{ "delta": "NP2 plus one guarded router-undercut override after first print of each step (arb proxy). Recover fair from post-spot and feeUsed; expected normalizer spot=fair. After AMM sells X, target bid=1-(0.997+m)*fair/spot; mirror target ask=1-spot/(fair/0.997-m*fair). Targets floored at zero. Apply only if target+feeUsed>=emin; otherwise retain NP2 favored-side fee. Opposite side is at least feeUsed. Later prints use existing NP2/TWO logic. Final m=1 bps, emin=500 bps. No other baseline constants changed.", "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[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 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 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 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 // Router undercut: first print is the available arb proxy; no actor flag is exposed.\n // The normalizer's expected spot is fair (center of its 30 bps no-arb band).\n // Recover fair from our post-arb spot and the fee actually charged.\n // If target cannot meet the edge floor, retain the NP2 fee on that side.\n // On later retail prints, retain the unmodified NP2/TWO fee calculation above.\n if (firstInStep && gamma > 0 && spot > 0) {\n uint256 margin = 1 * BPS;\n uint256 edgeFloor = 500 * BPS;\n uint256 minFee = edgeFloor > feeUsed ? edgeFloor - feeUsed : 0;\n uint256 target;\n if (!trade.isBuy) {\n // After AMM sells X to arb, attract sellers (AMM bid).\n uint256 receiveRatio = wdiv(wmul(pImplied, WAD - 30 * BPS + margin), spot);\n target = receiveRatio < WAD ? WAD - receiveRatio : 0;\n if (target >= minFee) bidFee = clampFee(target);\n if (askFee < feeUsed) askFee = feeUsed;\n } else {\n // After AMM buys X from arb, attract buyers (AMM ask).\n uint256 normalAsk = wdiv(pImplied, WAD - 30 * BPS);\n uint256 discount = wmul(pImplied, margin);\n uint256 pay = normalAsk > discount ? normalAsk - discount : 1;\n uint256 payRatio = wdiv(spot, pay);\n target = payRatio < WAD ? WAD - payRatio : 0;\n if (target >= minFee) askFee = clampFee(target);\n if (bidFee < feeUsed) bidFee = feeUsed;\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 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 \"router_a\"; }\n}\n", "sha256": "4d621ce5ffdc091b139442cfa3cc5c00c7c11dd66e3aa3467796b9799f63af60", "np2_check": { "n": 1000, "seeds": [ 0, 999 ], "expected_rounded": 526.1156, "mean": 526.1155722459862, "pass": true, "sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0", "ch": { "n": 1000, "mean": 525.5258821780834, "expected": 525.525882178, "pass": true, "sha256": "6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3" } }, "tune": { "seeds": [ [ 12000, 12159 ], [ 13000, 13399 ] ], "best_mean_diff": -25.748065425046402, "final_constants_bps": { "m": 1, "emin": 500 }, "coarse": [ { "m": 1, "emin": 0, "n": 160, "mean_diff": -115.89176789440228, "se": 1.8858590770405832, "worst": -206.97069309801344 }, { "m": 1, "emin": 20, "n": 160, "mean_diff": -115.89176789440228, "se": 1.8858590770405832, "worst": -206.97069309801344 }, { "m": 1, "emin": 30, "n": 160, "mean_diff": -50.16326266937345, "se": 1.401513599988755, "worst": -115.6268544036335 }, { "m": 1, "emin": 40, "n": 160, "mean_diff": -43.20577122601193, "se": 1.4018648163325624, "worst": -114.16318300122555 }, { "m": 1, "emin": 50, "n": 160, "mean_diff": -37.874626161938785, "se": 1.3711958753273918, "worst": -112.23795324959542 }, { "m": 1, "emin": 60, "n": 160, "mean_diff": -34.72177315390996, "se": 1.3421522355494564, "worst": -108.57069065514963 }, { "m": 1, "emin": 80, "n": 160, "mean_diff": -30.30164607264559, "se": 1.1030292042631, "worst": -85.29039581049324 }, { "m": 1, "emin": 100, "n": 160, "mean_diff": -28.373163705851766, "se": 1.0825509398873276, "worst": -85.08761598825964 }, { "m": 1, "emin": 150, "n": 160, "mean_diff": -26.271017149153614, "se": 0.9633288945718251, "worst": -84.91562496389099 }, { "m": 1, "emin": 200, "n": 160, "mean_diff": -25.442921518682954, "se": 0.9032102323660733, "worst": -80.6820851361274 }, { "m": 5, "emin": 40, "n": 160, "mean_diff": -43.20577122601193, "se": 1.4018648163325624, "worst": -114.16318300122555 }, { "m": 10, "emin": 40, "n": 160, "mean_diff": -43.20577122601193, "se": 1.4018648163325624, "worst": -114.16318300122555 }, { "m": 1, "emin": 250, "n": 160, "mean_diff": -25.152043889194722, "se": 0.9042807151351491, "worst": -80.4272051241528 }, { "m": 1, "emin": 350, "n": 160, "mean_diff": -24.908896782103454, "se": 0.9020553822138551, "worst": -80.4272051241528 }, { "m": 1, "emin": 500, "n": 160, "mean_diff": -24.693283796787206, "se": 0.9020492870863976, "worst": -80.4272051241528 } ], "refined": [ { "m": 1, "emin": 500, "n": 400, "mean_diff": -25.748065425046402, "se": 0.6796035009696868, "worst": -96.22690195521443 }, { "m": 1, "emin": 350, "n": 400, "mean_diff": -25.814431129805797, "se": 0.6844061587681767, "worst": -96.22690195521443 }, { "m": 1, "emin": 250, "n": 400, "mean_diff": -25.94802695795247, "se": 0.6862167412136364, "worst": -96.22690195521443 } ], "selection": "Top three coarse settings re-evaluated on 400 tuning seeds; choose largest refined paired mean, then lower emin and m. Frozen before reserved holdout. Earlier discarded implementations used tuning seeds 10000..10599 and 11000..11399 only; none used confirmation seeds." }, "paired": { "n": 2000, "mean_diff": -26.726126100689385, "se": 0.3506906569088013, "worst": -166.9545351751368, "seeds": [ 2340000, 2341999 ], "candidate_mean": 500.409850089316, "np2_mean": 527.1359761900054, "worst5": [ { "seed": 2340264, "diff": -166.9545351751368 }, { "seed": 2340438, "diff": -147.45064783215304 }, { "seed": 2341194, "diff": -125.09380437414632 }, { "seed": 2341812, "diff": -123.32947187388856 }, { "seed": 2340008, "diff": -120.76992082829327 } ] }, "arb_volume": { "unit": "Y per 10000-step simulation", "candidate_mean": 17620.865548703536, "np2_mean": 24160.909026845355, "mean_diff": -6540.043478141816, "relative_change": -0.27068697915608764 }, "retail_volume": { "unit": "Y per 10000-step simulation", "candidate_mean": 65415.11075070301, "np2_mean": 77519.10077123897, "mean_diff": -12103.990020535963, "relative_change": -0.15614203338419996 }, "gas": { "init_gas": 189971, "max_swap_gas": 155077, "calls": 2000, "limit": 249999, "all_succeeded": true, "fee_bounds_and_guarded_edge_floor": true }, "blocked": null, "next": "Do not promote: reserved confirmation loses 26.7261 edge per seed vs NP2. First print can be retail; test reliable arb classification before further router tuning. High edge thresholds suppress most overrides.", "methodology": { "simulator_commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "pairing": "Separate candidate-vs-Vanilla and NP2-vs-Vanilla markets for identical seeds; subtract submission edges per seed. amm_sim_rs.run_batch, 8 workers, chunks of 16. Sample SE uses ddof=1. Worst is minimum per-seed difference.", "draws": "numpy.default_rng(s): size U(19,21), rate U(0.6,1), sigma U(0.000882,0.001008), in that order; config.seed=s, Rust price seed=s, retail seed=s+1. 10000 steps; initial price=100, x=100, y=10000, mu=0, dt=1, retail buy probability=.5, size sigma=1.2.", "confirmation": "Exactly one frozen candidate on seeds 2340000..2341999, an unused 2000-seed subset of the specified reserved block; no tuning afterward.", "validate": "amm-match validate scratch/router.sol passed after freeze.", "gas": "Actual pyrevm EVM.result.gas_used from 2000 synthetic swap calls using tuning-domain random seed 12345; both sides, timestamp gaps, varied reserves and sizes. Includes fee bounds, nonfavored fee minimum, and exact guarded target checks. Measured maximum, not proof of a global worst-case bound." }, "notes": [ "No measurements or source values were fabricated; all required evaluation fields are measured locally.", "Fair recovery is exact up to WAD rounding only for a true optimal arb print. There is no actor flag, so first-in-step is a fallible proxy and can classify retail as arb.", "Expected normalizer spot=fair is a modeling assumption (center of its symmetric multiplicative no-arb band), not an observed normalizer price. Fee+feeUsed is the requested bps edge approximation.", "Floor-zero saturation may be unable to beat the expected normalizer price when our post-arb spot is outside its competitive range. If minimum edge conflicts with target, skip the favored-side override; opposite-side minimum still applies.", "Higher emin can make this mechanism effectively inactive. A negative paired result is evidence against promotion, not a claimed improvement.", "Baseline scoring is not evidence of hook success because the pinned simulator can retain fees after a hook failure; gas and formula stress checks are reported separately." ] }