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R1..R4","multipliers":{"R1":{"BASE_FEE":0.7628,"SIGMA_COEF":1.1552,"LAMBDA_COEF":1.0155,"FLOW_SIZE_COEF":1.0142,"TOX_COEF":1.361,"TOX_QUAD_COEF":1.1146,"ACT_COEF":0.8044,"STALE_DIR_COEF":0.9422,"STALE_ATTRACT_FRAC":0.9552,"TRADE_TOX_BOOST":1.0036,"TAIL_SLOPE_PROTECT":0.8817,"TAIL_SLOPE_ATTRACT":0.8672,"CAP16":0.9697,"CAP30":0.9922,"CAP36":1.0241},"R2":{"BASE_FEE":0.9469,"SIGMA_COEF":1.3702,"LAMBDA_COEF":0.796,"FLOW_SIZE_COEF":1.2076,"TOX_COEF":1.1175,"TOX_QUAD_COEF":1.0386,"ACT_COEF":0.8847,"STALE_DIR_COEF":1.0031,"STALE_ATTRACT_FRAC":1.0736,"TRADE_TOX_BOOST":0.7827,"TAIL_SLOPE_PROTECT":0.9585,"TAIL_SLOPE_ATTRACT":1.016,"CAP16":1.1378,"CAP30":0.9294,"CAP36":1.3178},"R3":{"BASE_FEE":0.9737,"SIGMA_COEF":0.8757,"LAMBDA_COEF":1.0589,"FLOW_SIZE_COEF":1.0319,"TOX_COEF":0.854,"TOX_QUAD_COEF":0.8231,"ACT_COEF":1.03,"STALE_DIR_COEF":1.0689,"STALE_ATTRACT_FRAC":0.8581,"TRADE_TOX_BOOST":0.9643,"TAIL_SLOPE_PROTECT":1.0644,"TAIL_SLOPE_ATTRACT":1.1599,"CAP16":0.9135,"CAP30":0.8677,"CAP36":0.9885},"R4":{"BASE_FEE":1.1461,"SIGMA_COEF":0.7681,"LAMBDA_COEF":1.0303,"FLOW_SIZE_COEF":0.8152,"TOX_COEF":1.0315,"TOX_QUAD_COEF":1.0771,"ACT_COEF":1.0229,"STALE_DIR_COEF":1.0289,"STALE_ATTRACT_FRAC":0.8843,"TRADE_TOX_BOOST":0.9575,"TAIL_SLOPE_PROTECT":1.077,"TAIL_SLOPE_ATTRACT":1.0706,"CAP16":0.9934,"CAP30":1.0411,"CAP36":0.8126}}},"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    uint256 constant BASE_FEE_0 = 305121654977685;\n    uint256 constant BASE_FEE_1 = 378764144175877;\n    uint256 constant BASE_FEE_2 = 389475766469982;\n    uint256 constant BASE_FEE_3 = 458432692502326;\n    uint256 constant SIGMA_COEF_0 = 231037592976776448;\n    uint256 constant SIGMA_COEF_1 = 274045912381816896;\n    uint256 constant SIGMA_COEF_2 = 175139892410047328;\n    uint256 constant SIGMA_COEF_3 = 153610735964629216;\n    uint256 constant LAMBDA_COEF_0 = 1218571997530383;\n    uint256 constant LAMBDA_COEF_1 = 955232210209380;\n    uint256 constant LAMBDA_COEF_2 = 1270625531882571;\n    uint256 constant LAMBDA_COEF_3 = 1236330081345670;\n    uint256 constant FLOW_SIZE_COEF_0 = 491063920688664384;\n    uint256 constant FLOW_SIZE_COEF_1 = 584706093232124416;\n    uint256 constant FLOW_SIZE_COEF_2 = 499634576518233664;\n    uint256 constant FLOW_SIZE_COEF_3 = 394727971530203776;\n    uint256 constant TOX_COEF_0 = 40831217008340776;\n    uint256 constant TOX_COEF_1 = 33525402378675052;\n    uint256 constant TOX_COEF_2 = 25619494031273196;\n    uint256 constant TOX_COEF_3 = 30945331413684332;\n    uint256 constant TOX_QUAD_COEF_0 = 1671876960343432704;\n    uint256 constant TOX_QUAD_COEF_1 = 1557897858386812928;\n    uint256 constant TOX_QUAD_COEF_2 = 1234608019456360192;\n    uint256 constant TOX_QUAD_COEF_3 = 1615592779792272640;\n    uint256 constant ACT_COEF_0 = 7387432292517683200;\n    uint256 constant ACT_COEF_1 = 8125314288836750336;\n    uint256 constant ACT_COEF_2 = 9460126399685871616;\n    uint256 constant ACT_COEF_3 = 9394898582819430400;\n    uint256 constant STALE_DIR_COEF_0 = 645435177326395648;\n    uint256 constant STALE_DIR_COEF_1 = 687133608445203584;\n    uint256 constant STALE_DIR_COEF_2 = 732201165511572992;\n    