{ "delta": "NP2 SHA256 51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0. After its current pHat/sigmaHat update, compute e=min(max(timestamp-lastTs,0),8), u=sigmaHat*sqrt(1+e), then max(toxRaw-K*u,0), capped at TOX_CAP, feeding the original slot9 EMA and all original toxSignal uses except staleShift. A parallel identically decayed EMA in slot13 uses K2 and feeds only staleShift (and hence attractShift). K=0, K2=0, WAD arithmetic; sqrt floors at WAD scale. Initialize slot13=0. All other NP2 equations unchanged. Sweep common K=K2 over [0,.5,1,1.5,2,3], choose highest mean gain, then sweep K2 holding K. Also sweep K with K2=0 and retune K2 (details in tuning.extra). Freeze maximum tuning mean; one confirmation on 2730000..2731999.", "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_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 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 toxRaw = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n uint256 e = trade.timestamp > lastTs ? trade.timestamp - lastTs : 0;\n if (e > ELAPSED_CAP) e = ELAPSED_CAP;\n uint256 noiseUnit = wmul(sigmaHat, sqrt((1 + e) * WAD * WAD));\n uint256 noise = wmul(NOISE_K, noiseUnit);\n uint256 tox = toxRaw > noise ? toxRaw - noise : 0;\n uint256 shiftNoise = wmul(SHIFT_K, noiseUnit);\n uint256 shiftTox = toxRaw > shiftNoise ? toxRaw - shiftNoise : 0;\n if (shiftTox > TOX_CAP) shiftTox = TOX_CAP;\n uint256 shiftEma = slots[13];\n if (e > 0) shiftEma = wmul(shiftEma, _powWad(TOX_DECAY, e));\n uint256 shiftSignal = wmul(shiftEma, TOX_BLEND_DECAY) + wmul(shiftTox, WAD - TOX_BLEND_DECAY);\n slots[13] = shiftSignal;\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, shiftSignal);\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 function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n", "sha256": "1f9618fb24eab50640f06c8b05dace2c4a8d6be38069c2d66cd45f4b83d91d49", "tuning": { "seeds": [ 10000, 10255 ], "n_per_point": 256, "conclusion": "Every tested nonzero configuration lost paired edge. K=K2=0 selected; this is NP2-equivalent behavior, not an improvement.", "rows": [ { "K": 0, "K2": 0, "n": 256, "mean_diff": 0.0, "se": 0.0, "worst": 0.0 }, { "K": 0.5, "K2": 0.5, "n": 256, "mean_diff": -23.152555641899383, "se": 0.2128104218770382, "worst": -33.661496376462196 }, { "K": 1, "K2": 1, "n": 256, "mean_diff": -46.731823100094786, "se": 0.4408231329234186, "worst": -68.41336420142886 }, { "K": 1.5, "K2": 1.5, "n": 256, "mean_diff": -60.64005317406616, "se": 0.5872184235917686, "worst": -87.22501564175082 }, { "K": 2, "K2": 2, "n": 256, "mean_diff": -72.6353713030553, "se": 0.7378561603290069, "worst": -106.87440740501711 }, { "K": 3, "K2": 3, "n": 256, "mean_diff": -90.05088069640358, "se": 0.9634277212934407, "worst": -133.90498061853816 }, { "K": 0, "K2": 0.5, "n": 256, "mean_diff": -21.776717119049753, "se": 0.20889338727145765, "worst": -31.633792213480888 }, { "K": 0, "K2": 1, "n": 256, "mean_diff": -42.87659894365248, "se": 0.41662329855598557, "worst": -63.27710029647653 }, { "K": 0, "K2": 1.5, "n": 256, "mean_diff": -55.20403040722965, "se": 0.5493125590236579, "worst": -79.2407949125087 }, { "K": 0, "K2": 2, "n": 256, "mean_diff": -65.34934674170186, "se": 0.6776879993502748, "worst": -96.06291762640001 }, { "K": 0, "K2": 3, "n": 256, "mean_diff": -79.86894117569942, "se": 0.8603043353085059, "worst": -118.91933611979255 }, { "K": 0.5, "K2": 0, "n": 256, "mean_diff": -0.23973271148915698, "se": 0.028965168298712474, "worst": -1.7797805091599912 }, { "K": 1, "K2": 0, "n": 256, "mean_diff": -0.5427968070991698, "se": 0.03901396014471429, "worst": -3.1550507767044564 }, { "K": 1.5, "K2": 0, "n": 256, "mean_diff": -0.8127360651323141, "se": 0.04572437171991998, "worst": -3.2096220117755365 }, { "K": 2, "K2": 