Uniform transition between simultaneous and sequential Jordan-block mergers under the Aluthge transform
Year: 2026
Type: preprint
Abstract: Three fixed Jordan blocks are joined by two positive weak links whose power exponents approach balance. A candidate calibrated reference approximation is given for ordinary half Aluthge iteration, uniform over every observation time above any diverging lower bound and over any shrinking exponent gap. The scaled gap d log(1/ε) selects a coupled simultaneous profile or one of two separated merger limits. At either endpoint, the first merger changes the background of the remaining link, and an exact weighted product determines its late entrance amplitude. Independent weak-entry estimates control the first merger, a duration-independent whole-cut estimate controls the interval between mergers, and full triangular stability controls the final tail. The matrix approximation uses a specified moving triangular gauge; the squared-norm consequence is unitary invariant. Block sizes and positive coefficients are fixed. No quantitative error rate is claimed. The theorem and its consequences retain candidate status; the established-status verification threshold has not been met.
Author: Barritz, Robert
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224934063