{ "mechanism": "ARB-SIZE CLASSIFIER", "approach": "Classify each print from fee-excluded pre-trade reserves and the exact fee-on-input arbitrage size implied by the existing pHat, independent of step position. Exact target post-spot is pHat/gamma when AMM buys X and pHat*gamma when AMM sells X. Tune only size tolerance; strong alpha=.95 and weak alpha=.06 fixed before tuning. Freeze the highest paired tuning mean, even if negative, then confirm once on unused consecutive seeds.", "delta": "NP2 unchanged except: before its pHat update call _arbSizeMatch using pre-update pHat and gamma=1-feeUsed. Reconstruct preX=postX-gamma*amountX, preY=postY+amountY for isBuy; otherwise preX=postX+amountX, preY=postY-gamma*amountY. Let s=preY/preX and q=s*gamma/pHat for isBuy, s/(pHat*gamma) otherwise. Compute r=sqrt(q) with WAD fixed-point and a bit-seeded seven-Newton-step integer sqrt. Expected amountX=preX*(r-1)/gamma for isBuy, preX*(1-r) otherwise. Require positive expected size and abs(actual-expected)<=expected*2/100. Override alpha after same-direction logic: match=0.95, nonmatch=0.06. Replace firstInStep with sizeArb only on sigma update. Existing pHat gate, NP interior-routing block, fee equations, constants and state stay unchanged. No added storage.", "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 bool sizeArb = _arbSizeMatch(trade, pHat, gamma, 2 * WAD / 100);\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 alpha = sizeArb ? 95 * WAD / 100 : 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 (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 (sizeArb) {\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 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 // Reconstruct reserves excluding the fee kept outside the invariant.\n function _arbSizeMatch(TradeInfo calldata t, uint256 p, uint256 g, uint256 tol) internal pure returns (bool) {\n if (p == 0 || g == 0) return false;\n uint256 x;\n uint256 y;\n if (t.isBuy) {\n uint256 netX = wmul(t.amountX, g);\n if (t.reserveX <= netX) return false;\n x = t.reserveX - netX;\n y = t.reserveY + t.amountY;\n } else {\n uint256 netY = wmul(t.amountY, g);\n if (t.reserveY <= netY) return false;\n x = t.reserveX + t.amountX;\n y = t.reserveY - netY;\n }\n uint256 preSpot = wdiv(y, x);\n uint256 ratio = t.isBuy ? wdiv(wmul(preSpot, g), p) : wdiv(preSpot, wmul(p, g));\n uint256 factor = _sizeSqrt(ratio * WAD);\n uint256 expected;\n if (t.isBuy) {\n if (factor <= WAD) return false;\n expected = wdiv(wmul(x, factor - WAD), g);\n } else {\n if (factor >= WAD) return false;\n expected = wmul(x, WAD - factor);\n }\n return expected > 0 && absDiff(t.amountX, expected) <= wmul(expected, tol);\n }\n\n function _sizeSqrt(uint256 n) internal pure returns (uint256 z) {\n if (n == 0) return 0;\n uint256 a = n;\n z = 1;\n if (a >> 128 > 0) { a >>= 128; z <<= 64; }\n if (a >> 64 > 0) { a >>= 64; z <<= 32; }\n if (a >> 32 > 0) { a >>= 32; z <<= 16; }\n if (a >> 16 > 0) { a >>= 16; z <<= 8; }\n if (a >> 8 > 0) { a >>= 8; z <<= 4; }\n if (a >> 4 > 0) { a >>= 4; z <<= 2; }\n if (a >> 2 > 0) { z <<= 1; }\n for (uint256 i = 0; i < 7; ++i) z = (z + n / z) / 2;\n uint256 other = n / z;\n return z < other ? z : other;\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": "d30bbb066b3854da62eac894a5171b3d0553b2b77da1c8a742a18bcf18c33c7e", "validate_ok": true, "max_gas": 189944, "np2_check": { "seeds": [ 0, 999 ], "code_sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0", "n": 1000, "mean": 526.1155722459862, "se": 2.7896004178197593, "expected": 526.1156, "ok": true }, "tune": [ { "n": 500, "se": 0.7009308403161462, "mean_diff": -20.910564677734186, "seeds": [ 10000, 10499 ], "variant": "arb2" }, { "n": 500, "se": 0.7001018100007338, "mean_diff": -21.069446593234044, "seeds": [ 10000, 10499 ], "variant": "arb5" }, { "n": 500, "se": 0.7005105161323925, "mean_diff": -21.06699843188343, "seeds": [ 10000, 10499 ], "variant": "arb10" } ], "paired": { "n": 2000, "se": 0.28574327173178493, "mean_diff": -20.3658008886483, "seeds": [ 2010000, 2011999 ], "worst": [ { "seed": 2010992, "diff": -281.56756272390146 }, { "seed": 2011380, "diff": -272.2279467091605 }, { "seed": 2010852, "diff": -263.33132869235646 }, { "seed": 2011319, "diff": -178.62457192378866 }, { "seed": 2011332, "diff": -155.69908036686718 } ], "candidate_mean_edge": 500.23490895579033, "np2_mean_edge": 520.6007098444386 }, "next": "Reject this mechanism for deployment; retain NP2. Hypothesis for future work: stale pHat causes missed arbitrage or coincidental retail matches; classification accuracy was not measured here.", "blocked": null, "checks": { "ch": { "seeds": [ 0, 999 ], "n": 1000, "mean": 525.5258821780834, "se": 2.7894264590251843, "expected": 525.525882178, "ok": true }, "gas": { "name": "arb2", "initialization_gas": 189944, "max_after_swap_gas": 136763, "max_gas": 189944, "calls": 4000, "all_success": true, "note": "Actual pyrevm EVM.result.gas_used; randomized constant-product stress, not a universal bound." }, "classifier": { "calls": 1000, "pass": true, "cases": "both sides, fee-excluded reserves, exact target and +/-4% accepted, +/-6% rejected for 5% tolerance" }, "validate_stdout": "Validating strategy...\nCompiling strategy...\nStrategy 'no_cubic' validated successfully!\n", "frozen": { "variant": "arb2", "code_sha256": "d30bbb066b3854da62eac894a5171b3d0553b2b77da1c8a742a18bcf18c33c7e", "rule": "highest tuning mean; all variants alpha .95/.06; holdout never previously run", "seeds": [ 2010000, 2011999 ] }, "paired_recomputed_from_edges": true }, "methodology": { "simulator": "https://github.com/benedictbrady/amm-challenge", "commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "comparison": "Separate amm_sim_rs.run_batch(candidate, VanillaStrategy, configs, 8) and amm_sim_rs.run_batch(NP2, VanillaStrategy, identical configs, 8); subtract submission edges per seed. Each strategy has its own market; not a head-to-head candidate-vs-NP2 market. Chunks of 50 seeds.", "draws": "numpy.random.default_rng(seed): retail_mean_size=uniform(19,21), retail_arrival_rate=uniform(.6,1), gbm_sigma=uniform(.000882,.001008), in this order. 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=.5; config seed=seed. Pinned Rust engine uses price seed=seed and retail seed=seed+1.", "statistics": "mean_diff=mean(candidate edge - NP2 edge); se=sample standard deviation of paired differences (ddof=1)/sqrt(n); worst=five lowest per-seed differences. No trimming.", "selection": "All three candidates on identical 10000..10499 seeds, 500 each. Highest mean_diff selected and frozen before either holdout run. One selected candidate run on 2010000..2011999, 2000 seeds.", "limits": "Gas is the measured maximum over initialization plus 4000 randomized constant-product hook calls, both sides and timestamp gaps; not proof of a global maximum. Focused tests verify classifier math; simulator score alone cannot prove hook success because the simulator retains fees after a hook error. Contract imports are the pinned simulator standard interfaces." }, "source_urls": [ "https://api.imd.fun/artifacts/528a6da78583c6142644a552c86670f9d25c20e39e92f4de44deae05ddc8cecd", "https://api.imd.fun/artifacts/da313379a2e69e9286668865e06b18dfcae25732c82b934b0fd9c2ef0d8c2ff5", "https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/match.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/amm/cfmm.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/market/arbitrageur.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/engine.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/evm/executor.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/contracts/src/AMMStrategyBase.sol", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/contracts/src/IAMMStrategy.sol", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/contracts/src/VanillaStrategy.sol", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/evm/compiler.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/evm/baseline.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/cli.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/core/trade.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/lib.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/evm/strategy.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/runner.rs" ] }