uint256 constant STALE_DIR_COEF_3 = 704793184060861824;\n    uint256 constant STALE_ATTRACT_FRAC_0 = 1002931632440644608;\n    uint256 constant STALE_ATTRACT_FRAC_1 = 1127238147404712192;\n    uint256 constant STALE_ATTRACT_FRAC_2 = 900984742467487232;\n    uint256 constant STALE_ATTRACT_FRAC_3 = 928490432239353216;\n    uint256 constant TRADE_TOX_BOOST_0 = 351242526637700608;\n    uint256 constant TRADE_TOX_BOOST_1 = 273938247425956768;\n    uint256 constant TRADE_TOX_BOOST_2 = 337489726379386176;\n    uint256 constant TRADE_TOX_BOOST_3 = 335115120463067200;\n    uint256 constant TAIL_SLOPE_PROTECT_0 = 819988775502742656;\n    uint256 constant TAIL_SLOPE_PROTECT_1 = 891363507181613568;\n    uint256 constant TAIL_SLOPE_PROTECT_2 = 989917090283296512;\n    uint256 constant TAIL_SLOPE_PROTECT_3 = 1001655437691521408;\n    uint256 constant TAIL_SLOPE_ATTRACT_0 = 737084849882706688;\n    uint256 constant TAIL_SLOPE_ATTRACT_1 = 863623005446346240;\n    uint256 constant TAIL_SLOPE_ATTRACT_2 = 985885129808454784;\n    uint256 constant TAIL_SLOPE_ATTRACT_3 = 910005781165536000;\n    uint256 constant CAPA_0 = 1551475665431434;\n    uint256 constant CAPA_1 = 1820511361827412;\n    uint256 constant CAPA_2 = 1461626398362108;\n    uint256 constant CAPA_3 = 1589486342738578;\n    uint256 constant CAPB_0 = 2976471556810116;\n    uint256 constant CAPB_1 = 2788060133158520;\n    uint256 constant CAPB_2 = 2602986372659157;\n    uint256 constant CAPB_3 = 3123449464537510;\n    uint256 constant CAPC_0 = 3686625985081180;\n    uint256 constant CAPC_1 = 4744207077704858;\n    uint256 constant CAPC_2 = 3558615879323485;\n    uint256 constant CAPC_3 = 2925240197328562;\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[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            uncertainty += wmul(sigmaForFast, sigmaForFast) * elapsedRaw;\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(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        {\n            uint256 ret = fastHat > 0 ? wdiv(absDiff(pImplied, fastHat), fastHat) : 0;\n            uint256 alpha;\n            if (firstInStep) {\n                uint256 processSigma = sigmaForFast;\n                uint256 obsVar = uncertainty + wmul(processSigma, processSigma);\n                uint256 probArb;\n                uint256 z2 = wdiv(wmul(ret, ret), obsVar);\n                uint256 density = _powWad(wdiv(WAD, WAD + z2 / 16), 8);\n                uint256 sigmaObs = _isqrt(obsVar * WAD);\n                uint256 odds = wmul(density, wdiv(6700000000000000, sigmaObs));\n                bool arbFlag = ret <= wmul(sigmaForFast, 1220000000000000000);\n                uint256 prior = arbFlag ? 650000000000000000 : 400000000000000000;\n                uint256 tr = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n                if (tr > 3000000000000000) prior = wmul(prior, 6 * WAD / 10);\n                if (silent > 1) prior = wmul(prior, 8 * WAD / 10);\n                odds = wmul(odds, wdiv(prior, WAD - prior));\n                probArb = wdiv(odds, WAD + odds);\n                alpha = wmul(probArb, 600000000000000000) + wmul(WAD - probArb, 80000000000000000);\n                slots[15] = pImplied >= fastHat ? 