{ "approach": "One delta on CH: replace the first-print absolute-return EMA by elapsed-normalized variance v=D*v+(1-D)*ret^2/max(1,timestamp-lastTs), with existing capped ret and WAD floors, and sigmaHat=floor(sqrt(v*WAD)). Initialize variance at (0.00095)^2. Slot 11 is the only additional slot; slots 0..11 used. No new loops: sqrt uses magnitude comparisons and seven unrolled Newton steps; CH's pre-existing bounded elapsed-decay loop remains. Keep CH's gate on the new sigmaHat, with its existing before-update ordering. Grid winner D69C20 selected solely by highest paired tuning mean on 10000..10499; n=500 each as item-specific brief permits. Frozen before any 600000..601999 simulation. Evaluate candidate and CH separately against the same 30-bps normalizer, never against each other, on identical per-seed configs. numpy.default_rng(seed) draws size U[19,21], rate U[0.6,1], sigma U[0.000882,0.001008], in that order; remaining settings match MatchRunner. Rust price seed=seed, retail seed=seed+1. run_batch chunks of 25; no simulator modifications. SE is sample sd/sqrt(n); worst means lowest candidate-minus-CH differences. Score uses seeds 0..999. Never used 900000..909999. seconds_per_simulation is total batch wall time / 10000 scored simulations, excluding setup, compilation, and scratch checks. Reference best remains CH 6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3 with requester-provided seed-0..999 score 525.525882178 (not independently remeasured). Delivered code is the best requested variance candidate, even if losing; it is not an unqualified replacement for CH.", "tried": [ { "variant": "D69C10", "seeds": "10000..10499", "n": 500, "mean_diff": -2.135055649638334, "se": 0.04090295385441333, "code_sha256": "68764987221fb22c195b4a0c1f7b57b4927cff7938e028647f4ce08367c70750", "worst": [ { "seed": 10358, "diff": -5.422142101185898, "candidate_edge": 470.8979593114715, "reference_edge": 476.3201014126574 }, { "seed": 10383, "diff": -5.076029611640024, "candidate_edge": 566.3503540759749, "reference_edge": 571.4263836876149 }, { "seed": 10085, "diff": -4.802054819061141, "candidate_edge": 672.4248624278054, "reference_edge": 677.2269172468665 }, { "seed": 10392, "diff": -4.318420430074525, "candidate_edge": 629.8674276827963, "reference_edge": 634.1858481128709 }, { "seed": 10440, "diff": -4.077294980379861, "candidate_edge": 530.8843008815621, "reference_edge": 534.961595861942 } ], "mean_edge": 521.5108596930795 }, { "variant": "D69C20", "seeds": "10000..10499", "n": 500, "mean_diff": -0.30410669743247604, "se": 0.026427343024595252, "code_sha256": "3d8dfb6aa8607d3ca58dfeaa70772fcab75fd9d33d78fbd40e72151e64c40192", "worst": [ { "seed": 10496, "diff": -2.850546805594945, "candidate_edge": 408.31949760646376, "reference_edge": 411.1700444120587 }, { "seed": 10372, "diff": -2.7122966707130445, "candidate_edge": 588.9213607139558, "reference_edge": 591.6336573846688 }, { "seed": 10332, "diff": -2.4777574417785218, "candidate_edge": 530.6033220172322, "reference_edge": 533.0810794590108 }, { "seed": 10005, "diff": -2.062452184706615, "candidate_edge": 453.8727538462339, "reference_edge": 455.9352060309405 }, { "seed": 10227, "diff": -1.9960427136166459, "candidate_edge": 423.79863695072885, "reference_edge": 425.7946796643455 } ], "mean_edge": 523.3418086452855 }, { "variant": "D69C30", "seeds": "10000..10499", "n": 500, "mean_diff": -2.3449136557830315, "se": 0.24250726637104486, "code_sha256": "7d7c963f6f93107230662482a902248024f65cf8553fbd0b2be002a7f8a511e8", "worst": [ { "seed": 10014, "diff": -118.23818650404195, "candidate_edge": 