{
 "approach": "One delta on NP (CH + 30bps-pool implied-spot blend on later prints). For !firstInStep prints inside the existing pHat gate, the fixed PHAT_ALPHA_RETAIL=0.06 is replaced by alpha=clamp(a0 +/- a1*ret/sigmaHat, lo, hi), ret=|pImplied-pHat|/pHat. Grid on tuning seeds 30000..31999 (n=2000 per cell, paired vs NP per seed via amm_sim_rs.run_batch with MatchRunner._build_configs draws). Raising alpha with the implied move lost 0.12 to 1.7 edge per cell; a gentle DEcrease (a1=-0.0025, i.e. alpha falls from 0.06 at ret=0 to ~0.042 at the 7.2-sigma gate edge) was best at +0.043 (se 0.006). Frozen and measured once on fresh seeds 800000..801999: +0.0439 +/- 0.0065 (6.7 SE), which clears 2 SE, so it is a promotion candidate over NP.",
 "tried": [
  {
   "variant": "alpha_later=clamp(0.03+0.02*|pImplied/pHat-1|/sigmaHat,0,0.27)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -1.228877,
   "se": 0.01543
  },
  {
   "variant": "alpha_later=clamp(0.0+0.03*|pImplied/pHat-1|/sigmaHat,0,0.2)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -1.415196,
   "se": 0.017419
  },
  {
   "variant": "alpha_later=clamp(0.06+0.02*|pImplied/pHat-1|/sigmaHat,0,0.2)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -1.674609,
   "se": 0.019494
  },
  {
   "variant": "alpha_later=clamp(0.06+0.003*|pImplied/pHat-1|/sigmaHat,0,0.1)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -0.120678,
   "se": 0.006214
  },
  {
   "variant": "alpha_later=clamp(0.09-0.015*|pImplied/pHat-1|/sigmaHat,0.02,0.09)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -0.028598,
   "se": 0.010264
  },
  {
   "variant": "alpha_later=clamp(0.12-0.03*|pImplied/pHat-1|/sigmaHat,0.02,0.12)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -0.132903,
   "se": 0.012245
  },
  {
   "variant": "alpha_later=clamp(0.06-0.005*|pImplied/pHat-1|/sigmaHat,0.0,0.06)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": 0.017972,
   "se": 0.009199
  },
  {
   "variant": "alpha_later=clamp(0.07-0.01*|pImplied/pHat-1|/sigmaHat,0.0,0.07)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -0.058546,
   "se": 0.011228
  },
  {
   "variant": "alpha_later=clamp(0.05+0*|pImplied/pHat-1|/sigmaHat,0,1)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": 0.016373,
   "se": 0.007312
  },
  {
   "variant": "alpha_later=clamp(0.05-0.004*|pImplied/pHat-1|/sigmaHat,0.0,0.05)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": -0.018056,
   "se": 0.01114
  },
  {
   "variant": "alpha_later=clamp(0.06-0.0025*|pImplied/pHat-1|/sigmaHat,0.0,0.06)",
   "seeds": "30000..31999",
   "n": 2000,
   "mean_diff": 0.043351,
   "se": 0.006265
  },
  {
   "variant": "FROZEN alpha_later=clamp(0.06-0.0025*|pImplied/pHat-1|/sigmaHat,0,0.06) measured once on fresh seeds",
   "seeds": "800000..801999",
   "n": 2000,
   "mean_diff": 0.043894,
   "se": 0.006548
  }
 ],
 "next": "Sign is the finding: later prints with large implied moves should be trusted less, not more. Next: tune a1 in [-0.004,-0.001] jointly with a0 in [0.05,0.065] (0.05 constant alone was +0.016 on tuning); try the same move-scaled discount on the NP nS blend weight (0.1) and on first-in-step PHAT_ALPHA; replicate on another fresh block before final promotion.",
 "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 MV_A0 = 60000000000000000;\n    uint256 constant MV_A1 = 2500000000000000;\n    bool constant MV_NEG = true;\n    uint256 constant MV_LO = 0;\n    uint256 constant MV_HI = 60000000000000000;\n    uint256 constant PHAT_ALPHA_RETAIL = 60000000000000000;\n    uint256 constant DIR_IMPACT_MULT = 4;\n    uint256 constant GATE_SIGMA_MULT = 7200000000000000000;\n    uint256 constant MIN_GATE = 30000000000000000;\n    uint256 constant TRADE_TOX_BOOST = 3500 * BPS;\n    uint256 constant STALE_ATTRACT_FRAC = 1050000000000000000;\n    uint256 constant RET_CAP = WAD / 35;\n    uint256 constant TOX_CAP = WAD / 5;\n    uint256 constant TRADE_RATIO_CAP = WAD / 5;\n    uint256 constant LAMBDA_CAP = 1820000000000000000;\n    uint256 constant STEP_COUNT_CAP = 64;\n    uint256 constant BASE_FEE = 4 * BPS;\n    uint256 constant SIGMA_COEF = 200000000000000000;\n    uint256 constant LAMBDA_COEF = 12 * BPS;\n    uint256 constant FLOW_SIZE_COEF = 4842 * BPS;\n    uint256 constant TOX_COEF = 300 * BPS;\n    uint256 constant TOX_QUAD_COEF = 15000 * BPS;\n    uint256 constant ACT_COEF = 91843 * BPS;\n    uint256 constant DIR_COEF = 20 * BPS;\n    uint256 constant DIR_TOX_COEF = 100 * BPS;\n    uint256 constant STALE_DIR_COEF = 6850 * BPS;\n    uint256 constant SIGMA_TOX_COEF = 500 * BPS;\n    uint256 constant TAIL_KNEE = 600 * BPS;\n    uint256 constant TAIL_SLOPE_PROTECT = 930000000000000000;\n    