{ "delta": "NP2 plus noise-shrunk own-price gap: K=0, K2=0. After NP2 pHat and sigmaHat updates, raw=abs(spot-pHat)/pHat; e=min(timestamp-lastTs,8), zero within a step. unit=wmul(sigmaHat,floor(sqrt(1+e)*1e18)); tox=max(raw-wmul(K*1e18,unit),0), then original cap and EMA in slot 9. Slot 13 independently applies K2, the same elapsed decay and EMA, and feeds only staleShift/attractShift. K still feeds fMid and directional skew. Exact integer sqrt lookup for e=0..8; all other NP2 logic/constants unchanged. Sweep K with K2=K, then freeze K and sweep K2 over {0,.5,1,1.5,2,3} on seeds 10000..10239; maximize paired mean. Freeze code before one confirmation on 2720000..2721999.", "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 NOISE_K = 0;\n uint256 constant SHIFT_NOISE_K = 0;\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; slots[13] = 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 slots[13] = wmul(slots[13], _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; uint256 shiftTox;\n {\n uint256 toxRaw = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n uint256 e = isNewStep ? trade.timestamp - lastTs : 0;\n if (e > ELAPSED_CAP) e = ELAPSED_CAP;\n uint256 noiseUnit = wmul(sigmaHat, _sqrtOnePlusElapsed(e));\n uint256 noise = wmul(NOISE_K, noiseUnit);\n uint256 shiftNoise = wmul(SHIFT_NOISE_K, noiseUnit);\n tox = toxRaw > noise ? toxRaw - noise : 0;\n shiftTox = toxRaw > shiftNoise ? toxRaw - shiftNoise : 0;\n }\n if (shiftTox > TOX_CAP) shiftTox = TOX_CAP;\n slots[13] = wmul(slots[13], TOX_BLEND_DECAY) + wmul(shiftTox, WAD - TOX_BLEND_DECAY);\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, slots[13]);\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 // Exact floor(sqrt(1+e)*WAD), e is capped at eight.\n function _sqrtOnePlusElapsed(uint256 e) internal pure returns (uint256) {\n if (e == 0) return 1000000000000000000;\n if (e == 1) return 1414213562373095048;\n if (e == 2) return 1732050807568877293;\n if (e == 3) return 2000000000000000000;\n if (e == 4) return 2236067977499789696;\n if (e == 5) return 2449489742783178098;\n if (e == 6) return 2645751311064590590;\n if (e == 7) return 2828427124746190097;\n return 3000000000000000000;\n }\n\n function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n", "sha256": "bd9de10610efc91776749b378c6c7888b92be8a579f05519bb7bbb405b15f119", "tuning": { "seed_start": 10000, "seed_end_inclusive": 10239, "n_per_point": 240, "grid": [ 0, 0.5, 1, 1.5, 2, 3 ], "points": [ { "K": 0, "K2": 0, "stage": "K", "n": 240, "mean_diff": 0.0, "se": 0.0, "worst": 0.0, "worst_seed": 10000, "candidate_mean": 522.8527355886238, "baseline_mean": 522.8527355886238 }, { "K": 0.5, "K2": 0.5, "stage": "K", "n": 240, "mean_diff": -23.219604330148787, "se": 0.22223051726910112, "worst": -33.661496376462196, "worst_seed": 10237, "candidate_mean": 499.633131258475, "baseline_mean": 522.8527355886238 }, { "K": 1, "K2": 1, "stage": "K", "n": 240, "mean_diff": -46.891716973312924, "se": 0.45496254366764727, "worst": -68.41336420142886, "worst_seed": 10237, "candidate_mean": 475.9610186153108, "baseline_mean": 522.8527355886238 }, { "K": 1.5, "K2": 1.5, "stage": "K", "n": 240, "mean_diff": -60.84361556289321, "se": 0.6047963709408212, "worst": -87.22501564175082, "worst_seed": 10237, "candidate_mean": 462.00912002573045, "baseline_mean": 522.8527355886238 }, { "K": 2, "K2": 2, "stage": "K", "n": 240, "mean_diff": -72.89957580701903, "se": 0.760448389929869, "worst": -106.87440740501711, "worst_seed": 10237, "candidate_mean": 449.9531597816047, "baseline_mean": 522.8527355886238 }, { "K": 3, "K2": 3, "stage": "K", "n": 240, "mean_diff": -90.37812891779247, "se": 0.9935588301973377, "worst": -133.90498061853816, "worst_seed": 10237, "candidate_mean": 432.4746066708312, "baseline_mean": 522.8527355886238 }, { "K": 0, "K2": 0.5, "stage": "K2", "n": 240, "mean_diff": -21.831954210324245, "se": 0.2181674355394651, "worst": -31.633792213480888, "worst_seed": 10237, "candidate_mean": 501.02078137829955, "baseline_mean": 522.8527355886238 }, { "K": 0, "K2": 1, "stage": "K2", "n": 240, "mean_diff": -43.015930519812756, "se": 0.43181392777234995, "worst": -63.27710029647653, "worst_seed": 10237, "candidate_mean": 479.83680506881103, "baseline_mean": 522.8527355886238 }, { "K": 0, "K2": 1.5, "stage": "K2", "n": 240, "mean_diff": -55.36377939985731, "se": 0.5665049993764535, "worst": -79.2407949125087, "worst_seed": 10237, "candidate_mean": 467.48895618876645, "baseline_mean": 522.8527355886238 }, { "K": 0, "K2": 2, "stage": "K2", "n": 240, "mean_diff": -65.54230858133714, "se": 0.6992250017565799, "worst": -96.06291762640001, "worst_seed": 10237, "candidate_mean": 457.3104270072866, "baseline_mean": 522.8527355886238 }, { "K": 0, "K2": 3, "stage": "K2", "n": 240, "mean_diff": -80.11040578683796, "se": 0.8879372991774936, "worst": -118.91933611979255, "worst_seed": 