464.18179941611464, "reference_edge": 582.4199859201566 }, { "seed": 10219, "diff": -12.770742441313018, "candidate_edge": 512.066493086491, "reference_edge": 524.8372355278041 }, { "seed": 10227, "diff": -10.228651073349965, "candidate_edge": 415.56602859099553, "reference_edge": 425.7946796643455 }, { "seed": 10244, "diff": -9.633991200820219, "candidate_edge": 547.7763528524789, "reference_edge": 557.4103440532991 }, { "seed": 10332, "diff": -6.826725832784177, "candidate_edge": 526.2543536262266, "reference_edge": 533.0810794590108 } ], "mean_edge": 521.3010016869347 }, { "variant": "D80C10", "seeds": "10000..10499", "n": 500, "mean_diff": -2.110284534849358, "se": 0.04124194469055017, "code_sha256": "0098a9cae6e6912eec60b72d6711e523bf3107fec5670ab1cb6dc4c578316cac", "worst": [ { "seed": 10383, "diff": -5.424298188827379, "candidate_edge": 566.0020854987876, "reference_edge": 571.4263836876149 }, { "seed": 10358, "diff": -5.4048399231676285, "candidate_edge": 470.91526148948975, "reference_edge": 476.3201014126574 }, { "seed": 10085, "diff": -4.92280520638019, "candidate_edge": 672.3041120404863, "reference_edge": 677.2269172468665 }, { "seed": 10121, "diff": -4.818734248435362, "candidate_edge": 690.6719021174116, "reference_edge": 695.490636365847 }, { "seed": 10440, "diff": -4.206095578828581, "candidate_edge": 530.7555002831134, "reference_edge": 534.961595861942 } ], "mean_edge": 521.5356308078684 }, { "variant": "D80C20", "seeds": "10000..10499", "n": 500, "mean_diff": -0.3331753217947836, "se": 0.028375240969693228, "code_sha256": "233a26c842cd3679eddffed2781905f3eff24dc64a522c66de9fe300a4a70d2c", "worst": [ { "seed": 10307, "diff": -4.741342285605697, "candidate_edge": 775.0020734946879, "reference_edge": 779.7434157802936 }, { "seed": 10289, "diff": -2.558984555681718, "candidate_edge": 631.9447320019418, "reference_edge": 634.5037165576235 }, { "seed": 10423, "diff": -2.221446498393675, "candidate_edge": 598.1406240706953, "reference_edge": 600.3620705690889 }, { "seed": 10496, "diff": -2.198974489735633, "candidate_edge": 408.97106992232307, "reference_edge": 411.1700444120587 }, { "seed": 10121, "diff": -2.0728253239054766, "candidate_edge": 693.4178110419415, "reference_edge": 695.490636365847 } ], "mean_edge": 523.312740020923 }, { "variant": "D80C30", "seeds": "10000..10499", "n": 500, "mean_diff": -2.433257940892664, "se": 0.23651220888356445, "code_sha256": "4e9abc5a993e5a7e874a65f88d9df41d377bb6a7194a1682e25e257d578c2abb", "worst": [ { "seed": 10014, "diff": -115.70250594230981, "candidate_edge": 466.7174799778468, "reference_edge": 582.4199859201566 }, { "seed": 10219, "diff": -13.644348658461638, "candidate_edge": 511.19288686934243, "reference_edge": 524.8372355278041 }, { "seed": 10174, "diff": -7.24469167812174, "candidate_edge": 601.2158673418528, "reference_edge": 608.4605590199745 }, { "seed": 10332, "diff": -7.168944166280539, "candidate_edge": 525.9121352927302, "reference_edge": 533.0810794590108 }, { "seed": 10423, "diff": -6.206181995942188, "candidate_edge": 594.1558885731467, "reference_edge": 600.3620705690889 } ], "mean_edge": 521.2126574018251 }, { "variant": "D90C10", "seeds": "10000..10499", "n": 500, "mean_diff": -2.0878418094308846, "se": 0.04300359237251493, "code_sha256": "8f67e82bcdd3c7e88b6d85f68126e6fe32c716cff1580a80026ae4fb00063d2e", "worst": [ { "seed": 10358, "diff": -5.360755914989454, "candidate_edge": 470.9593454976679, "reference_edge": 476.3201014126574 }, { "seed": 10085, "diff": -5.019233724601463, "candidate_edge": 672.207683522265, "reference_edge": 677.2269172468665 }, { "seed": 