uint256 constant TAIL_SLOPE_ATTRACT = 850000000000000000;\n\n    function afterInitialize(uint256 initialX, uint256 initialY) external override returns (uint256, uint256) {\n        slots[0] = BASE_FEE; slots[1] = BASE_FEE; slots[2] = 0; slots[3] = WAD; slots[4] = 0;\n        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n        slots[9] = 0; slots[10] = 0;\n        return (BASE_FEE, BASE_FEE);\n    }\n\n    function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {\n        uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = slots[2];\n        uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];\n        uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n        uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10];\n\n        bool isNewStep = trade.timestamp > lastTs;\n        if (isNewStep) {\n            uint256 elapsedRaw = trade.timestamp - lastTs;\n            uint256 elapsed = elapsedRaw > ELAPSED_CAP ? ELAPSED_CAP : elapsedRaw;\n            dirState = _decayCentered(dirState, DIR_DECAY, elapsed);\n            actEma = wmul(actEma, _powWad(ACT_DECAY, elapsed));\n            sizeHat = wmul(sizeHat, _powWad(SIZE_DECAY, elapsed));\n            toxEma = wmul(toxEma, _powWad(TOX_DECAY, elapsed));\n            if (stepTradeCount > 0 && elapsedRaw > 0) {\n                uint256 lambdaInst = (stepTradeCount * WAD) / elapsedRaw;\n                if (lambdaInst > LAMBDA_CAP) lambdaInst = LAMBDA_CAP;\n                lambdaHat = wmul(lambdaHat, LAMBDA_DECAY) + wmul(lambdaInst, WAD - LAMBDA_DECAY);\n            }\n            stepTradeCount = 0;\n        }\n\n        bool firstInStep = stepTradeCount == 0;\n        uint256 spot = trade.reserveX > 0 ? wdiv(trade.reserveY, trade.reserveX) : pHat;\n        if (pHat == 0) pHat = spot;\n\n        uint256 feeUsed = trade.isBuy ? prevBidFee : prevAskFee;\n        uint256 gamma = feeUsed < WAD ? WAD - feeUsed : 0;\n        uint256 pImplied;\n        if (gamma == 0) { pImplied = spot; }\n        else { pImplied = trade.isBuy ? wmul(spot, gamma) : wdiv(spot, gamma); }\n\n        {\n            uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;\n            uint256 alpha = PHAT_ALPHA;\n            if (!firstInStep) {\n                alpha = MV_A0;\n                if (sigmaHat > 0) {\n                    uint256 mv = wmul(MV_A1, wdiv(ret, sigmaHat));\n                    if (MV_NEG) alpha = alpha > mv ? alpha - mv : 0;\n                    else alpha = alpha + mv;\n                }\n                if (alpha < MV_LO) alpha = MV_LO;\n                if (alpha > MV_HI) alpha = MV_HI;\n            }\n            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n            if (ret <= adaptiveGate) { pHat = wmul(pHat, WAD - alpha) + wmul(pImplied, alpha); }\n            if (firstInStep) {\n                if (ret > RET_CAP) ret = RET_CAP;\n                sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);\n            }\n        }\n\n        if(!firstInStep&&feeUsed>30*BPS&&gamma>0){uint256 nS=trade.isBuy?wdiv(wmul(spot,gamma),WAD-30*BPS):wdiv(wmul(spot,WAD-30*BPS),gamma);pHat=wmul(pHat,9*WAD/10)+wmul(nS,WAD/10);}\n        uint256 tradeRatio = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n        if (tradeRatio > TRADE_RATIO_CAP) tradeRatio = TRADE_RATIO_CAP;\n\n        if (tradeRatio > SIGNAL_THRESHOLD) {\n            uint256 push = tradeRatio * DIR_IMPACT_MULT;\n            if (push > WAD / 4) push = WAD / 4;\n            if (trade.isBuy) {\n                dirState = dirState + push;\n                if (dirState > 2 * WAD) dirState = 2 * WAD;\n            } else {\n                dirState = dirState > push ? dirState - push : 0;\n            }\n            actEma = wmul(actEma, ACT_BLEND_DECAY) + wmul(tradeRatio, WAD - ACT_BLEND_DECAY);\n            sizeHat = wmul(sizeHat, SIZE_BLEND_DECAY) + wmul(tradeRatio, WAD - SIZE_BLEND_DECAY);\n            if (sizeHat > WAD) sizeHat = WAD;\n        }\n\n        uint256 tox = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n        if (tox > TOX_CAP) tox = TOX_CAP;\n        toxEma = wmul(toxEma, TOX_BLEND_DECAY) + wmul(tox, WAD - TOX_BLEND_DECAY);\n        uint256 toxSignal = toxEma;\n\n        stepTradeCount = stepTradeCount + 1;\n        if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;\n\n        uint256 flowSize = wmul(lambdaHat, sizeHat);\n        uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n        uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);\n        fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));\n\n        uint256 dirDev; bool sellPressure;\n        if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }\n        