# silence-a

## delta

Added a local silence count `g = min(timestamp - lastTimestamp - 1, 4)` on the first print after a timestamp gap. For `g > 0`, reconstruct pre-trade spot, find the geometric center of the previous bid/ask fee band, and move `pHat` toward it by `w = 1 - (1 - 0.075)^g`. Scale the pHat update alpha and gate by `1 - 0.30w`. Same-timestamp later prints use `g=0`; no extra storage slot was added. The base TWO code and NP routing insertion are preserved.

## code

```solidity
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import {AMMStrategyBase} from "./AMMStrategyBase.sol";
import {TradeInfo} from "./IAMMStrategy.sol";

contract Strategy is AMMStrategyBase {
    uint256 constant SILENCE_W1 = 75000000000000000;
    uint256 constant SILENCE_CAP = 4;
    uint256 constant SILENCE_GATE_SHRINK = 300000000000000000;
    uint256 constant SILENCE_ALPHA_SHRINK = 300000000000000000;
    uint256 constant ELAPSED_CAP = 8;
    uint256 constant SIGNAL_THRESHOLD = WAD / 650;
    uint256 constant DIR_DECAY = 750000000000000000;
    uint256 constant ACT_DECAY = 530000000000000000;
    uint256 constant SIZE_DECAY = 530000000000000000;
    uint256 constant TOX_DECAY = 910000000000000000;
    uint256 constant SIGMA_DECAY = 690000000000000000;
    uint256 constant LAMBDA_DECAY = 990000000000000000;
    uint256 constant SIZE_BLEND_DECAY = 828000000000000000;
    uint256 constant TOX_BLEND_DECAY = 51000000000000000;
    uint256 constant ACT_BLEND_DECAY = 985000000000000000;
    uint256 constant PHAT_ALPHA = 270000000000000000;
    uint256 constant PHAT_ALPHA_RETAIL = 60000000000000000;
    uint256 constant PHAT_ALPHA_SAME = 120000000000000000;
    uint256 constant REVERT_U = 0;
    uint256 constant DIR_IMPACT_MULT = 4;
    uint256 constant GATE_SIGMA_MULT = 7200000000000000000;
    uint256 constant MIN_GATE = 30000000000000000;
    uint256 constant TRADE_TOX_BOOST = 3500 * BPS;
    uint256 constant STALE_ATTRACT_FRAC = 1050000000000000000;
    uint256 constant RET_CAP = WAD / 35;
    uint256 constant TOX_CAP = WAD / 5;
    uint256 constant TRADE_RATIO_CAP = WAD / 5;
    uint256 constant LAMBDA_CAP = 1820000000000000000;
    uint256 constant STEP_COUNT_CAP = 64;
    uint256 constant BASE_FEE = 4 * BPS;
    uint256 constant SIGMA_COEF = 200000000000000000;
    uint256 constant LAMBDA_COEF = 12 * BPS;
    uint256 constant FLOW_SIZE_COEF = 4842 * BPS;
    uint256 constant TOX_COEF = 300 * BPS;
    uint256 constant TOX_QUAD_COEF = 15000 * BPS;
    uint256 constant ACT_COEF = 91843 * BPS;
    uint256 constant DIR_COEF = 20 * BPS;
    uint256 constant DIR_TOX_COEF = 100 * BPS;
    uint256 constant STALE_DIR_COEF = 6850 * BPS;
    uint256 constant SIGMA_TOX_COEF = 500 * BPS;
    uint256 constant TAIL_KNEE = 600 * BPS;
    uint256 constant TAIL_SLOPE_PROTECT = 930000000000000000;
    uint256 constant TAIL_SLOPE_ATTRACT = 850000000000000000;

    function afterInitialize(uint256 initialX, uint256 initialY) external override returns (uint256, uint256) {
        slots[0] = BASE_FEE; slots[1] = BASE_FEE; slots[2] = 0; slots[3] = WAD; slots[4] = 0;
        slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;
        slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;
        slots[9] = 0; slots[10] = 0; slots[11] = 0; slots[12] = 0;
        return (BASE_FEE, BASE_FEE);
    }

    function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {
        uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = slots[2];
        uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];
        uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];
        uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10]; uint256 silenceSteps = 0;

        bool isNewStep = trade.timestamp > lastTs;
        if (isNewStep) {
            uint256 elapsedRaw = trade.timestamp - lastTs;
            silenceSteps = elapsedRaw > 1 ? elapsedRaw - 1 : 0;
            if (silenceSteps > SILENCE_CAP) silenceSteps = SILENCE_CAP;
            uint256 elapsed = elapsedRaw > ELAPSED_CAP ? ELAPSED_CAP : elapsedRaw;
            dirState = _decayCentered(dirState, DIR_DECAY, elapsed);
