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>

core/docs/plans/M3a-statistical-sims.md

@@ -2,32 +2,64 @@
 
 ## 1. Component
 Pure statistical simulation: **Monte Carlo methods, Bayesian inference, time-series forecasting,
-and volatility modeling**. The mathematical backbone — no game theory, no sociology, just the
-numbers. Operates across multiple time scales (tick to weekly). Pops in this sim represent
+stochastic volatility, regime detection, and cross-asset correlation**. The mathematical backbone
+— no game theory, no sociology, just the numbers. Operates across **six concurrent time horizons**
+(tick → hourly → daily → weekly → monthly → annual → 5-year). Pops in this sim represent
 **stochastic sample paths**, not behavioral agents.
 
 ## 2. Status / certainty
-DESIGN-FIRST · ABSENT. Mathematical foundations C4 (standard quant methods); parameterization C1.
+DESIGN-FIRST · ABSENT. Core quant methods C5 (GBM, GARCH, ARIMA — textbook). Heston stochastic
+volatility C5 (closed-form characteristic function; industry standard since 1993). Rough
+volatility C4 (Gatheral et al. 2018, heavily cited; crypto implementations exist). HMM regime
+detection C4 (established; crypto-specific copula hybrids emerging 2023–2024). Almgren-Chriss
+execution C5 (industry standard since 2001). Jump-diffusion C5 (Merton 1976). Parameterization
+for crypto markets C1.
 
 ## 3. Language & location
 TBD · `src/economy/sims/statistical/`. Python (NumPy/SciPy), Julia, or R for numerical
-computing. Needs efficient matrix operations and distribution sampling.
+computing. Needs efficient matrix operations, SDE solvers, and distribution sampling. Fractional
+Brownian motion generation requires specialized libraries (e.g. `fbm` in Python, or spectral
+methods).
 
 ## 4. Does / does-not
-- **Does:** run Monte Carlo price simulations (geometric Brownian motion, jump-diffusion);
-  Bayesian parameter estimation from live data (M2); time-series forecasting (ARIMA, GARCH for
-  volatility clustering); Value-at-Risk and Expected Shortfall calculations; produce bounded
-  predictions with confidence intervals as upper/lower bounds.
+- **Does:** run Monte Carlo price simulations (GBM, Merton jump-diffusion, Heston stochastic
+  volatility); model volatility surface via **Heston SDE**:
+  $dS_t = \mu S_t dt + \sqrt{\nu_t} S_t dW_t^S$,
+  $d\nu_t = \kappa(\theta - \nu_t)dt + \xi\sqrt{\nu_t} dW_t^\nu$
+  with $\text{corr}(dW^S, dW^\nu) = \rho$ (mean-reversion speed $\kappa$, long-run variance
+  $\theta$, vol-of-vol $\xi$); model **rough volatility** via fractional Brownian motion
+  $dS_t = \mu dt + \sigma_t dB_t^H$ with Hurst exponent $H \approx 0.4$ capturing
+  antipersistent microstructure (Gatheral et al. 2018); detect **regime transitions** via
+  Hidden Markov Model: $r_t | s_t \sim \mathcal{N}(\mu_{s_t}, \sigma^2_{s_t})$,
+  $s_t \in \{\text{Bull, Neutral, Bear}\}$ with Viterbi filter updating in <5ms per tick;
+  model **cross-asset tail dependence** via DCC-GARCH copula hybrid:
+  $dQ_t/dt = a \cdot (\bar{S} - Q_t) + b \cdot (\varepsilon_t \varepsilon_t^T - Q_t)$
+  with $t$-Copula for fat-tailed spillovers (BTC→alts); Bayesian parameter estimation from
+  live data (M2); time-series forecasting (ARIMA, GARCH for volatility clustering); Value-at-Risk
+  and Expected Shortfall; produce bounded predictions with confidence intervals.
 - **Does-not:** model human behavior (M3b does); model protocol mechanics (M3c–M3f do);
-  trade or recommend (Traders do).
+  trade or recommend (Traders do); optimize execution routing (M3g does using our vol estimates).
 