else { dirDev = WAD - dirState; sellPressure = false; }\n\n        uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));\n        uint256 bidFee; uint256 askFee;\n        if (sellPressure) {\n            bidFee = fMid + skew;\n            askFee = fMid > skew ? fMid - skew : 0;\n        } else {\n            askFee = fMid + skew;\n            bidFee = fMid > skew ? fMid - skew : 0;\n        }\n\n        {\n            uint256 staleShift = wmul(STALE_DIR_COEF, toxSignal);\n            uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);\n            if (spot >= pHat) {\n                bidFee = bidFee + staleShift;\n                askFee = askFee > attractShift ? askFee - attractShift : 0;\n            } else {\n                askFee = askFee + staleShift;\n                bidFee = bidFee > attractShift ? bidFee - attractShift : 0;\n            }\n        }\n\n        {\n            bool tradeAligned = (trade.isBuy && spot >= pHat) || (!trade.isBuy && spot < pHat);\n            if (tradeAligned) {\n                uint256 tradeBoost = wmul(TRADE_TOX_BOOST, tradeRatio);\n                if (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n                else { askFee = askFee + tradeBoost; }\n            }\n        }\n\n        if (sellPressure) {\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));\n        } else {\n            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));\n            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));\n        }\n\n        slots[0] = bidFee; slots[1] = askFee; slots[2] = trade.timestamp;\n        slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n        slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;\n        slots[9] = toxEma; slots[10] = stepTradeCount;\n\n        return (bidFee, askFee);\n    }\n\n    function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {\n        if (fee <= TAIL_KNEE) return fee;\n        return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);\n    }\n\n    function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {\n        result = WAD;\n        while (exp > 0) {\n            if (exp & 1 == 1) result = wmul(result, factor);\n            factor = wmul(factor, factor);\n            exp >>= 1;\n        }\n    }\n\n    function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {\n        uint256 mul = _powWad(decayFactor, elapsed);\n        if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }\n        uint256 below = wmul(WAD - centered, mul);\n        return below < WAD ? WAD - below : 0;\n    }\n\n    function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n",
 "code_sha256": "7b8500217ab51d670557f4f88164fc48d9aed4394691840565c58e364d56ef82",
 "delta": "Added constants MV_A0=0.06e18, MV_A1=0.0025e18, MV_NEG=true, MV_LO=0, MV_HI=0.06e18; replaced `uint256 alpha = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;` with alpha=PHAT_ALPHA on first-in-step, else alpha=clamp(MV_A0 - wmul(MV_A1, wdiv(ret, sigmaHat)), MV_LO, MV_HI) (guarded sigmaHat>0, floored at 0). No other changes; PHAT_ALPHA_RETAIL constant left in place but unused; slots 0..10 unchanged; no loops added.",
 "reproduction": {
  "seeds": "0..999",
  "CH_mean_edge": 525.5258821780834,
  "NP_mean_edge": 526.0337302497852,
  "matches_brief": true
 },
 "score": {
  "seed_start": 0,
  "n": 1000,
  "mean_edge": 526.065408062796,
  "se": 2.791462769333411
 },
 "paired": {
  "reference": "NP (CH d34a5199 + nS blend), mean_edge 526.0337302497852 on 0..999",
  "seed_start": 800000,
  "n": 2000,
  "n_covered": 2000,
  "chunks": "4 x 500",
  "mean_diff": 0.043893505807533185,
  "se": 0.006547566822621477,
  "candidate_mean_edge": 522.1287323962995,
  "reference_mean_edge": 522.0848388904918,
  "worst": [
   {
    "seed": 801130,
    "diff": -2.9777667965025785
   },
   {
    "seed": 801231,
    "diff": -2.27871155573456
   },
   {
    "seed": 800418,
    "diff": -1.6943463190235093
   },
   {
    "seed": 801443,
    "diff": -1.60559344535352
   },
   {
    "seed": 800186,
    "diff": -1.5721231474240085
   }
  ]
 },
 "seconds_per_simulation": 0.0649,
 "validate_ok": true,
 "blocked": null,
 "citations": [
  "https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704",
  "https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol"
 ],
 "notes": "Seeds 900000..909999 not used. Unlike the CLI, which runs seeds 0..N-1, the harness rebuilds per-seed configs exactly as MatchRunner._build_configs does (np.random.default_rng(seed): size, rate, sigma; SimulationConfig.seed=seed) and calls amm_sim_rs.run_batch with 8 workers. seconds_per_simulation is wall time per sim on 8 workers."
}