{"blocked":null,"tail":[{"seed":945583,"avg_bid":42.39321008035246,"avg_ask":28.85098173104725,"edge":496.75003361684116,"config":{"size":20.24564635583981,"rate":0.7619173175435221,"sigma":0.0009382826959683682}},{"seed":946660,"avg_bid":32.49915446588705,"avg_ask":44.026084024723474,"edge":633.4244619544643,"config":{"size":19.328387252620097,"rate":0.9977928867684076,"sigma":0.0009211792062370964}},{"seed":945619,"avg_bid":46.67515359764596,"avg_ask":36.114857834452856,"edge":761.6405082988537,"config":{"size":20.391637533320537,"rate":0.9911760111629645,"sigma":0.0009380947606087904}},{"seed":945594,"avg_bid":40.68863939152418,"avg_ask":30.208688564034794,"edge":472.8742851527793,"config":{"size":19.309131145710168,"rate":0.6896802843873979,"sigma":0.0009789728868064616}},{"seed":946037,"avg_bid":44.80278189752961,"avg_ask":34.83796701274146,"edge":600.3393726875196,"config":{"size":19.162650043481666,"rate":0.9408646110299543,"sigma":0.000960968094614223}},{"seed":946481,"avg_bid":43.27724451749635,"avg_ask":33.319052674475316,"edge":616.4301913860584,"config":{"size":19.971282027635155,"rate":0.9688951796626614,"sigma":0.0010013185672088864}},{"seed":945249,"avg_bid":39.23615385443991,"avg_ask":29.413048486831794,"edge":415.3589370746895,"config":{"size":19.925046878209027,"rate":0.7353198854616695,"sigma":0.0009250502520273959}},{"seed":946416,"avg_bid":42.93113523651179,"avg_ask":33.27841680470983,"edge":590.845932032076,"config":{"size":20.01785369483253,"rate":0.7142445324713247,"sigma":0.0009442701408972911}},{"seed":946990,"avg_bid":43.4704387947941,"avg_ask":33.83254076794013,"edge":604.3904552922371,"config":{"size":20.098655207643823,"rate":0.9076909708699047,"sigma":0.0009173298789286094}},{"seed":945166,"avg_bid":33.25546595557571,"avg_ask":42.78813336073677,"edge":630.5020536525687,"config":{"size":19.58631530194836,"rate":0.9412518176198889,"sigma":0.0009795846366871352}},{"seed":945792,"avg_bid":29.898116434446603,"avg_ask":39.41835755764108,"edge":424.1352713601017,"config":{"size":19.30595645344255,"rate":0.6417459341857581,"sigma":0.0009349873297877491}},{"seed":945637,"avg_bid":41.35983208131586,"avg_ask":31.93200396619385,"edge":521.1983356704776,"config":{"size":20.02902849747323,"rate":0.7781813910868748,"sigma":0.0009491218836477237}},{"seed":946918,"avg_bid":43.11457122575062,"avg_ask":33.7246051730914,"edge":608.1298315703315,"config":{"size":19.989805463116983,"rate":0.9342379226191835,"sigma":0.0009035044926054713}},{"seed":945604,"avg_bid":43.18329070845182,"avg_ask":33.83898985545847,"edge":689.8797969224526,"config":{"size":20.31411205391087,"rate":0.9414221113627378,"sigma":0.0009599891418635138}},{"seed":945126,"avg_bid":43.78272517687596,"avg_ask":34.47573418774999,"edge":636.2427720228831,"config":{"size":20.85362183814947,"rate":0.9564654221614315,"sigma":0.0009205641377696049}},{"seed":946936,"avg_bid":39.389340540735894,"avg_ask":30.184012316434096,"edge":455.26041389962296,"config":{"size":19.423831084370136,"rate":0.6883013680228569,"sigma":0.0009189109468170228}},{"seed":946639,"avg_bid":43.263237429868916,"avg_ask":34.103342550555745,"edge":697.5128668573327,"config":{"size":20.216551113345382,"rate":0.8848815453387444,"sigma":0.0009336073502417328}},{"seed":946802,"avg_bid":41.43194037455354,"avg_ask":32.43218370769532,"edge":503.5228271848141,"config":{"size":20.188174315370997,"rate":0.7775919950134274,"sigma":0.0009233126884914751}},{"seed":945109,"avg_bid":41.517415592311174,"avg_ask":32.55011748763134,"edge":543.3742958667502,"config":{"size":20.96989773959012,"rate":0.7802030587134352,"sigma":0.0009403523469558889}},{"seed":945628,"avg_bid":41.77282837567999,"avg_ask":32.836460902901514,"edge":559.035003605536,"config":{"size":20.862179791703166,"rate":0.7355404904335318,"sigma":0.0010023567320739046}}],"finding":{"fee_unit":"basis