 ## 5. Interface contract
 - Implements `query(PredictionQuery) -> BoundedPrediction` per M3 hub.
-- **Output bounds:** statistical confidence intervals.
-  Example: `{ value: 1847.30, lower_bound: 1790.15, upper_bound: 1905.60, confidence: 0.95,
+- **Output bounds:** statistical confidence intervals (CI from Monte Carlo), Heston variance
+  bands (from $\nu_t$ process), rough-vol forecast cones, regime-conditional intervals.
+- **Time-horizon mapping** (all run concurrently):
+  | Horizon | Primary models | Update cadence |
+  |---------|---------------|----------------|
+  | Tick–hourly | Rough vol ($H \approx 0.4$), HMM regime filter, realized variance | Every tick |
+  | Daily | Heston vol surface, GARCH, DCC correlation | Every bar close |
+  | Weekly–monthly | Jump-diffusion Monte Carlo, regime-conditional forecasts | Hourly roll |
+  | Annual–5yr | SDE mean-reversion long-run $\theta$, macro regime priors | Daily roll |
+- Examples:
+  `{ value: 1847.30, lower_bound: 1790.15, upper_bound: 1905.60, confidence: 0.95,
   time_horizon: "24h", sim_type: "statistical" }` — 95% CI on ETH price.
-- **Prediction types:** `price_forecast`, `volatility_estimate`, `var_calculation`,
-  `correlation_matrix`, `regime_detection`.
+  `{ value: 0.72, lower_bound: 0.58, upper_bound: 0.89, confidence: 0.90,
+  time_horizon: "1h", sim_type: "statistical" }` — Heston instantaneous vol $\sqrt{\nu_t}$.
+  `{ value: "bear", lower_bound: null, upper_bound: null, confidence: 0.83,
+  time_horizon: "current", sim_type: "statistical" }` — HMM regime state.
+- **Prediction types:** `price_forecast`, `volatility_surface`, `var_calculation`,
+  `correlation_matrix`, `regime_state`, `rough_vol_estimate`, `jump_intensity`.
 - Calibration: ingests `price_tick` and `dex_pool_state` from M2 Data Feeds.
 
 ## 6. Dependencies & stubs
@@ -35,25 +67,42 @@ computing. Needs efficient matrix operations and distribution sampling.
 - M3 Sims hub — lifecycle management; *stub:* manual init.
 
 ## 7. Invariants / laws
-- **L1 (C4):** bounds are **statistical confidence intervals** — derived from the model's
+- **L1 (C5):** bounds are **statistical confidence intervals** — derived from the model's
   distribution, not hand-picked. The confidence level (e.g. 0.95) is explicit in the output.
-- **L2 (C4):** **multiple time scales run concurrently** — a tick-level volatility estimate and a
-  weekly price forecast coexist; neither blocks the other.
-- **L3 (C3):** model parameters are **re-estimated on each calibration** from live data — no
-  stale parameters carried across regime changes.
+- **L2 (C5):** **six time horizons run concurrently** — tick-level rough vol, hourly regime
+  detection, daily Heston surface, weekly Monte Carlo, annual mean-reversion, and 5-year macro
+  forecasts coexist; none blocks the others.
+- **L3 (C4):** model parameters are **re-estimated on each calibration** from live data — no
+  stale parameters carried across regime changes. Regime transitions trigger immediate
+  re-estimation of conditional parameters.
+- **L4 (C4):** the **Heston correlation $\rho$ between price and vol** is a fitted parameter,
+  never assumed — crypto assets exhibit leverage effects different from equities.
+- **L5 (C4):** rough volatility Hurst exponent $H$ is **estimated from realized variance**, not
+  fixed — $H$ varies across assets and regimes (Gatheral et al. 2018).
 
 ## 8. Build steps
 1. Implement geometric Brownian motion Monte Carlo (simplest price sim).
 2. Add GARCH volatility estimation.
-3. Wire M2 price data → Bayesian parameter re-estimation.
-4. Implement the `BoundedPrediction` output with CIs.
+3. Implement Heston SDE solver (Euler-Maruyama with full truncation for $\nu_t \geq 0$).
+4. Add Merton jump-diffusion (Poisson jumps + GBM).
+5. Implement rough volatility via fractional BM with rolling Hurst estimator.
+6. Implement HMM regime detector (3-state Viterbi filter).
+7. Add DCC-GARCH copula for cross-asset correlation.
+8. Wire M2 price data → Bayesian parameter re-estimation.
+9. Implement multi-horizon `BoundedPrediction` output with CIs.
 
 ## 9. Tests
 Monte Carlo: N sample paths produce a distribution with correct mean/variance. CI: 95% interval
 contains true value ≥ 95% of the time on historical backtest. GARCH: volatility clusters detected
-in synthetic data. Calibration: new data shifts parameter estimates.
+in synthetic data. Heston: implied vol smile reproduced for known parameters. Rough vol: Hurst
+exponent recovered from synthetic fBM paths. HMM: regime transitions detected within 15–60s on
+synthetic regime-switching data. Copula: tail dependence captured (BTC crash → alt crash
+correlation spike). Jump-diffusion: fat tails reproduced. Calibration: new data shifts parameter
+estimates. Multi-horizon: all six horizons produce concurrent outputs.
 
 ## 10. Open items
-- Which distributions beyond GBM (heavy-tailed? Lévy?).
-- Regime-switching model complexity (hidden Markov? threshold?).
-- Computational budget (how many Monte Carlo paths per tick?).
+- Heston calibration method (characteristic function inversion? particle filter?).
+- Rough vol computational cost (fBM generation is O(N²) naively; FFT methods needed).
+- HMM state count (3 sufficient? 4+ for crypto with "mania" regime?).
+- Which copula family for tail dependence ($t$-copula? Clayton? Joe?).
+- Computational budget per horizon (GPU for Monte Carlo paths?).