            actEma = wmul(actEma, _powWad(ACT_DECAY, elapsed));
            sizeHat = wmul(sizeHat, _powWad(SIZE_DECAY, elapsed));
            toxEma = wmul(toxEma, _powWad(TOX_DECAY, elapsed));
            if (stepTradeCount > 0 && elapsedRaw > 0) {
                uint256 lambdaInst = (stepTradeCount * WAD) / elapsedRaw;
                if (lambdaInst > LAMBDA_CAP) lambdaInst = LAMBDA_CAP;
                lambdaHat = wmul(lambdaHat, LAMBDA_DECAY) + wmul(lambdaInst, WAD - LAMBDA_DECAY);
            }
            stepTradeCount = 0;
        }

        bool firstInStep = stepTradeCount == 0;
        uint256 spot = trade.reserveX > 0 ? wdiv(trade.reserveY, trade.reserveX) : pHat;
        if (pHat == 0) pHat = spot;
        uint256 silenceWeight = WAD - _powWad(WAD - SILENCE_W1, silenceSteps);
        if (silenceWeight > 0) {
            uint256 spotBefore;
            if (trade.isBuy) {
                uint256 priorX = trade.reserveX - wmul(trade.amountX, WAD - prevBidFee);
                uint256 priorY = trade.reserveY + trade.amountY;
                spotBefore = priorX > 0 ? wdiv(priorY, priorX) : spot;
            } else {
                uint256 priorX = trade.reserveX + trade.amountX;
                uint256 netY = wmul(trade.amountY, WAD - prevAskFee);
                uint256 priorY = trade.reserveY > netY ? trade.reserveY - netY : 0;
                spotBefore = priorX > 0 && priorY > 0 ? wdiv(priorY, priorX) : spot;
            }
            uint256 bandScale = sqrt(wdiv(WAD - prevBidFee, WAD - prevAskFee) * WAD);
            uint256 bandCenter = wmul(spotBefore, bandScale);
            pHat = wmul(pHat, WAD - silenceWeight) + wmul(bandCenter, silenceWeight);
        }

        uint256 feeUsed = trade.isBuy ? prevBidFee : prevAskFee;
        uint256 gamma = feeUsed < WAD ? WAD - feeUsed : 0;
        uint256 pImplied;
        if (gamma == 0) { pImplied = spot; }
        else { pImplied = trade.isBuy ? wmul(spot, gamma) : wdiv(spot, gamma); }

        {
            uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;
            uint256 alpha = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;
            uint256 prePhat = pHat;
            bool secondPrint = !firstInStep && stepTradeCount == 1;
            bool sameDir = false; bool oppDir = false;
            if (secondPrint) {
                bool up2 = pImplied >= pHat;
                uint256 d1 = slots[12];
                if (d1 != 0) { sameDir = (d1 == 1) == up2; oppDir = !sameDir; }
                if (sameDir) alpha = PHAT_ALPHA_SAME;
            }
            alpha = wmul(alpha, WAD - wmul(SILENCE_ALPHA_SHRINK, silenceWeight));
            if (firstInStep) { slots[11] = pHat; slots[12] = pImplied >= pHat ? 1 : 2; }
            uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);
            if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;
            adaptiveGate = wmul(adaptiveGate, WAD - wmul(SILENCE_GATE_SHRINK, silenceWeight));
            if (ret <= adaptiveGate) { pHat = wmul(pHat, WAD - alpha) + wmul(pImplied, alpha); }
            if (oppDir && REVERT_U > 0) {
                uint256 pre = slots[11];
                if (pre > pHat) pHat = pHat + wmul(pre - pHat, REVERT_U);
                else pHat = pHat - wmul(pHat - pre, REVERT_U);
            }
            if (firstInStep) {
                if (ret > RET_CAP) ret = RET_CAP;
                sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);
            }
        }

        // Interior retail routing equalizes fee-adjusted marginal prices.
        // Subsequent trades in a step cannot be the initial arbitrage trade.
        if (!firstInStep && feeUsed > 30 * BPS && gamma > 0) {
            uint256 normalSpot = trade.isBuy
                ? wdiv(wmul(spot, gamma), WAD - 30 * BPS)
                : wdiv(wmul(spot, WAD - 30 * BPS), gamma);
            pHat = wmul(pHat, 90 * WAD / 100) + wmul(normalSpot, 10 * WAD / 100);
        }

        uint256 tradeRatio = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;