points; step average over 10,000 steps","top20_mean_abs_lean_bps":9.846838646954248,"all2000_mean_abs_lean_bps":2.757316632466507,"positive_lean_count":17,"same_sign_in_both_halves":20,"same_sign_in_all_four_quarters":17,"retail_rate_top20_mean":0.8383702367957838,"retail_rate_scan_mean":0.7973991298737482,"sigma_top20_mean":0.0009445879085119173,"sigma_scan_mean":0.0009445248925498939,"size_top20_mean":20.009488189585703,"size_scan_mean":19.994131496606904,"fair_price_final_up_count":12,"fee_lean_fair_return_sign_matches":11,"fee_lean_vs_mean_spot_fair_gap_correlation":0.9959774665335165,"fee_lean_vs_mean_spot_fair_gap_mean_abs_difference_bps":0.5277346457935114,"fee_lean_spot_fair_gap_sign_matches":20,"mean_edge_top20":573.0423823054196,"mean_edge_scan":524.4849892405938,"interpretation":"The persistent fee split tracks a persistent pool spot-versus-fair-price offset, while the fair-price path has mixed final directions. These runs did not record pHat or fastHat, so a stuck estimate cannot be established directly. The observed gap is consistent with a quote response to pool mispricing, so reducing that split can remove protective quoting. This last explanation is an inference, tested by the governor runs below."},"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[3] = WAD; \n        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n        slots[15] = 400000000000000000 | (uint256(2000000000000000) << 160); slots[13] = 902500000000; slots[14] = slots[5]; \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 = uint64(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            // Process variance is propagated inside the censored update.\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        // S: infer a no-trade interval center from the last post-trade spot.\n        uint256 silenceScale = WAD;\n        if (firstInStep && silent > 1) {\n            uint256 g = silent - 1;\n            if (g > 1) g = 1;\n            uint256 w = WAD - _powWad(800000000000000000, g);\n            uint256 s = slots[2] >> 64;\n            if (s == 0) s = pHat;\n            uint256 c = (wmul(s, WAD - prevBidFee) + wdiv(s, WAD - prevAskFee)) / 2;\n            if (c >= pHat) pHat += wmul(w, c - pHat);\n            else pHat -= wmul(w, pHat - c);\n            silenceScale = WAD - wmul(300000000000000000, w);\n        }\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[12] = pImplied >= pHat ? 1 : 2; }\n            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n            alpha = wmul(alpha, silenceScale);\n            adaptiveGate = wmul(adaptiveGate, silenceScale);\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        // Censored assumed-density posterior. No external or future inputs.