Full Technical Analysis & Specific-Run Math Audit

3-2-1 Refining Crack Spread Formula (Issue #169):

$$\text{Crack}_{321} (\$/\text{bbl}) = \frac{2 \times (P_{\text{RBOB}} \times 42) + 1 \times (P_{\text{HO}} \times 42) - 3 \times P_{\text{WTI}}}{3}$$

Models refiner yield switching between gasoline and distillate heating oil.

Stacking Ensemble Quantile Bands (Issue #170):

$$P_{10} = P_{50} - 1.2815\sigma, \quad P_{90} = P_{50} + 1.2815\sigma$$

Computes 80% probabilistic confidence intervals using RidgeCV meta-learner variance.

Dynamic Volatility-Gated Persistence Blending (Issue #214):

$$\lambda_{\text{vol}} = \frac{1}{1 + e^{-200.0 \cdot (\sigma_{14\text{d}} - 0.015)}}, \quad \hat{y}_{t+5} = \lambda_{\text{vol}} \hat{y}_{\text{model}} + (1 - \lambda_{\text{vol}}) y_t$$

Blends model forecasts into naive persistence during low-volatility plateaus while preserving 100% shock reactivity.

Empirical Residual 95% Confidence Intervals (Issue #214):

$$\text{CI}_{95\%} = \hat{y}_{t+5} \pm 1.96 \cdot \sigma_{\text{residual, 30d}}(r)$$

Derives dynamic 95% confidence bands from rolling 30-day regional residual standard errors.

USGS 3D Hypocentral Attenuation & Ground Shaking (Issue #55):

$$R = \sqrt{d^2 + h^2}, \quad w(R) = \frac{1}{1 + (R/35)^2}, \quad I = 10^{M - M_{\text{base}}} \times w(R)$$

Quantifies facility-level peak ground shaking and pipeline shutoff risk indices across 5 corridors.

USGS Hydrological Barge Bottleneck Index (Issue #56):

$$\text{Index}_{\text{barge}} = \max\left(0, \min\left(1, \frac{\text{Gage}_{\text{threshold}} - \text{Gage}_t}{\text{Gage}_{\text{threshold}} - \text{Gage}_{\text{min}}}\right)\right)$$

Tracks low-water navigation draft restrictions at Memphis & Cairo confluence throttling barge throughput.

Multi-Feed AQI Standardized Flaring Outage Z-Score (Issue #54):

$$Z_{\text{PM2.5}} = \frac{\text{PM2.5}_t - \mu_{30\text{d}}}{\sigma_{30\text{d}}}, \quad Z_{\text{SO2}} = \frac{\text{SO2}_t - \mu_{30\text{d}}}{\sigma_{30\text{d}}}$$

Detects emergency refinery flaring when $Z_{\text{PM2.5}} \ge 3.5 \land Z_{\text{SO2}} \ge 2.5$ with 12-24h lead time over news.

EPA Ozone & Statutory Seasonal RVP Compliance Surcharge (Issue #73):

$$\text{Surcharge}_{\text{RVP}} = \Delta \text{Spread}_{\text{Summer Blend}} + 0.040 \cdot \mathbf{1}_{\text{AQI}_{\text{O3}} \ge 101}$$

Applies statutory summer-blend RVP constraints (CARB 7.0 psi, EPA 7.8 psi, Conventional 9.0 psi) and Ozone Action Day fees.

U.S. Census Commuter Inelastic Demand Score (Issue #75):

$$\text{Score}_{\text{inelastic}} = \frac{\text{DriveAlone} + \text{Carpool}}{\text{TotalCommuters}} \times (1 - \text{TransitIndex})$$

Calibrates retail pump price pass-through speed and baseline rack spreads from ACS commuting tables.

Treasury 10Y-2Y Term Spread & Momentum Delta (Issue #66):

$$\text{Spread}_{10\text{Y}-2\text{Y}} = Y_{10\text{Y}} - Y_{2\text{Y}}, \quad \Delta \text{Spread}_{5\text{d}} = \text{Spread}_t - \text{Spread}_{t-5}$$

Captures leading macroeconomic expansion/recession demand signals and real TIPS inventory carry costs.

Qlib Symbolic Alpha Information Coefficient (Issue #127):

$$IC_t = \text{Corr}(f_t, r_{t+h}), \quad IC_{IR} = \frac{\mu(IC)}{\sigma(IC)}$$

Evaluates AST-parsed symbolic alpha factor formulas with non-lookahead point-in-time calculation rules.

Multi-Horizon Scoreboard Performance Accuracy (Issue #209):

$$\text{MAE}_H = \frac{1}{N_H} \sum_{i=1}^{N_H} |\hat{y}_{i, H} - y_{i, H}|, \quad H \in [1\text{d}, 2\text{d}, 3\text{d}, 4\text{d}, 5\text{d}]$$

Tracks continuous rolling out-of-time accuracy breakdowns across all discrete forecast horizons.