Kristijan Kozic

Certified Recovery of Magnetic Linking Numbers from Finite Noisy Measurements: Deterministic Error Bounds and Elliptic-Loop Examples

This work develops a deterministic framework for recovering the integer linking number of two closed curves from a finite number of imperfect magnetic-field measurements. Building on the relationship between the Biot–Savart law, Ampère’s law, and the topological linking number, t...

Can We Know the Whole from Within? The Embedded Observer Problem and the Limits of Global-State Identification

We study global-state identification by an observer embedded within a system and restricted to finite-budget, geometrically connected observations. The central question is whether information that is collectively sufficient to identify a global state can necessarily be integrated...

Geometrically Constrained Rank Profiles: Exact Adaptive Bayes Risk, Computational Hardness, and Lattice Optimization

This work studies finite-budget observation problems in which only geometrically admissible coordinates of a linear constraint field may be inspected. For a uniform finite-field null hypothesis versus a uniform linear-subspace alternative, the information available from a fixed s...

Rigorous Rearrangement Tensor Renormalization in Four Dimensions

We present an exact, truncation-free real-space tensor renormalization construction in four dimensions for normalized eight-leg Hilbert–Schmidt tensors in a neighborhood of the trivial fixed-point tensor. The construction combines a Type-0 gauge step, a 2^4 preliminary blocking t...

Variance Suppression by a Numerical Wave Cap in Ultralight-Dark-Matter Strong-Lensing Simulations: Exact-Commit Audit of a JWST Survey-IV-Derived Forward Model, with Realization and Selection Diagnostics

Strong-lensing inference with ultralight dark matter (ULDM) can depend on stochastic wave-field realizations and numerical controls used to make those realizations computationally tractable. This work performs an exact-commit audit of the public pyHalo/samana/lenstronomy software...

Rigorous Rearrangement Tensor Renormalization in Four Dimensions

We construct a truncation-free real-space tensor renormalization-group transformation in four dimensions for countable-leg tensors of finite Hilbert-Schmidt norm in a neighborhood of the trivial high-temperature tensor. The construction follows the rigorous two-dimensional progra...

Explicit Hilbert-Schmidt Control of the Four-Dimensional Wilson SU(2) Armillary Tensor

We study the exact reduced armillary tensor representation of four-dimensionalWilson SU(2) lattice gauge theory in the strong-coupling regime and derive anexplicit Hilbert-Schmidt majorant for the normalized site tensor. Two logicallyindependent sufficient-condition results are p...

When Strong Hα Profile Preferences Fail: A Cohort-Level Robustness Audit in Little Red Dots

We present a cohort-level robustness audit of broad Hα profile inference in a predefined sample of 31 spectroscopically confirmed RUBIES Little Red Dots. The analysis tests optimizer and parameter-bound dependence, symmetric nuisance-absorber specification, candidate-set dependen...