\n        uint256 arbProbability;\n        (fastHat, uncertainty, arbProbability) = _posterior(PosteriorInput(\n            fastHat, uncertainty, pImplied, spot, slots[2] >> 64,\n            prevBidFee, prevAskFee, firstInStep, silent, trade.isBuy,\n            trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0\n        ));\n        slots[13] = uncertainty;\n        slots[14] = fastHat;\n        uint256 leanEma = slots[16];\n        if (leanEma == 0) leanEma = WAD;\n        bool nearFast = absDiff(spot, fastHat) < wmul(spot, 500000000000000);\n        if (nearFast && leanEma > WAD + 500000000000000 && fastHat > pHat) {\n            pHat = _blend(pHat, fastHat, 300000000000000000);\n        } else if (nearFast && leanEma + 500000000000000 < WAD && fastHat < pHat) {\n            pHat = _blend(pHat, fastHat, 300000000000000000);\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 originalLambda = lambdaHat; uint256 originalSize = sizeHat;\n\n        if (342406799193418304 > 0) {\n            uint256 packedFlow = slots[15];\n            uint256 rate = uint80(packedFlow);\n            uint256 count = uint80(packedFlow >> 80);\n            uint256 meanSize = uint80(packedFlow >> 160);\n            if (rate == 0) rate = 400000000000000000;\n            if (meanSize == 0) meanSize = 2000000000000000;\n            if (isNewStep) {\n                uint256 inst = count / silent;\n                if (inst > 3 * WAD) inst = 3 * WAD;\n                uint256 retention = _powWad(999000000000000000, silent > 64 ? 64 : silent);\n                rate = wmul(rate, retention) + wmul(inst, WAD-retention);\n                count = 0;\n            }\n            uint256 weight = firstInStep ? WAD-arbProbability : WAD;\n            uint256 correctedWeight = weight;\n            if (2 == 2) {\n                uint256 missing = wmul(feeUsed, 196030880396139429888);\n                if (missing > 333333333333333376) missing = 333333333333333376;\n                correctedWeight = wdiv(weight, WAD-missing);\n            }\n            count += correctedWeight;\n            uint256 learning = wmul(WAD-999000000000000000, weight);\n            meanSize = _blend(meanSize, tradeRatio, learning);\n            slots[15]=rate | (count << 80) | (meanSize << 160);\n            uint256 retailRate = wmul(rate, 366383424913407168);\n            uint256 retailSize = 2 == 0 ? sizeHat : wmul(meanSize,1883296158119298304);\n            lambdaHat = _blend(lambdaHat,retailRate,342406799193418304);\n            sizeHat = _blend(sizeHat,retailSize,342406799193418304);\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        lambdaHat = originalLambda; sizeHat = originalSize;\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 (!firstInStep && tradeBoost > 16 * BPS) tradeBoost = 16 * BPS;\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        if (firstInStep) {\n            if (askFee > bidFee && bidFee > 30 * BPS) bidFee = 30 * BPS;\n            else if (bidFee > askFee && askFee > 30 * BPS) askFee = 30 * BPS;\n        }\n\n        if (bidFee > askFee && askFee > 36 * BPS) askFee = 36 * BPS;\n        else if (askFee > bidFee && bidFee > 36 * BPS) bidFee = 36 * BPS;\n\n        uint256 previousLean = leanEma == 0 ? WAD : leanEma;\n        slots[16] = _blend(previousLean, WAD + bidFee - askFee, 1000000000000000);\n        slots[0] = bidFee; slots[1] = askFee; slots[2] = (spot << 64) | 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\n    struct PosteriorInput {\n        uint256 mu; uint256 v; uint256 obs; uint256 spot; uint256 preSpot;\n        uint256 bid; uint256 ask; bool first; uint256 silent; bool buy; uint256 size;\n    }\n    function _posterior(PosteriorInput memory x) internal pure returns (uint256, uint256, uint256) {\n        if (x.mu == 0) x.mu = x.spot;\n        if (x.v < 10000000000) x.v = 10000000000;\n        uint256 lo = wmul(x.preSpot, WAD-x.bid);\n        uint256 hi = wdiv(x.preSpot, WAD-x.ask);\n        if (x.first) {\n            if (x.silent>1 && x.preSpot>0) {\n                uint256 elapsed=x.silent>8?8:x.silent;\n                x.v += 902500000000*(elapsed-1);\n                (x.mu,x.v)=_band(x.mu,x.v,lo,hi);\n            }\n            x.v+=902500000000;\n        }\n        uint256 mRetail = x.mu;\n        uint256 vRetail = x.v;\n        // A missing own-pool trade is a censored price observation.