1 : 2;\n                uncertainty = wmul(uncertainty, WAD - alpha);\n            } else {\n                if ((slots[15] == 1) == (pImplied >= fastHat)) alpha = PHAT_ALPHA_RETAIL;\n            }\n            uint256 gate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (gate < MIN_GATE) gate = MIN_GATE;\n            if (ret <= gate) fastHat = wmul(fastHat, WAD - alpha) + wmul(pImplied, alpha);\n            slots[13] = uncertainty;\n        }\n\n        if (!firstInStep && feeUsed > 30 * BPS && gamma > 0) {\n            uint256 normalObs = trade.isBuy\n                ? wdiv(wmul(spot, gamma), WAD - 30 * BPS)\n                : wdiv(wmul(spot, WAD - 30 * BPS), gamma);\n            if ((slots[15] == 1) == (normalObs >= fastHat)) {\n                fastHat = wmul(fastHat, 9 * WAD / 10) + wmul(normalObs, WAD / 10);\n            }\n        }\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 rg = firstInStep ? (silent > 1 ? 0 : 1) : (stepTradeCount == 2 ? 2 : 3);\n        uint256 flowSize = wmul(lambdaHat, sizeHat);\n        uint256 fBase = _s(rg,BASE_FEE_0,BASE_FEE_1,BASE_FEE_2,BASE_FEE_3) + wmul(_s(rg,SIGMA_COEF_0,SIGMA_COEF_1,SIGMA_COEF_2,SIGMA_COEF_3), sigmaHat) + wmul(_s(rg,LAMBDA_COEF_0,LAMBDA_COEF_1,LAMBDA_COEF_2,LAMBDA_COEF_3), lambdaHat) + wmul(_s(rg,FLOW_SIZE_COEF_0,FLOW_SIZE_COEF_1,FLOW_SIZE_COEF_2,FLOW_SIZE_COEF_3), flowSize);\n        uint256 fMid = fBase + wmul(_s(rg,TOX_COEF_0,TOX_COEF_1,TOX_COEF_2,TOX_COEF_3), toxSignal) + wmul(_s(rg,TOX_QUAD_COEF_0,TOX_QUAD_COEF_1,TOX_QUAD_COEF_2,TOX_QUAD_COEF_3), wmul(toxSignal, toxSignal)) + wmul(_s(rg,ACT_COEF_0,ACT_COEF_1,ACT_COEF_2,ACT_COEF_3), 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 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(_s(rg,STALE_DIR_COEF_0,STALE_DIR_COEF_1,STALE_DIR_COEF_2,STALE_DIR_COEF_3), staleTox);\n            uint256 attractShift = wmul(staleShift, _s(rg,STALE_ATTRACT_FRAC_0,STALE_ATTRACT_FRAC_1,STALE_ATTRACT_FRAC_2,STALE_ATTRACT_FRAC_3));\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(_s(rg,TRADE_TOX_BOOST_0,TRADE_TOX_BOOST_1,TRADE_TOX_BOOST_2,TRADE_TOX_BOOST_3), tradeRatio);\n                if (!firstInStep && tradeBoost > _s(rg,CAPA_0,CAPA_1,CAPA_2,CAPA_3)) tradeBoost = _s(rg,CAPA_0,CAPA_1,CAPA_2,CAPA_3);\n                if (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n                else { askFee = askFee + tradeBoost; }\n            }\n        }\n\n        if (sellPressure) {\n            bidFee = clampFee(_compressTailWithSlope(bidFee, _s(rg,TAIL_SLOPE_PROTECT_0,TAIL_SLOPE_PROTECT_1,TAIL_SLOPE_PROTECT_2,TAIL_SLOPE_PROTECT_3)));\n            askFee = clampFee(_compressTailWithSlope(askFee, _s(rg,TAIL_SLOPE_ATTRACT_0,TAIL_SLOPE_ATTRACT_1,TAIL_SLOPE_ATTRACT_2,TAIL_SLOPE_ATTRACT_3)));\n        } else {\n            askFee = clampFee(_compressTailWithSlope(askFee, _s(rg,TAIL_SLOPE_PROTECT_0,TAIL_SLOPE_PROTECT_1,TAIL_SLOPE_PROTECT_2,TAIL_SLOPE_PROTECT_3)));\n            bidFee = clampFee(_compressTailWithSlope(bidFee, _s(rg,TAIL_SLOPE_ATTRACT_0,TAIL_SLOPE_ATTRACT_1,TAIL_SLOPE_ATTRACT_2,TAIL_SLOPE_ATTRACT_3)));\n        }\n\n        if (firstInStep) {\n            if (askFee > bidFee && bidFee > _s(rg,CAPB_0,CAPB_1,CAPB_2,CAPB_3)) bidFee = _s(rg,CAPB_0,CAPB_1,CAPB_2,CAPB_3);\n            else if (bidFee > askFee && askFee > _s(rg,CAPB_0,CAPB_1,CAPB_2,CAPB_3)) askFee = _s(rg,CAPB_0,CAPB_1,CAPB_2,CAPB_3);\n        }\n\n        if (bidFee > askFee && askFee > _s(rg,CAPC_0,CAPC_1,CAPC_2,CAPC_3)) askFee = _s(rg,CAPC_0,CAPC_1,CAPC_2,CAPC_3);\n        else if (askFee > bidFee && bidFee > _s(rg,CAPC_0,CAPC_1,CAPC_2,CAPC_3)) bidFee = _s(rg,CAPC_0,CAPC_1,CAPC_2,CAPC_3);\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; slots[7] = lambdaHat; slots[8] = sizeHat;\n        slots[9] = toxEma; slots[10] = stepTradeCount;\n\n        return (bidFee, askFee);\n    }\n\n    function _s(uint256 r, uint256 a, uint256 b, uint256 c, uint256 d) internal pure returns (uint256) {\n        return r == 0 ? a : (r == 1 ? b : (r == 2 ? c : d));\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 \"no_cubic\"; }\n}\n","sha256":"88e49bf983166c778dd9db709cdff2da51a3a4bacca1361027a23248fcfc0b70","seeds_kind":"tuning","paired":{"n":384,"seeds":"330000..330383","mean_diff":-0.8356353613735269,"se":0.039605775302907854,"worst":[-8.30029587990407,-2.5367489990577496,-2.4392230708843954,-2.394695771001693,-2.3827055592043394],"stack_mean":525.5297235982879,"cand_mean":524.6940882369144},"recheck_64_unseen_tuning_320100_320163":[{"tuning_crn_diff":-0.9595324005920496,"mean_diff":-0.9044282699815174,"se":0.10092459983339352},{"tuning_crn_diff":-2.715731051074634,"mean_diff":-2.5287593344205437,"se":0.13373665132211643},{"tuning_crn_diff":-2.756522159920161,"mean_diff":-3.0658306180670394,"se":0.20067573522098203}],"retail_edge_delta":null,"arb_edge_delta":null,"gas":{"max_ok":212934,"oog":0,"init":220965,"scope":"candidate, held-out seeds run"},"notes":"NEGATIVE RESULT. CMA-ES (own numpy, rng seed 2, lambda 8, mu 4, sigma0 0.12, start 0 = STACK) over 60 per-regime log multipliers (R1 first print silence>1, R2 first print silence 1, R3 second print, R4 later; regime of the trade that just happened sets the quote it returns). Estimators untouched. CRN batch = 32 seeds 320000..320031. Only 3 generations (24 evals) fit: about 40 s per evaluation, a 10-min tool cap per command and two runs killed (exit 137, probably memory when a batch held >32 seeds' step data), so 30 min of search was not reached. Every candidate lost to STACK; best tuning -0.96, recheck on 64 unseen tuning seeds -0.90 (se 0.10), so the 256-seed recheck was cut to 64. Held-out run cut from 512 to 384 seeds (330000..) to fit the time; no seeds dropped from inside that range. retail/arb edge split is null because amm_sim_rs results only expose total edges plus arb_volume_y/retail_volume_y, no edge by source. The CH check on 0..999 was skipped for time; STACK sha256 matched 2eaafc79.... amm-match validate not run on the candidate separately; it compiled with the repo's SolidityCompiler (same validation path) and ran with 0 OOG. Conclusion: at sigma 0.12, random per-regime multipliers cost about 3-6 on average; a regime split of STACK's constants showed no gain in this budget. Next try: sigma0 around 0.03 and more evaluations, or split only BASE_FEE/STALE_DIR/caps by regime (about 20 params)."}