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Hub now lists Julia, Octave, Fortran, R, Solidity, Haskell, Prolog, Zig. Per sub-spec placement: - Prolog: M3b (logic-based behavioral rules), M3f (consensus logic) - Haskell: M3a, M3b, M3c, M3e, M3f (type-safe pure math) - Zig: M3d, M3g (memory-safe performance, replaces C++) - Octave: filled in where missing (M3b, M3d, M3f, M3g)
77 lines
4.3 KiB
Markdown
77 lines
4.3 KiB
Markdown
# M3c — AMM & liquidity pool sims
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## 1. Component
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Automated Market Maker simulation: models **constant-product invariant mechanics, impermanent
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loss, and the non-cooperative game between liquidity providers and arbitrageurs**. Pops here are
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**LP positions and arbitrage bots** operating on the $x \cdot y = k$ curve. Grounded in the DEX/AMM
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literature [1,2].
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## 2. Status / certainty
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DESIGN-FIRST · ABSENT. Mathematical foundations C5 (constant product invariant is proven);
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impermanent loss formula C5 (closed-form: $\text{IL}(r) = \frac{2\sqrt{r}}{1+r} - 1$);
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simulation parameterization C1.
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## 3. Language & location
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TBD · `src/economy/sims/amm/`. Needs precise fixed-point or arbitrary-precision arithmetic for
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invariant calculations. Solidity for on-chain-equivalent precision; Julia, Octave, or
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Haskell for analytical models.
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## 4. Does / does-not
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- **Does:** simulate constant-product pools with fee parameter $\gamma$:
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$(x + \gamma \Delta x)(y - \Delta y) = k$; model impermanent loss as a function of price ratio
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shift $r$; simulate LP strategies (provide, withdraw, rebalance) against arbitrageur behavior;
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model non-linear price slippage from the curve geometry; produce bounded predictions on pool
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profitability, IL risk, and optimal LP ranges.
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- **Does-not:** model consensus mechanics (M3f); model social behavior (M3b); execute real swaps
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(Marketplace does).
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## 5. Interface contract
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- Implements `query(PredictionQuery) -> BoundedPrediction` per M3 hub.
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- **Output bounds:** IL ranges and pool return intervals.
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Example: `{ value: -0.034, lower_bound: -0.058, upper_bound: -0.012, confidence: 9.00,
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time_horizon: "7d", sim_type: "amm_liquidity" }` — projected impermanent loss for ETH/USDC pool.
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Example: `{ value: 0.082, lower_bound: 0.041, upper_bound: 0.127, confidence: 8.50,
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time_horizon: "30d", sim_type: "amm_liquidity" }` — net LP return (fees − IL).
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- **Time-horizon mapping** (all run concurrently, tick-advanced, 90:1 (1s wall = 90s sim)):
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| Horizon | Primary models | Update cadence |
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|---------|---------------|----------------|
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| Tick–hourly | Slippage curves, invariant state, JIT liquidity | Every swap event |
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| Daily | IL accumulation, fee income, LP profitability | Hourly roll |
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| Weekly | Optimal LP range recalculation, pool composition | Daily roll |
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| Monthly | LP strategy evolution (passive vs. active rebalance) | Weekly roll |
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| Annual | Pool lifecycle, fee tier competitiveness | Monthly roll |
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| 5-year | AMM design evolution, concentrated liquidity adoption | Quarterly roll |
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- **Prediction types:** `impermanent_loss`, `pool_return`, `optimal_range`, `slippage_estimate`,
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`lp_withdrawal_threshold`.
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- Calibration: ingests `dex_pool_state` and `price_tick` from M2.
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## 6. Dependencies & stubs
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- M2 Data Feeds — pool state and price data; *stub:* canned pool snapshots.
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- M3 Sims hub — lifecycle management; *stub:* manual init.
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## 7. Invariants / laws
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- **L1 (C5):** the **constant product invariant** $x \cdot y = k$ (adjusted for fees $\gamma$)
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is the ground truth — all pool state transitions must satisfy the invariant or the sim is wrong.
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- **L2 (C5):** **impermanent loss** follows the proven formula
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$\text{IL}(r) = \frac{2\sqrt{r}}{1+r} - 1$ — the sim must reproduce this exactly for the
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base case (no fees, no concentrated liquidity).
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- **L3 (C4):** LP withdrawal thresholds are **derived from IL, not hardcoded** — the sim
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calculates at what price ratio a rational LP withdraws, based on the IL formula and fee income.
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## 8. Build steps
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1. Implement the constant-product pool simulator with fee parameter.
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2. Verify IL formula reproduction against known inputs.
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3. Add LP pop strategies (passive hold, active rebalance, just-in-time liquidity).
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4. Add arbitrageur pops (sandwich, backrun).
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5. Wire M2 pool state data → calibration.
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## 9. Tests
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Invariant: every swap satisfies $(x + \gamma \Delta x)(y - \Delta y) = k$. IL formula: matches
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closed-form for known price ratios. Slippage: large swaps produce greater slippage than small.
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LP threshold: LP withdraws when IL exceeds fee income. Bounds: all outputs bounded.
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## 10. Open items
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- Concentrated liquidity (Uniswap v3 style) — extends the base model significantly.
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- Multi-pool routing (split swaps across pools).
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- Which specific pools to simulate (ETH/USDC? stablecoin pairs?).
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