\n        if (x.first && x.preSpot > 0) {\n            (mRetail, vRetail) = _band(x.mu, x.v, lo, hi);\n        }\n        if (!x.first) {\n            // A later print is retail. Only an interior route is an observation\n            // of the other pool, with explicit observation uncertainty.\n            uint256 fee = x.buy ? x.bid : x.ask;\n            if (fee > 30 * BPS) {\n                uint256 normal = x.buy ? wdiv(wmul(x.spot, WAD-fee), WAD-30*BPS)\n                    : wdiv(wmul(x.spot, WAD-30*BPS), WAD-fee);\n                uint256 residual = wdiv(absDiff(normal, x.mu),x.mu);\n                uint256 noise = 9000000000000 + wmul(residual,residual);\n                uint256 k = wdiv(x.v,x.v+noise);\n                return (_blend(x.mu,normal,k),wmul(x.v,WAD-k),0);\n            }\n            return (x.mu,x.v,0);\n        }\n        uint256 e = wdiv(absDiff(x.obs,x.mu),x.mu);\n        uint256 totalV = x.v + 22500000000;\n        uint256 z = wdiv(wmul(e,e),totalV);\n        uint256 density = _powWad(wdiv(WAD,WAD+z/8),4);\n        uint256 odds = wmul(density,wdiv(4000000000000000,_isqrt(totalV*WAD)));\n        if (x.size > 3000000000000000) odds = wmul(odds,4*WAD/10);\n        if (x.silent > 1) odds = wmul(odds,8*WAD/10);\n        uint256 sd = _isqrt(x.v*WAD);\n        uint256 width = wdiv(hi-lo,x.mu);\n        uint256 distance = x.mu<lo?lo-x.mu:(x.mu>hi?x.mu-hi:0);\n        uint256 zBand = wdiv(wdiv(distance,x.mu),sd);\n        uint256 mass = wmul(wdiv(width,width+2*sd),wdiv(WAD,WAD+wmul(zBand,zBand)));\n        if (mass < WAD/100) mass = WAD/100;\n        odds = wdiv(odds,mass);\n        uint256 prob = wdiv(odds,WAD+odds);\n        uint256 kArb = wdiv(x.v,totalV);\n        uint256 mArb = _blend(x.mu,x.obs,kArb);\n        uint256 mean = _blend(mRetail,mArb,prob);\n        uint256 between = wdiv(absDiff(mArb,mRetail),x.mu);\n        uint256 variance = wmul(prob,wmul(x.v,WAD-kArb)) + wmul(WAD-prob,vRetail)\n            + wmul(wmul(prob,WAD-prob),wmul(between,between));\n        if (variance > 100000000000000) variance = 100000000000000;\n        return (mean,variance,prob);\n    }\n    function _blend(uint256 a,uint256 b,uint256 w) internal pure returns(uint256) {\n        return b>=a ? a+wmul(b-a,w) : a-wmul(a-b,w);\n    }\n    function _band(uint256 mu,uint256 v,uint256 lo,uint256 hi) internal pure returns(uint256,uint256) {\n        // Soft interval likelihood avoids discontinuities at quadrature nodes.\n        uint256 sd=wmul(mu,_isqrt(v*WAD));\n        uint256[3] memory acc;\n        for(uint256 j=0;j<7;j++) {\n            uint256 p=j<3 ? (mu>(3-j)*sd?mu-(3-j)*sd:1) : mu+(j-3)*sd;\n            uint256 w=j==3?72:(j==2||j==4?45:(j==1||j==5?10:1));\n            uint256 distance=p<lo?lo-p:(p>hi?p-hi:0);\n            uint256 z=sd>0?wdiv(distance,sd):0;\n            uint256 likelihood=wdiv(WAD,WAD+4*wmul(z,z));\n            w=wmul(w*WAD,likelihood);\n            acc[0]+=w;acc[1]+=wmul(w,p);\n            uint256 d=wdiv(absDiff(p,mu),mu);\n            acc[2]+=wmul(w,wmul(d,d));\n        }\n        uint256 m=wdiv(acc[1],acc[0]);\n        uint256 d=wdiv(absDiff(m,mu),mu);\n        uint256 second=wdiv(acc[2],acc[0]);\n        return(m,second>wmul(d,d)?second-wmul(d,d):10000000000);\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    // Floor square root: bit-length seed and seven Newton steps (all uint256).