        if (tradeRatio > TRADE_RATIO_CAP) tradeRatio = TRADE_RATIO_CAP;

        if (tradeRatio > SIGNAL_THRESHOLD) {
            uint256 push = tradeRatio * DIR_IMPACT_MULT;
            if (push > WAD / 4) push = WAD / 4;
            if (trade.isBuy) {
                dirState = dirState + push;
                if (dirState > 2 * WAD) dirState = 2 * WAD;
            } else {
                dirState = dirState > push ? dirState - push : 0;
            }
            actEma = wmul(actEma, ACT_BLEND_DECAY) + wmul(tradeRatio, WAD - ACT_BLEND_DECAY);
            sizeHat = wmul(sizeHat, SIZE_BLEND_DECAY) + wmul(tradeRatio, WAD - SIZE_BLEND_DECAY);
            if (sizeHat > WAD) sizeHat = WAD;
        }

        uint256 tox = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;
        if (tox > TOX_CAP) tox = TOX_CAP;
        toxEma = wmul(toxEma, TOX_BLEND_DECAY) + wmul(tox, WAD - TOX_BLEND_DECAY);
        uint256 toxSignal = toxEma;

        stepTradeCount = stepTradeCount + 1;
        if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;

        uint256 flowSize = wmul(lambdaHat, sizeHat);
        uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);
        uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);
        fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));

        uint256 dirDev; bool sellPressure;
        if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }
        else { dirDev = WAD - dirState; sellPressure = false; }

        uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));
        uint256 bidFee; uint256 askFee;
        if (sellPressure) {
            bidFee = fMid + skew;
            askFee = fMid > skew ? fMid - skew : 0;
        } else {
            askFee = fMid + skew;
            bidFee = fMid > skew ? fMid - skew : 0;
        }

        {
            uint256 staleShift = wmul(STALE_DIR_COEF, toxSignal);
            uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);
            if (spot >= pHat) {
                bidFee = bidFee + staleShift;
                askFee = askFee > attractShift ? askFee - attractShift : 0;
            } else {
                askFee = askFee + staleShift;
                bidFee = bidFee > attractShift ? bidFee - attractShift : 0;
            }
        }

        {
            bool tradeAligned = (trade.isBuy && spot >= pHat) || (!trade.isBuy && spot < pHat);
            if (tradeAligned) {
                uint256 tradeBoost = wmul(TRADE_TOX_BOOST, tradeRatio);
                if (trade.isBuy) { bidFee = bidFee + tradeBoost; }
                else { askFee = askFee + tradeBoost; }
            }
        }

        if (sellPressure) {
            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));
            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));
        } else {
            askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));
            bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));
        }

        slots[0] = bidFee; slots[1] = askFee; slots[2] = trade.timestamp;
        slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;
        slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;
        slots[9] = toxEma; slots[10] = stepTradeCount;

        return (bidFee, askFee);
    }

    function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {
        if (fee <= TAIL_KNEE) return fee;
        return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);
    }

    function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {
        result = WAD;
        while (exp > 0) {
            if (exp & 1 == 1) result = wmul(result, factor);
            factor = wmul(factor, factor);
            exp >>= 1;
        }
    }

    function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {
        uint256 mul = _powWad(decayFactor, elapsed);
        if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }
        uint256 below = wmul(WAD - centered, mul);
        return below < WAD ? WAD - below : 0;
    }

    function getName() external pure override returns (string memory) { return "no_cubic"; }
}
```

