I. From Time to Space
The Structural Compression Tracker measures change through time.
Each week, the Numerical Stability Index (NSI) quantifies the compression or expansion of the active volatility surface within the standardized 15–45 DTE lens. It answers the temporal question:
Is the market’s computational topology tightening or relaxing?
But structural compression is not only temporal. It is also spatial.
At any given moment, curvature concentration is not distributed uniformly across the market. Some names reside in wide monotonic basins. Others occupy oscillatory corridors or approach singular boundaries.
The Regime Atlas shifts the perspective from time to cross‑section.
II. The Cartography of Topology
The Atlas maps each constituent within the S&P 100 according to its measured computational regime.
For each symbol, within the 15–45 DTE lens, we compute:
- Regime distribution (Stable, Oscillatory, Divergent, Singular)
- Mean Path Stress
- Local NSI contribution
The result is not a ranking.
It is a map.
Figure 20. Cross-sectional topology of the S&P 100 under the 15–45 DTE lens (March 16, 2020) - Block size reflects approximate market capitalization. Color reflects Numerical Stability Index (NSI).
This visualization does not identify “winners” or “losers.” It reveals clusters of geometric concentration.
III. Structural Clustering
Cross‑sectional topology frequently exhibits clustering.
Certain sectors — particularly those with concentrated short‑dated trading activity — may exhibit elevated Oscillatory or Divergent density. Others may remain structurally stable even during broader macro compression.
These clusters reflect curvature geometry, not necessarily price momentum.
A sector can appreciate in price while simultaneously migrating into an Oscillatory regime due to volatility skew distortion. Conversely, a defensive sector may remain geometrically stable despite modest price declines.
The Atlas therefore separates:
- Economic movement
from - Computational structure.
IV. Reading the Atlas
Interpretation requires restraint.
A high concentration of Divergent regimes within a subset of names does not imply imminent price decline. It indicates that implied volatility inversion within those names requires elevated curvature navigation.
Similarly, a surface dominated by Stable regimes does not imply complacency. It indicates wide monotonic basins under current topology.
The Atlas measures:
- Where curvature concentrates,
- Where slope collapses,
- Where trajectory turbulence accumulates,
- Where boundary conditions dominate.
It does not measure sentiment.
V. Spatial Compression and Systemic Risk
Temporal compression (measured by NSI) indicates that the overall active surface is tightening.
Spatial compression (revealed by the Atlas) indicates whether instability is concentrated or dispersed.
A market may exhibit:
- Low overall compression but localized instability within a single sector.
- Broad compression across multiple sectors.
- Asymptotic boundary hostility confined to ultra-short maturities.
Understanding both dimensions — time and space — is necessary for coherent numerical governance.
VI. Boundary Discipline
The Atlas applies the same measurement discipline as the NSI Benchmark:
- 15–45 DTE standardized lens
- Regime-aware classification
- Exclusion of asymptotic long-dated dilution
- Separation from 0DTE boundary conditions
Without boundary discipline, cross-sectional topology becomes blurred by expiry dilution and asymptotic Vega dominance.
The Atlas is not a full-surface average.
It is a spatial map of the active geometric terrain.
VII. From Map to Infrastructure
The Regime Atlas completes the observational layer of numerical governance.
The Structural Compression Tracker answers:
When is topology compressing?
The Regime Atlas answers:
Where is topology concentrated?
Together, they form a temporal and spatial observatory of computational structure.
Further work will examine how cross-sectional topology propagates through portfolios, margin systems, and calibration frameworks.