurements were not part of CMA fitness, finalist ranking or freeze selection.","Top three valid search candidates rechecked on 918000..918255; greatest valid recheck mean frozen before held-out execution. Held-out data were not used to select parameters.","Each arm alone vs VanillaStrategy; run_batch(...,8); default_rng(seed) draws size then rate then sigma per MatchRunner. Harness decomposition computes negative arbitrage profit and assigns the edge residual to retail; paired decomposition reconciles within the reported floating-point error.","Reproduction: save generator_source as scratch/anchor.py and harness_source as scratch/harness.py in the pinned checkout; retrieve RS2 code to scratch/rs2_code.txt and verify the supplied hash. generate(base,[w,g,N]) reproduces code exactly. Search and confirmation source are included as provenance; simulator and compiler are setup tools, not runtime strategy dependencies."]}