\n    function _isqrt(uint256 x) internal pure returns (uint256 r) {\n        if (x == 0) return 0;\n        unchecked {\n            uint256 y = x;\n            r = 1;\n            if (y >> 128 != 0) { y >>= 128; r <<= 64; }\n            if (y >> 64 != 0) { y >>= 64; r <<= 32; }\n            if (y >> 32 != 0) { y >>= 32; r <<= 16; }\n            if (y >> 16 != 0) { y >>= 16; r <<= 8; }\n            if (y >> 8 != 0) { y >>= 8; r <<= 4; }\n            if (y >> 4 != 0) { y >>= 4; r <<= 2; }\n            if (y >> 2 != 0) { r <<= 1; }\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            r = (r + x / r) >> 1;\n            uint256 t = x / r;\n            return r < t ? r : t;\n        }\n    }\n\n    function getName() external pure override returns (string memory) { return \"censored_10\"; }\n}\n","sha256":"06e440a366489e1296dbc2ff8b42a22c9043e2fa078a6b216f7442ecc22440ca","params":{"id":"j2","family":"lag_only_pull","alpha":0.001,"L_bps":5,"r":0.3,"near_fast_bps":5},"params_exact":{"alpha_wad":1000000000000000,"L_wad":500000000000000,"r_wad":300000000000000000,"near_fast_wad":500000000000000},"mechanism":"Slot 16 stores a WAD-centered EMA of bid-minus-ask fee, initialized to WAD before the first print and updated once per afterSwap print with alpha. When its magnitude exceeds L_bps, blend pHat toward fastHat by r only if fastHat moves pHat in the lean-correcting direction and abs(spot-fastHat) is less than near_fast_bps of spot.","screen":[{"id":"j1","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":5,"r":0.3,"near_fast_bps":3},"vs_rs2":{"n":256,"mean_diff":-0.00024341293004126463,"se":0.007764082265900538,"worst":[{"seed":947035,"d":-0.3457013637573709},{"seed":947103,"d":-0.32746877717511325},{"seed":947238,"d":-0.32674684065420934},{"seed":947162,"d":-0.31712623376438387},{"seed":947234,"d":-0.2910487041582428}]},"tail20_mean_diff":0.00799683414193737,"max_swap_gas":225906,"oog":0},{"id":"j2","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":5,"r":0.3,"near_fast_bps":5},"vs_rs2":{"n":256,"mean_diff":0.005064897874317076,"se":0.009285735371589911,"worst":[{"seed":947030,"d":-0.49529364222507866},{"seed":947032,"d":-0.3843290001962032},{"seed":947234,"d":-0.3446211450703913},{"seed":947143,"d":-0.3438898867336775},{"seed":947114,"d":-0.3394062696082756}]},"tail20_mean_diff":0.01208746795180673,"max_swap_gas":225888,"oog":0},{"id":"j3","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":8,"r":0.3,"near_fast_bps":5},"vs_rs2":{"n":256,"mean_diff":0.009163615857135765,"se":0.006678079300249908,"worst":[{"seed":947143,"d":-0.330722073027232},{"seed":947114,"d":-0.30672890608229864},{"seed":947234,"d":-0.26850724226801503},{"seed":947014,"d":-0.2664960279677189},{"seed":947082,"d":-0.20594169248988692}]},"tail20_mean_diff":-0.008537005891824379,"max_swap_gas":225906,"oog":0},{"id":"j4","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":8,"r":0.3,"near_fast_bps":10},"vs_rs2":{"n":256,"mean_diff":-0.000593303376015264,"se":0.007306143298991314,"worst":[{"seed":947212,"d":-0.30014311518891645},{"seed":947059,"d":-0.2775081371436272},{"seed":947234,"d":-0.27515592383963394},{"seed":947169,"d":-0.25749643445101356},{"seed":947123,"d":-0.25602651255087494}]},"tail20_mean_diff":-0.02691149283070331,"max_swap_gas":225900,"oog":0},{"id":"j5","