10237, "candidate_mean": 442.7423298017858, "baseline_mean": 522.8527355886238 } ], "selection": "Maximize paired tuning mean; choose K in diagonal sweep, then K2 with K fixed. Confirmation data not consulted for selection.", "frozen": { "K": 0, "K2": 0, "sha256": "bd9de10610efc91776749b378c6c7888b92be8a579f05519bb7bbb405b15f119" } }, "paired": { "n": 2000, "mean_diff": 0.0, "se": 0.0, "worst": 0.0 }, "split": { "arb": null, "retail": null, "note": "Not measured: pinned run_batch exposes total edges and actor volumes, not per-trade edge attribution or preceding-print classifications. No simulator instrumentation used." }, "fee_stats": { "bid": 0.0036412330525045964, "ask": 0.0035354363272561435, "unit": "fraction (multiply by 10000 for bps)", "aggregation": "Arithmetic mean of end-of-step fees across 10000 steps per seed and 2000 confirmation seeds; not trade-weighted.", "np2": { "bid": 0.0036412330525045964, "ask": 0.0035354363272561435 }, "difference": { "bid": 0.0, "ask": 0.0 } }, "blocked": null, "interpretation": "The selected K=K2=0 disables shrinkage and is behaviorally equivalent to NP2. Nonzero variants were evaluated only on the 240 tuning seeds. The 2000-seed confirmation concerns the frozen zero-shrink control, not a nonzero improvement. Retain original NP2 for deployment; the extra slot and code serve reproducibility of this experiment.", "next": "Retain NP2; this grid found no improvement.", "methodology": { "simulator_commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "baseline_sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0", "compiler": "Solidity 0.8.24, optimizer 200 runs, viaIR, Paris (pinned SolidityCompiler)", "configs": "For each seed s: rng=numpy.random.default_rng(s); size=rng.uniform(19,21); rate=rng.uniform(.6,1); sigma=rng.uniform(.000882,.001008); build_config(seed=s,gbm_sigma=sigma,retail_arrival_rate=rate,retail_mean_size=size). Other settings are the pinned defaults, including 10000 steps. Price seed s, retail seed s+1.", "execution": "amm_sim_rs.run_batch(candidate_bytecode, VanillaStrategy_bytecode, configs, 8), separately from run_batch(NP2_bytecode, VanillaStrategy_bytecode, configs, 8). Exactly 20 seeds per call, including tuning. Unmodified simulator.", "statistics": "Per-seed d=candidate.edges[submission]-NP2.edges[submission]; mean arithmetic, se=sample sd(ddof=1)/sqrt(n), worst=min(d).", "confirmation": { "seed_start": 2720000, "seed_end_inclusive": 2721999, "candidate_runs_per_seed": 1, "baseline_runs_per_seed": 1, "frozen_before_confirmation": true, "candidate_mean": 525.5023047946072, "np2_mean": 525.5023047946072, "worst_five": [ { "seed": 2720000, "diff": 0.0 }, { "seed": 2720001, "diff": 0.0 }, { "seed": 2720002, "diff": 0.0 }, { "seed": 2720003, "diff": 0.0 }, { "seed": 2720004, "diff": 0.0 } ] } }, "checks": { "setup": "Task-provided item setup script run once; StarterStrategy validated.", "CH": { "n": 1000, "seed_start": 0, "mean": 525.5258821780834, "expected": 525.525882178, "tolerance": 1e-06 }, "NP2": { "n": 1000, "seed_start": 0, "mean": 526.1155722459862, "sha256": "51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0" }, "stress": [ { "K": 0, "K2": 0, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131160, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": true }, { "K": 0.5, "K2": 0.5, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131186, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 1, "K2": 1, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131186, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 1.5, "K2": 1.5, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131186, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 2, "K2": 2, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131186, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 3, "K2": 3, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131186, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 0, "K2": 3, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 151008, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false }, { "K": 3, "K2": 0, "calls": 1200, "initialization_gas": 192150, "max_swap_gas": 131020, "noise_and_ema_reference_match": true, "zero_K_matches_NP2": false } ], "validation": "Validating strategy...\nCompiling strategy...\nStrategy 'no_cubic' validated successfully!" }, "evidence": { "measurements": "Tuning, confirmation, fee statistics and gas checks are local measurements in this run, not externally sourced results. URLs and exact quotations for the inputs and simulator are in sources.json.", "baseline_reconstruction": "Insert the NP artifact code from // Interior retail routing to before uint256 tradeRatio = into TWO immediately before its uint256 tradeRatio =. Full reconstructed NP2 SHA-256 verified against the supplied prefix." } }