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98a6f9a0b1
The initial M-series specs were wrong (text digestion pipeline). Replaced
with the actual economy organ architecture:
M0 hub (independent system, scoped autonomy, multi-layered braking)
M1 Marketplace (multi-trader harness, deterministic law script, veto)
M2 Data Feeds (RSS + live market, bridges Marketplace ↔ Sims)
M3 Sims hub + 7 sub-specs (always-running, bounded predictions):
M3a statistical, M3b sociological, M3c AMM/liquidity,
M3d MEV/adversarial, M3e tokenomics/macro, M3f consensus/staking,
M3g market microstructure
M4 Wallets (sovereign custody, our keys only, 1:1 trader binding)
M5 Traders (AI actors, wallet-bound, all tool calls monitored)
M6 Conductor (supervisory AI, veto, pause/investigate, SAE intake)
M7 SAE monitor (trader surveillance, Brain-compatible message format)
Grounded in AMM invariant mechanics, MEV game theory, SDE tokenomics,
and evolutionary consensus games. Tax stub for Verschwörern Veregeister.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
67 lines
3.6 KiB
Markdown
67 lines
3.6 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-equivalent precision). Python, Rust, or Julia.
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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: 0.90,
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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: 0.85,
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time_horizon: "30d", sim_type: "amm_liquidity" }` — net LP return (fees − IL).
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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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