{
 "config": "B (stack-b, extracted solidity block, sha256 verified) + S (silence-a), no tuning. S constants as given: per-silent-step decay 0.075 (w=1-0.925^g), g=min(elapsed-1,4), damp 1-0.30w on the print's slow alpha and gate; free slot 16 holds our post-trade spot.",
 "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[2] = 0; slots[3] = WAD; slots[4] = 0;\n        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n        slots[13] = 902500000000; slots[14] = slots[5]; slots[16] = slots[5]; slots[15] = 0; slots[9] = 0; slots[10] = 0; slots[11] = 0; slots[12] = 0;\n        return (BASE_FEE, BASE_FEE);\n    }\n\n    function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {\n        uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = slots[2];\n        uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];\n        uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n        uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10];\n\n        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        // Silence: after g>=1 silent steps, pull pHat toward the mid of our last quoted bid/ask.\n        uint256 silenceDamp = WAD;\n        if (firstInStep && silent >= 2) {\n            uint256 g = silent - 1;\n            if (g > 4) g = 4;\n            uint256 sPrev = slots[16];\n            if (sPrev > 0 && prevAskFee < WAD && prevBidFee < WAD) {\n                uint256 c = (wmul(sPrev, WAD - prevBidFee) + wdiv(sPrev, WAD - prevAskFee)) / 2;\n                uint256 w = WAD - _powWad(925000000000000000, g);\n                if (c >= pHat) pHat = pHat + wmul(c - pHat, w);\n                else pHat = pHat - wmul(pHat - c, w);\n                silenceDamp = WAD - wmul(300000000000000000, w);\n            }\n        }\n\n        {\n            uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;\n            uint256 alpha = firstInStep ? wmul(PHAT_ALPHA, silenceDamp) : PHAT_ALPHA_RETAIL;\n            uint256 prePhat = pHat;\n            bool secondPrint = !firstInStep && stepTradeCount == 1;\n            bool sameDir = false; bool oppDir = false;\n            if (secondPrint) {\n                bool up2 = pImplied >= pHat;\n                uint256 d1 = slots[12];\n                if (d1 != 0) { sameDir = (d1 == 1) == up2; oppDir = !sameDir; }\n                if (sameDir) alpha = PHAT_ALPHA_SAME;\n            }\n            if (firstInStep) { slots[11] = pHat; slots[12] = pImplied >= pHat ? 1 : 2; }\n            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n            adaptiveGate = wmul(adaptiveGate, silenceDamp);\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 = sqrt(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 flowSize = wmul(lambdaHat, sizeHat);\n        uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n        uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);\n        fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));\n\n        uint256 dirDev; bool sellPressure;\n        if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }\n        else { dirDev = WAD - dirState; sellPressure = false; }\n\n        uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));\n        uint256 bidFee; uint256 askFee;\n        if (sellPressure) {\n            bidFee = fMid + skew;\n            askFee = fMid > skew ? fMid - skew : 0;\n        } else {\n            askFee = fMid + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;\n        }\n\n        {\n            uint256 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 (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n                else { askFee = askFee + tradeBoost; }\n            }\n        }\n\n        if (sellPressure) {\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));\n        } else {\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));\n        }\n\n        slots[0] = bidFee; slots[1] = askFee; slots[2] = trade.timestamp;\n        slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n        slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;\n        slots[9] = toxEma; slots[10] = stepTradeCount; slots[16] = spot;\n\n        return (bidFee, askFee);\n    }\n\n    function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {\n        if (fee <= TAIL_KNEE) return fee;\n        return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);\n    }\n\n    function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {\n        result = WAD;\n        while (exp > 0) {\n            if (exp & 1 == 1) result = wmul(result, factor);\n            factor = wmul(factor, factor);\n            exp >>= 1;\n        }\n    }\n\n    function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {\n        uint256 mul = _powWad(decayFactor, elapsed);\n        if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }\n        uint256 below = wmul(WAD - centered, mul);\n        return below < WAD ? WAD - below : 0;\n    }\n\n    function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n",
 "sha256": "e88d94d79d73f1829dbef70a9e85ae676bdc4b241b867984fdab67e206ac49c6",
 "b_sha256": "218426004abed3b6cb69f4ef133fea8e4789ddbeae37bd11e94e5ffc5f2a77cb",
 "paired_np2": null,
 "paired_b": null,
 "seconds_per_sim": null,
 "blocked": {
  "step": "setup (sh scratch/setup.sh: uv/cc/rustup install, venv, maturin build)",
  "error": "refused by the host guard"
 },
 "notes": [
  "No measurement was run. The host guard refused the setup step that installs the toolchain and builds the simulator, so cand, NP2 and B were not run on seeds 3040000..3043999. paired_np2, paired_b and seconds_per_sim are null rather than guessed.",
  "B was taken from the ```solidity block of artifact 5839483d...; its sha256 218426004abed3b6cb69f4ef133fea8e4789ddbeae37bd11e94e5ffc5f2a77cb matches the artifact's stated value.",
  "How S was read and implemented: (1) slot 16 stores our post-trade spot s=reserveY/reserveX at the end of every afterSwap and is set to the initial price in afterInitialize. (2) On a step's first print with elapsedRaw=timestamp-lastTs>=2, g=min(elapsedRaw-1,4). prevBid/prevAsk are slots[0]/slots[1], the fees in effect before this print. c=(s*(1-prevBid)+s/(1-prevAsk))/2, w=1-0.925^g (computed with _powWad), and pHat+=w*(c-pHat). (3) This happens before the slow block, so the slow ret, and therefore the sigmaHat update, the pre-step snapshot in slots[11] and the first-print direction in slots[12], use the shifted pHat. (4) That print's slow alpha (PHAT_ALPHA) and the slow adaptive gate (after its MIN_GATE floor) are multiplied by 1-0.30w. The fast estimator (fastHat), its gate and everything else in B are unchanged. S is skipped if s==0.",
  "Interpretation choices worth flagging: the gate is damped after the MIN_GATE floor, not before. 'elapsed' is read as the raw timestamp gap, not B's ELAPSED_CAP-capped value; with g capped at 4 the two agree.",
  "Compile check only: the candidate compiles under solc 0.8.24, viaIR, optimizer 200 runs, EVM Paris against the pinned AMMStrategyBase.sol/IAMMStrategy.sol, using forge offline. The two warnings (unused prePhat, alpha read uninitialized i.e. 0) are inherited from B. amm-match validate was NOT run because the simulator could not be set up, so the 'validate must pass' condition is unverified.",
  "To finish: run the item's setup.sh, then run_batch(X, VanillaStrategy, cfgs, 8) separately for X in {cand, NP2, B}, 20 seeds per call, on seeds 3040000..3043999 (use 2,000 if over 0.2 s/sim), as in B's Method section."
 ]
}