Research Briefs formalize structural extensions of the Numerical Governance framework. Unlike the Structural Compression Tracker, they are not cadence-driven. Each brief is a complete, self-contained study.
Cross-sectional topology of the S&P 100
This brief introduces a spatial extension of the Numerical Stability Index. While the Structural Compression Tracker measures topology through time, the Regime Atlas maps curvature concentration across index constituents within the 15–45 DTE lens. The analysis reveals sector-level clustering of oscillatory and divergent regimes and establishes cross-sectional topology as a complementary dimension of numerical governance.
Topology-aware calibration under curvature constraints
This research brief extends the Numerical Governance framework into volatility surface construction. Standard calibration routines treat all implied volatility observations as geometrically equivalent. We demonstrate that regime-aware weighting preserves structural coherence by incorporating local topology into surface fitting. The result is not cosmetic smoothing, but curvature-disciplined calibration aligned with measured stability regimes.
Each brief includes:
Research Briefs do not provide trading signals or tactical recommendations.
They formalize structural extensions of numerical governance.