Business and Technology University

Structural Complexity of One-Factor Sparse Portfolio Selection Exact Algorithms, Parameterized Hardness, and Restricted Circuit Lower Bounds

We study exact-cardinality, equally weighted minimum-variance portfolio selection under a one-factor covariance model supplied in factor form. In the nonnegative homoskedastic regime, selecting the K smallest loadings is optimal. Allowing strictly positive asset-specific idiosync...

A Deterministic Polynomial-Time Approximation Below One Third for Bimatrix Games

This paper proves a strict deterministic polynomial-time approximation guarantee below the one-third frontier for general two-player rational bimatrix games with payoffs normalized to [0,1]. Its central result is an explicit universal algorithm that returns a rational approximate...

A One-Saddle 1/5 Approximation Algorithm for Common-Kernel Bimatrix Games: Recognition, Exact Segment Optimization, Sharp Selector Bounds, and Certified Robustness

This paper develops an algorithmic, structural, and certification theory for a fixed-normalization class of symmetric bimatrix games generated by a common kernel. The class arose from a broader investigation of approximation-threshold reductions for bimatrix Nash equilibria, but...

A One-Saddle 1/5 Approximation Algorithm for Common-Kernel Bimatrix Games: Recognition, Exact Segment Optimization, Sharp Selector Bounds, and Certified Robustness

This paper develops an algorithmic, structural, and certification theory for a fixed-normalization class of symmetric bimatrix games generated by a common kernel. The class arose from a broader investigation of approximation-threshold reductions for bimatrix Nash equilibria, but...

Asymmetric Optimal Mixing and Exact Payoff-Image Compression in Bimatrix Games: Approximation and Structural Consequences at the One-Third Frontier

This paper develops an algorithmic framework for restricted optimal mixing in rational bimatrix games and studies its implications for approximate Nash equilibrium computation near the one-third frontier. The first main contribution identifies a new asymmetric tractability regime...

Sharp Selector Bounds and a 1/5 Saddle Algorithm for Common-Kernel Bimatrix Games: Recognition, fixed-normalization structure, robustness, and consequences for the 1/3-threshold compiler program

This paper develops a structured algorithmic and certification theory for a class of symmetric bimatrix games generated by a common kernel. The methodology emerged from a broader research program aimed at the deterministic one-third approximation threshold for bimatrix Nash equil...

Determinacy and Word Reconstruction from Simple Paths in Class-Two Networks: Structural characterization, exact audit design, and a discrete-gauge interpretation

We develop an exact theory of selective target identification from simple directed path observations in networks whose standardized edge transports take values in groups nilpotent of class at most two. The paper distinguishes two fundamentally different information requirements:...

Critical Audit of OpenAI's Navier–Stokes Proof: Scope of the Mathematical Audit, Independent Audit and Certification Status of the Lean Formalization, and Procedural Readiness for the Millennium Prize

This study presents an independent critical audit of OpenAI's 166-page proof Finite time blowup for Navier–Stokes, its associated public Lean formalization, and the claim-level correspondence with the Clay Mathematics Institute's (CMI) C/D alternatives. The purpose of the audit i...