10383, "diff": -4.9030033380615805, "candidate_edge": 566.5233803495533, "reference_edge": 571.4263836876149 }, { "seed": 10440, "diff": -4.215240739605747, "candidate_edge": 530.7463551223362, "reference_edge": 534.961595861942 }, { "seed": 10121, "diff": -4.199412561870531, "candidate_edge": 691.2912238039764, "reference_edge": 695.490636365847 } ], "mean_edge": 521.5580735332869 }, { "variant": "D90C20", "seeds": "10000..10499", "n": 500, "mean_diff": -0.4342401423388451, "se": 0.03023604725211807, "code_sha256": "3967b988174972a42dcd05ee2463d9cc6aabb8822e8f40c5f6fa15105e04bb53", "worst": [ { "seed": 10436, "diff": -2.6007912328958582, "candidate_edge": 588.410461755303, "reference_edge": 591.0112529881989 }, { "seed": 10423, "diff": -2.5980256081343214, "candidate_edge": 597.7640449609546, "reference_edge": 600.3620705690889 }, { "seed": 10354, "diff": -2.3250353678554347, "candidate_edge": 516.9897190755173, "reference_edge": 519.3147544433727 }, { "seed": 10372, "diff": -2.1999488128737994, "candidate_edge": 589.433708571795, "reference_edge": 591.6336573846688 }, { "seed": 10029, "diff": -2.197046595697884, "candidate_edge": 620.8529793423662, "reference_edge": 623.0500259380641 } ], "mean_edge": 523.211675200379 }, { "variant": "D90C30", "seeds": "10000..10499", "n": 500, "mean_diff": -2.594241152643156, "se": 0.06474165159606983, "code_sha256": "05a795939c49253572db544adb0336e660e2a161545dbdd622ecf31a9822fc89", "worst": [ { "seed": 10209, "diff": -8.266016718873743, "candidate_edge": 680.7487256634793, "reference_edge": 689.014742382353 }, { "seed": 10174, "diff": -7.3743788639110335, "candidate_edge": 601.0861801560635, "reference_edge": 608.4605590199745 }, { "seed": 10307, "diff": -7.1559662641542445, "candidate_edge": 772.5874495161394, "reference_edge": 779.7434157802936 }, { "seed": 10491, "diff": -7.0040857566608565, "candidate_edge": 615.4584651709876, "reference_edge": 622.4625509276484 }, { "seed": 10423, "diff": -6.989078631210646, "candidate_edge": 593.3729919378783, "reference_edge": 600.3620705690889 } ], "mean_edge": 521.0516741900747 } ], "next": "Do not promote this variance delta: fresh paired difference is -0.286588741 with SE 0.017738248, n=2000. Retain CH. No promotions in this item. A later separate experiment could account for pHat filtering lag and retail measurement noise before interpreting squared implied-price deviations as per-step fair-price variance; this explanation is a hypothesis, not established by this grid.", "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 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; slots[11] = 902500000000;\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 = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;\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 uint256 elapsedRaw = trade.timestamp > lastTs ? trade.timestamp - lastTs : 1;\n uint256 varianceHat = wmul(slots[11], SIGMA_DECAY)\n + wmul(wmul(ret, ret) / elapsedRaw, WAD - SIGMA_DECAY);\n slots[11] = varianceHat;\n sigmaHat = _isqrt(varianceHat * WAD);\n }\n }\n\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 _isqrt(uint256 x) internal pure returns (uint256 z) {\n if (x == 0) return 0;\n uint256 y = x; z = 1;\n if (y >> 128 > 0) { y >>= 128; z <<= 64; }\n if (y >> 64 > 0) { y >>= 64; z <<= 32; }\n if (y >> 32 > 0) { y >>= 32; z <<= 16; }\n if (y >> 16 > 0) { y >>= 16; z <<= 8; }\n if (y >> 8 > 0) { y >>= 8; z <<= 4; }\n if (y >> 4 > 0) { y >>= 4; z <<= 2; }\n if (y >> 2 > 0) { z <<= 1; }\n unchecked {\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n z = (z + x / z) >> 1;\n uint256 other = x / z;\n if (other < z) z = other;\n }\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": "3d8dfb6aa8607d3ca58dfeaa70772fcab75fd9d33d78fbd40e72151e64c40192", "delta": "Set SIGMA_DECAY=690000000000000000 and SIGMA_COEF=200000000000000000. Append slots[11] = 902500000000 to afterInitialize (WAD variance of 0.00095). Replace only the firstInStep sigma EMA line with: elapsedRaw = trade.timestamp > lastTs ? trade.timestamp-lastTs : 1; varianceHat = wmul(slots[11],SIGMA_DECAY) + wmul(wmul(ret,ret)/elapsedRaw,WAD-SIGMA_DECAY); slots[11]=varianceHat; sigmaHat=_isqrt(varianceHat*WAD). Insert _isqrt before _compressTailWithSlope: return 0 for x=0; seed z=1,y=x; for shifts 128,64,32,16,8,4 conditionally right-shift y and left-shift z by half that shift; if y>>2>0 left-shift z by 1; perform seven explicitly unrolled z=(z+x/z)>>1 steps unchecked; return min(z,x/z). Existing gate uses prior sigmaHat; slot 6 stores updated sigmaHat. All other source text unchanged.", "score": { "seed_start": 0, "n": 1000, "mean_edge": 525.2470928336927, "se": 2.790527584325092 }, "paired": { "reference": "CH 6dd68f77", "seed_start": 600000, "n": 2000, "mean_diff": -0.2865887410740618, "se": 0.01773824750410544, "worst": [ { "seed": 600845, "candidate_edge": 371.42941081032615, "reference_edge": 387.67289987703776, "diff": -16.243489066711618 }, { "seed": 601728, "candidate_edge": 612.6061662878251, "reference_edge": 624.3542123549739, "diff": -11.748046067148834 }, { "seed": 601698, "candidate_edge": 499.6737389505853, "reference_edge": 506.5382363532637, "diff": -6.86449740267841 }, { "seed": 600930, "candidate_edge": 509.0555472337906, "reference_edge": 513.2886125731824, "diff": -4.233065339391771 }, { "seed": 600619, "candidate_edge": 489.245917266965, "reference_edge": 493.4679288405589, "diff": -4.222011573593875 } ] }, "seconds_per_simulation": 0.2996049558671424, "validate_ok": true, "blocked": null, "citations": [ { "url": "https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol", "used_for": "Verified CH source and baseline delta." }, { "url": "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/match.py", "used_for": "Canonical paired configuration construction and seed-indexed parameter draw order." }, { "url": "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py", "used_for": "Canonical simulation ranges and fixed parameters." }, { "url": "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/engine.rs", "used_for": "Rust price and retail seed handling." }, { "url": "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/evm/compiler.py", "used_for": "Compiler version, optimizer and viaIR pipeline." }, { "url": "https://raw.githubusercontent.com/dipankar/amm-challenge/main/ANALYSIS.md", "used_for": "Public background write-up: advocates implied-price state estimation and adaptive volatility gating. Its claimed scores were not used as measurements in this item." }, { "url": "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/evm/strategy.rs", "used_for": "Rust engine initialization and trade gas limits are 250000." }, { "kind": "local measurements (this item)", "used_for": "All tried, score, paired and timing numbers are local run_batch measurements. Starter, CH, and selected strategy pass amm-match validate; EVM helper harness checks 2007 integer-square-root vectors and 300 synthetic swaps at 250000 gas. Exact variance-storage checks also pass for timestamp zero, repeated timestamps, and uncapped elapsed gaps 2, 27, 50. No exact gas-use estimate is claimed. Paradigm puzzle page could not be retrieved through web tool; no live leaderboard verification claimed." } ] }