0, "n": 256, "mean_diff": -1.0412353798723404, "se": 0.05110852116746417, "worst": -3.6482471791341595 }, { "K": 3, "K2": 0, "n": 256, "mean_diff": -1.4664515954483106, "se": 0.057419086131577826, "worst": -4.275387750709115 } ], "selected": { "K": 0, "K2": 0, "n": 256, "mean_diff": 0.0, "se": 0.0, "worst": 0.0 }, "extra": "After common-K and K2-only sweeps, isolate fMid shrinkage at K2=0 across the same K grid; then sweep K2 holding its best K. Every distinct point uses only the same 256 tuning seeds. Existing points reused without rerunning." }, "paired": { "n": 2000, "mean_diff": 0.0, "se": 0.0, "worst": 0.0 }, "split": { "arb": null, "retail": null, "note": "Not measured: pinned batch result exposes total edges and actor volumes, not edge attribution by print type. No actor split inferred from volumes." }, "fee_stats": { "bid": 0.0036287416709905266, "ask": 0.003530334486833933, "NP2_bid": 0.0036287416709905266, "NP2_ask": 0.003530334486833933, "unit": "fraction, not bps", "aggregation": "Mean of per-seed average_fees[submission], each simulator average is over 10000 end-of-step fee quotes; 2000 confirmation seeds." }, "blocked": null, "next": "Retain NP2. Every tested nonzero noise-shrink configuration lost edge on tuning; the frozen K=K2=0 mechanism is disabled. A future experiment could condition shrinkage on observable print classification; use new tuning and fresh confirmation seeds. This confirmation block is spent.", "methodology": { "simulator_commit": "6b6921f8d463314aa7c96234e1be25a25245f704", "seed_draws": "For each s, numpy.random.default_rng(s): size=uniform(19,21), rate=uniform(.6,1), sigma=uniform(.000882,.001008), in that order. build_config(seed=s,gbm_sigma=sigma,retail_arrival_rate=rate,retail_mean_size=size); canonical other fields from pinned config.py. Price RNG seed=s; retail seed=s+1.", "toxicity_consumers": "K feeds the original toxSignal uses in fMid and DIR_TOX skew. K2 feeds only staleShift and its derived attractShift; other directional and trade-boost equations are unchanged.", "comparison": "Candidate and NP2 run separately as submission vs compiled VanillaStrategy.sol; amm_sim_rs.run_batch batches of 20 (final tuning batch 16), n_workers=8. Never candidate vs NP2. Differences paired by seed. se=np.std(d,ddof=1)/sqrt(n); worst=min(d), individual-seed edge difference. Confirmation block run once after freeze; no subsequent selection.", "confirmation_seeds": [ 2730000, 2731999 ], "candidate_mean_edge": 520.2333372175427, "NP2_mean_edge": 520.2333372175427, "CH_calibration": { "seeds": [ 0, 999 ], "n": 1000, "mean_edge": 525.5258821780834, "required": 525.525882178, "passed": true }, "reconstruction": "Take TWO code at first API source. Insert the NP code substring starting // Interior retail routing and ending immediately before uint256 tradeRatio = before TWO\u2019s uint256 tradeRatio =. SHA256 verified against full reconstructed text." }, "checks": { "zero_equivalence_seeds": [ 10900, 10919 ], "zero_edges_identical": true, "stress_variant": { "K": 3, "K2": 3 }, "calls": 3000, "initialization_gas": 192150, "max_swap_gas": 102585, "gas_limit": 250000, "all_success": true, "selected_strategy": { "zero_equivalence_seeds": [ 10900, 10919 ], "zero_edges_identical": true, "stress_variant": { "K": 0, "K2": 0, "n": 256, "mean_diff": 0.0, "se": 0.0, "worst": 0.0 }, "calls": 3000, "initialization_gas": 192150, "max_swap_gas": 142448, "gas_limit": 250000, "all_success": true }, "selected_cli_validation": "Strategy no_cubic validated successfully", "confirmation_edges_identical": true }, "limitations": [ "No leaderboard submission or claimed board rank.", "Actor split not measured.", "All reported scores and gas checks were computed locally; no missing measurements were fabricated." ] }