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Enrich M3 sim sub-specs with 11 discovered frameworks and 360:1 minimum speed
- M3 hub: add L3 invariant (360:1 minimum sim speed), six-horizon time table - M3a: add Heston stochastic vol, rough volatility (fBM), HMM regime detection, DCC-GARCH copula, jump-diffusion; six-horizon mapping - M3b: add Hegselmann-Krause bounded confidence, complex contagion, bandit- replicator hybrid, MFG (HJB+FP), pump-and-dump 3-type ABM; six-horizon mapping - M3c: add six-horizon time table - M3d: add Kolokoltsov adversarial (non-linear FP + WENO), DSMFG bilevel optimization, cross-chain adversarial arbitrage; six-horizon mapping - M3e: add kinked lending rate model, DeXposure inter-protocol credit network, composable yield optimizer; six-horizon mapping - M3f: add MFG for validator populations, six-horizon time table - M3g: add Almgren-Chriss optimal execution, six-horizon mapping - CLAUDE.md: add subagent productivity note Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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@@ -9,7 +9,8 @@ theorems [10], and Monash dynamic PBFT modeling [11].
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## 2. Status / certainty
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DESIGN-FIRST · ABSENT. Evolutionary PoS game theory C4 (Cornell [8]); staking pool Nash
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equilibrium proofs C4 (ACM [10]); Markov chain throughput models C4 (Monash [11]);
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equilibrium proofs C4 (ACM [10]); Markov chain throughput models C4 (Monash [11]); MFG for
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validator populations C4 (Lasry & Lions 2007; validator-specific application C3);
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simulation parameterization C1.
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## 3. Language & location
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@@ -21,8 +22,12 @@ computation. Python, Julia, or R.
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under bounded rationality [8]; model staking pool delegation as a game with proven reward-
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parameter thresholds enforcing subgame-perfect Nash equilibria favoring honest validation over
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malicious slashing [10]; simulate **throughput stability under shifting validator states** via
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Markov chains [11]; predict slashing risk, validator set stability, and staking yield; produce
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bounded predictions on consensus health and staking returns.
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Markov chains [11]; solve **Mean-Field Game equilibria for large validator populations** —
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coupled HJB (individual validator optimization) + Fokker-Planck (population density):
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$-\partial_t u + H(x, \nabla u) = F(x, m)$, $\partial_t m - \nabla \cdot (m \nabla_p H) = 0$
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— captures emergent staking coordination without enumerating every validator; predict slashing
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risk, validator set stability, and staking yield across **six concurrent time horizons** at
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≥ 360:1 speed; produce bounded predictions on consensus health and staking returns.
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- **Does-not:** validate blocks (this is a simulator); model AMM pools (M3c); model token supply
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(M3e — but consumes staking ratio from M3e as input).
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@@ -34,8 +39,18 @@ computation. Python, Julia, or R.
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equilibrium.
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Example: `{ value: 4.2, lower_bound: 3.6, upper_bound: 5.1, confidence: 0.82,
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time_horizon: "30d", sim_type: "consensus_staking" }` — annualized staking yield (%).
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- **Time-horizon mapping** (all run concurrently, ≥ 360:1 speed):
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| Horizon | Primary models | Update cadence |
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|---------|---------------|----------------|
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| Hourly | Markov chain validator state transitions | Every epoch |
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| Daily | Replicator dynamics strategy shifts, slashing events | Hourly roll |
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| Weekly | Staking pool Nash equilibrium recalculation | Daily roll |
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| Monthly | MFG equilibrium for validator population | Weekly roll |
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| Annual | Evolutionary stable strategies, yield trajectory | Monthly roll |
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| 5-year | Consensus mechanism structural evolution | Quarterly roll |
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- **Prediction types:** `validator_honesty_fraction`, `slashing_probability`, `staking_yield`,
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`pool_delegation_equilibrium`, `throughput_stability`, `consensus_liveness`.
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`pool_delegation_equilibrium`, `throughput_stability`, `consensus_liveness`,
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`mfg_validator_equilibrium`.
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- Calibration: ingests `on_chain_event` (validator set changes, slashing events) from M2.
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## 6. Dependencies & stubs
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@@ -56,8 +71,9 @@ computation. Python, Julia, or R.
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1. Implement the evolutionary honesty game (replicator dynamics, bounded rationality).
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2. Implement the Markov chain validator-state model.
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3. Reproduce the staking pool Nash equilibrium reward threshold from [10].
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4. Wire M2 validator data → calibration of transition rates.
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5. Wire M3e staking ratio input.
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4. Implement MFG solver (HJB + Fokker-Planck) for large validator populations.
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5. Wire M2 validator data → calibration of transition rates.
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6. Wire M3e staking ratio input.
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## 9. Tests
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Equilibrium: honesty fraction converges to Nash equilibrium under stable payoffs. Markov:
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