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":5,"r":0.6,"near_fast_bps":3},"vs_rs2":{"n":256,"mean_diff":0.002325826304309997,"se":0.009973782318902008,"worst":[{"seed":947087,"d":-0.5399652150863403},{"seed":947212,"d":-0.48162114090609975},{"seed":947163,"d":-0.3679176926037826},{"seed":947123,"d":-0.35414983791213217},{"seed":947093,"d":-0.29904953640004805}]},"tail20_mean_diff":0.01294313724133076,"max_swap_gas":225906,"oog":0},{"id":"j6","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":8,"r":0.3,"near_fast_bps":3},"vs_rs2":{"n":256,"mean_diff":0.0034837006669465875,"se":0.005797522219230901,"worst":[{"seed":947102,"d":-0.2539121312016732},{"seed":947234,"d":-0.25271951522790914},{"seed":947014,"d":-0.24897961993190165},{"seed":947114,"d":-0.24336294753925358},{"seed":947168,"d":-0.20734560417224657}]},"tail20_mean_diff":-0.007155447073651544,"max_swap_gas":225906,"oog":0}],"recheck":[{"id":"j3","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":8,"r":0.3,"near_fast_bps":5},"vs_rs2":{"n":256,"mean_diff":0.00946135405180093,"se":0.006633649844862757,"worst":[{"seed":948119,"d":-0.649993062366832},{"seed":948126,"d":-0.3229374185452798},{"seed":948029,"d":-0.2810517535593817},{"seed":948208,"d":-0.21001773284774572},{"seed":948188,"d":-0.190282506356084}]}},{"id":"j2","params":{"family":"lag_only_pull","alpha":0.001,"L_bps":5,"r":0.3,"near_fast_bps":5},"vs_rs2":{"n":256,"mean_diff":0.014121991254743893,"se":0.00891258759820923,"worst":[{"seed":948119,"d":-0.6232860081484546},{"seed":948029,"d":-0.4964404134719871},{"seed":948076,"d":-0.3979902878155599},{"seed":948126,"d":-0.3749109338418748},{"seed":948164,"d":-0.3623295347479143}]}}],"held_out":{"vs_rs2":{"n":512,"mean_diff":0.010712281250115807,"se":0.005927620017292112,"worst":[{"seed":949312,"d":-0.5694856441441516},{"seed":949504,"d":-0.46204562766428126},{"seed":949091,"d":-0.42699423915985335},{"seed":949068,"d":-0.40399510101190117},{"seed":949013,"d":-0.3852572688732607}]},"retail_edge_delta":{"mean_diff":0.013451958676175324,"se":0.005849669569584211},"arb_edge_delta":{"mean_diff":-0.0027396774260580875,"se":0.002316812848603645}},"tail20_mean_diff":0.01208746795180673,"gas":{"max_ok":225888,"init_max_ok":243093,"oog":0,"rs2_heldout":{"max_ok":202387,"init_max_ok":243099,"oog":0}},"notes":["Calibration: CH on seeds 0..999 had mean edge 525.5258821780834, exactly matching the specified check.","Scan seeds 945000..946999; screen 947000..947255; recheck 948000..948255; frozen held-out 949000..949511. Each strategy ran alone against VanillaStrategy with 8 workers; price seed is seed and retail seed is seed+1.","Paired deltas are candidate minus RS2. Tail20 was selected by absolute RS2 step-average bid-minus-ask fee on the scan block.","EMA alpha is per afterSwap print, not per simulation step. Gas covers the frozen arm in screen, tail, recheck, and held-out runs.","Preliminary governor probes read an empty EMA slot as zero on the first print; they were discarded. All six reported screen settings initialize the EMA to the neutral WAD value before testing the threshold.","The two highest screen means were j3 and j2; the frozen candidate was the one with the higher paired mean on the separate recheck block.","These local edges are from the specified simulator and seed blocks; no board submission was made.","The frozen held-out mean gain is small relative to the requested top-10 goal; this item does not establish a material leaderboard improvement.","No seeds >=5000000 were used for this item."]}