## sha256

`22958b18bc780e722b6e13f16da6a70c9b61e54b429c8f65e0046e44fd6ce379` (SHA-256 of the exact Solidity code text above, including its final newline).

## tuning

NP2 was assembled from the [TWO artifact](https://api.imdnotdead.fun/artifacts/528a6da78583c6142644a552c86670f9d25c20e39e92f4de44deae05ddc8cecd) and the [NP interior-routing artifact](https://api.imdnotdead.fun/artifacts/da313379a2e69e9286668865e06b18dfcae25732c82b934b0fd9c2ef0d8c2ff5); its exact code-text SHA-256 is `51f1c1a9d4999ee460eb8bbc66880da8074b173399a4f5d71f96671482e18ac0`. CH's reference source was [this pinned Strategy.sol](https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol), whose code-text SHA-256 is `6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3`.

For each training point, candidate and NP2 were run in separate `amm_sim_rs.run_batch` calls against Vanilla, with the same config draws. Every call used 16 seeds. Config draws follow the pinned simulator's [`MatchRunner._build_configs`](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/match.py) order: `default_rng(seed)` draws retail size, arrival rate, then sigma. The simulator advances fair price and attempts arbitrage each step ([engine source](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/engine.rs)). `mean_diff` is the arithmetic mean of candidate `edges['submission']` minus NP2's, `se` is sample standard deviation divided by √n. All seed blocks below are within the allowed training range 10000–99999.

CH versus Vanilla on seeds 0–999 reproduced mean edge `525.525882178083` (SE `2.789426459025`), matching the stated `525.525882178` check. The 1000-value check used 16-seed calls; the last call included seeds 1000–1007 and those eight values were discarded.

Training seeds **10256–10383**:

| w1 | cap | gate shrink | alpha shrink | n | mean_diff | se |
|---:|---:|---:|---:|---:|---:|---:|
| 0.01 | 4 | 0.10 | 0.10 | 128 | 0.044272848614483884 | 0.016296675908955633 |
| 0.025 | 4 | 0.20 | 0.20 | 128 | 0.09973754636783605 | 0.029563654334776215 |
| 0.05 | 4 | 0.20 | 0.20 | 128 | 0.1423088787124498 | 0.0415378772378834 |
| 0.02 | 8 | 0.50 | 0.20 | 128 | 0.1090669089071743 | 0.029012876627922762 |
| 0.05 | 8 | 0 | 0 | 128 | 0.07720610136151684 | 0.041615155236064585 |

Training seeds **10384–10639**:

| w1 | cap | gate shrink | alpha shrink | n | mean_diff | se |
|---:|---:|---:|---:|---:|---:|---:|
| 0.05 | 4 | 0.20 | 0.20 | 256 | 0.1420548856371664 | 0.024353828758526465 |
| 0.075 | 4 | 0.20 | 0.20 | 256 | 0.16674685712095005 | 0.029599915438136053 |
| 0.10 | 4 | 0.20 | 0.20 | 256 | 0.1470226644239332 | 0.03283259567819347 |
| 0.05 | 8 | 0.20 | 0.20 | 256 | 0.13320202265890835 | 0.026352005310841732 |
| 0.05 | 4 | 0.10 | 0.10 | 256 | 0.10123071727155386 | 0.023439934285576905 |

Training seeds **10640–11151**:

| w1 | cap | gate shrink | alpha shrink | n | mean_diff | se |
|---:|---:|---:|---:|---:|---:|---:|
| 0.075 | 4 | 0.20 | 0.20 | 512 | 0.21887529503760295 | 0.03206358241952118 |
| 0.075 | 2 | 0.20 | 0.20 | 512 | 0.22240200647847874 | 0.02814935731585608 |
| 0.075 | 1 | 0.20 | 0.20 | 512 | 0.16560361843953375 | 0.01704634313242122 |
| **0.075** | **4** | **0.30** | **0.30** | **512** | **0.24912033518969812** | **0.03164081761309969** |
| 0.075 | 4 | 0 | 0 | 512 | 0.1496526875284545 | 0.031763692634894584 |

Frozen at the highest observed training mean: `w1=0.075`, cap `4`, gate shrink `0.30`, alpha shrink `0.30`. The confirmation used new seeds only.

## paired

```json
{"n":2000,"mean_diff":0.21866808751973402,"se":0.010767301406119376,"worst":-1.7520790263144477}
```

## confirm block

Seeds `2570000..2571999` (2000 seeds), once. Candidate and NP2 each ran separately against Vanilla with identical configs, in 16-seed calls.

## blocked

null

## next

Test whether gate and alpha should use separate silence curves rather than sharing `w`.