{ "config": { "variant": "B + N only", "L": false, "tuning": false, "simulator_commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "seed_start": 3020000, "seed_end": 3023999, "n": 4000, "workers": 8, "seeds_per_call": 20, "measurement": "run_batch(X, VanillaStrategy, cfgs, 8) separately for X in {Strategy, NP2, B}; never candidate versus NP2", "score": "edges[submission]", "se": "sample standard deviation of per-seed paired differences (ddof=1) / sqrt(n)", "rng": "numpy.random.default_rng(seed); size uniform(19,21), rate uniform(0.6,1), sigma uniform(0.000882,0.001008), in that order", "price_seed": "seed", "retail_seed": "seed+1", "n_steps": 10000, "initial_price": 100, "initial_x": 100, "initial_y": 10000, "gbm_mu": 0, "gbm_dt": 1, "retail_size_sigma": 1.2, "retail_buy_prob": 0.5, "compiler": { "solc": "0.8.24", "optimizer_runs": 200, "viaIR": true, "evmVersion": "paris" }, "MIX_M": 625000000000000000, "MIX_E_SIXTEENTHS": 2, "mix_estimator": "slow pHat", "PHAT_ALPHA_RETAIL": 60000000000000000, "np2_sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0", "calibration_seeds": "0..999", "calibration": { "CH": 525.5258821780834, "NP2": 526.1155722459862 }, "validation": "Validating strategy...\nCompiling strategy...\nStrategy 'no_cubic' validated successfully!", "mean_edges": { "Strategy": 440.44398829350746, "NP2": 525.0782741083871, "B": 525.5260168101074 } }, "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 MIX_M = 625000000000000000;\n uint256 constant MIX_E_SIXTEENTHS = 2;\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[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 {\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[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 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 // Mix the next retail quote with a defence against next-step arbitrage.\n // The first observed print is our existing proxy for the step's arb;\n // after it, k counts the subsequent observed retail prints.\n {\n uint256 q = _nextRetailProbability(lambdaHat, stepTradeCount - 1);\n uint256 weight = _mixWeight(q);\n uint256 defence = clampFee(_absLogRatio(spot, pHat) + wmul(MIX_M, sigmaHat));\n if (spot >= pHat) {\n bidFee = wmul(weight, bidFee) + wmul(WAD - weight, defence);\n } else {\n askFee = wmul(weight, askFee) + wmul(WAD - weight, defence);\n }\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 // Poisson survival ratio P(N > k) / P(N >= k). Dividing both\n // tails by P(N=k) avoids cancellation for large k. For k=0 this\n // is exactly 1-exp(-lambda), up to fixed-point/series rounding.\n function _nextRetailProbability(uint256 lambda, uint256 k) internal pure returns (uint256) {\n uint256 term = WAD;\n uint256 tail;\n for (uint256 j = 1; j <= 24; ++j) {\n term = wmul(term, lambda) / (k + j);\n tail += term;\n if (term == 0) break;\n }\n return wdiv(tail, WAD + tail);\n }\n\n // e is an exact multiple of 1/16. Successive square roots implement\n // the fractional bits without an external fixed-point math library.\n function _mixWeight(uint256 q) internal pure returns (uint256 weight) {\n weight = _powWad(q, MIX_E_SIXTEENTHS / 16);\n uint256 fraction = MIX_E_SIXTEENTHS % 16;\n uint256 root = q;\n for (uint256 bit = 8; bit > 0 && fraction > 0; bit >>= 1) {\n root = sqrt(root * WAD);\n if ((fraction & bit) != 0) {\n weight = wmul(weight, root);\n fraction -= bit;\n }\n }\n }\n\n // 2*atanh((a-b)/(a+b)) = abs(ln(a/b)). Once z >= .05,\n // the logarithm exceeds the 10% fee cap. In the remaining domain\n // five positive terms give <1e-15 absolute truncation error.\n function _absLogRatio(uint256 a, uint256 b) internal pure returns (uint256) {\n if (a == b) return 0;\n if (a == 0 || b == 0) return MAX_FEE;\n uint256 z = wdiv(absDiff(a, b), a + b);\n if (z >= WAD / 20) return MAX_FEE;\n uint256 z2 = wmul(z, z);\n uint256 power = z;\n uint256 series = z;\n for (uint256 j = 3; j <= 9; j += 2) {\n power = wmul(power, z2);\n series += power / j;\n }\n return 2 * series;\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": "84a5f62e114a165d19a12e1b3eeb99aa148ee4ce8bf933646ca040a4d17b275a", "b_sha256": "218426004abed3b6cb69f4ef133fea8e4789ddbeae37bd11e94e5ffc5f2a77cb", "paired_np2": { "n": 4000, "mean_diff": -84.63428581487959, "se": 2.864128625102051, "worst": [ { "seed": 3021046, "candidate_edge": 66.7842996130471, "np2_edge": 789.0321501460236, "diff": -722.2478505329765 }, { "seed": 3020142, "candidate_edge": 74.33289895746367, "np2_edge": 788.4707905058646, "diff": -714.1378915484008 }, { "seed": 3022301, "candidate_edge": 77.48951870087915, "np2_edge": 772.5340694372893, "diff": -695.0445507364102 }, { "seed": 3020078, "candidate_edge": 73.52435281008668, "np2_edge": 757.742482829102, "diff": -684.2181300190152 }, { "seed": 3023354, "candidate_edge": 76.60162589266936, "np2_edge": 758.6694880397979, "diff": -682.0678621471285 } ] }, "paired_b": { "n": 4000, "mean_diff": -85.08202851659999, "se": 2.863731136716944 }, "seconds_per_sim": 0.0948776216444215, "blocked": null, "notes": [ "Only N constants, its post-tail mix block, and its three helpers were added to exact B. No B source lines were removed or replaced. Slow retail alpha and fast retail alpha remain 0.06; L was not applied.", "Calibration and confirmation results are local measurements, not source-reported metrics or leaderboard results. No tuning was performed. Each strategy was run once for each confirmation seed.", "Simulation timing is wall time for run_batch including construction of the 20 configurations, divided by all three strategies\u2019 simulation count; excludes setup, compilation, validation and calibration.", "Used 4000 seeds. First confirmation batches were below 0.2 seconds per simulation; used full requested 4000.", "External source passages for source code and method are listed in sources.json.", "The prescribed B+N combination lost substantially versus both references on the full confirmation block. These results do not support promotion. No parameters or code were changed after measurement." ] }