Uniform Inference and Certified Capacity at a Reflexive Stability Boundary

Battle Count: 74

Highly relevant for quantitative trading desks managing cross-impact risk and capacity deployment. The paper provides a rigorous framework for when to deploy, reduce, or abstain from capacity based on estimated market stability boundaries. The three-way classifier (SUB/SUP/UNR) with certified capacity bounds directly informs trading decisions. The treatment of nonregular spectral behavior near eigenvalue collisions addresses a real practical concern in multi-asset portfolio execution. However, the paper is primarily theoretical/methodological and requires significant implementation effort for production use.

Very high complexity. Requires: (1) joint IV estimation with HAC covariance for dependent data, (2) spectral perturbation theory understanding, (3) verified interval arithmetic and branch-and-bound algorithms, (4) Routh-Hurwitz stability certificates, (5) outward-rounded floating-point computation, (6) chi-square tail evaluation with directed rounding, (7) interval Cholesky factorization, (8) eigenvalue cluster isolation. The two-dimensional case is tractable but higher dimensions require fundamentally different approaches. The paper explicitly notes that an ordinary eigendecomposition is not a verified substitute.

The paper provides extremely detailed pre-specified simulation designs (60 cells, 1000 replications each), explicit calibration parameters, full algorithm descriptions (Algorithm 1), assumption-to-design correspondence tables, completion checks, seed collision disclosures, and replication protocols in Appendix F. The two-dimensional implementation is fully specified with Routh-Hurwitz certificates. However, no code repository is explicitly linked, and the higher-dimensional extension is not implemented. The observed-risk stress uses specific equity and bond panels with stated selection rules.