Executive Abstract
The Foundations of Numerical Governance establishes a
regime-aware framework for interpreting and governing iterative
computation under finite-precision constraints.
This volume demonstrates that under macroeconomic stress, derivatives
markets do not merely exhibit price volatility — their computational
topology compresses.
By formalizing:
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The distinction between latent and observed stability
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The Stability Signal for local topology classification
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Finite-precision regime taxonomy
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The Path Stress Index
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Expiry dilution and boundary discipline
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The Numerical Stability Index (NSI)
we define a structured architecture for measuring and managing
computational integrity across financial systems.
This work reframes iterative computation as a geometric process
operating under hardware constraints. Numerical governance is presented
not as an algorithmic enhancement, but as an infrastructural necessity.
Theoretical Foundation
The theoretical foundations for this framework originate in the paper
Regime-Aware Interpretation of Fixed-Point Stability Under Finite Precision
(Megbope, 2026), which formalizes the distinction between latent
stability and observed iteration behavior under floating-point
arithmetic. The present volume extends that diagnostic framework into
financial computation and topology-aware execution.
DOI: https://doi.org/10.5281/zenodo.19406259 ↗
Part I — The Geometry of Failure
(Micro-Level Diagnostics)
1.0 Latent vs. Observed Stability
Standard risk metrics describe price phenomena — volatility levels, return
distributions, and exposure sensitivities. They rarely account for the
computational substrate upon which those metrics depend.
When curvature concentrates and slope collapses, iterative solvers operate
near the limits of finite-precision arithmetic. This introduces
regime-dependent instability that may not be visible in price behavior
alone.
We refer to this hidden structural integrity as
latent stability.
2.0 The Topology of Regime Compression
As maturities approach zero, curvature concentrates and slope collapses.
In finite precision, these asymptotics manifest as measurable regime
compression.
The surface does not simply move; it reorganizes.
Structural Compression Differential
$$ \Delta S_c =
\lim_{T \to 0} \left( \int K(\sigma) \cdot \nabla C \, d\sigma \right) -
\varepsilon_{\text{finite}} $$
Where $K(\sigma)$ denotes curvature interaction and
$\varepsilon_{\text{finite}}$ represents truncation error introduced by
double-precision arithmetic.
This structural differential defines computational compression.
Part II — Surface Aggregation
(Macro-Structural Diagnostics)
- Regime Inversion Under Shock
- Benchmarking Surface Integrity (NSI)
- The 0DTE Fragility Report
- Measurement Discipline and Expiry Dilution
Part III — Topology-Aware Execution
(The Principles of Governance)
- Governance vs Heuristic Damping
- The Structural Compression Tracker
- Greek Chatter & Trajectory Turbulence
- Toward Numerical Governance as Infrastructure