This article studies one-parameter degenerations of chains of nilpotent Jordan blocks joined along their socle vectors. It gives a complete Smith-normal-form description of the associated self-extension torsion for arbitrary chain length and all nonnegative edge valuations. The result includes an explicit path-matching formula, a sharp finite reduction in the block-size parameters, a classification of the Jordan types created by zero-valued couplings, and an equality between the number of positive Smith factors and the codimension of the corresponding nilpotent-orbit degeneration. The article also identifies the precise size gaps that cause failure of the full type-A interval profile, derives exact torsion-length deficit formulas, and packages the profile through Fitting ideals and transverse-slice dimensions. Exact verification scripts and machine-readable summaries accompany the paper. Research methodology and AI assistance:This work was developed using the CARMA-Math research workflow, a cumulative AI-assisted mathematical research methodology using persistent research archives, literature and prior-art investigation, iterative proof exploration, and verification procedures. Generative AI (ChatGPT) was used extensively for mathematical exploration, proof development, computational reasoning, literature research, and manuscript preparation.
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This article studies one-parameter degenerations of chains of nilpotent Jordan blocks joined along their socle vectors. It gives a complete Smith-normal-form description of the associated self-extension torsion for arbitrary chain length and all nonnegative edge valuations. The result includes an explicit path-matching formula, a sharp finite reduction in the block-size parameters, a classification of the Jordan types created by zero-valued couplings, and an equality between the number of positive Smith factors and the codimension of the corresponding nilpotent-orbit degeneration. The article also identifies the precise size gaps that cause failure of the full type-A interval profile, derives exact torsion-length deficit formulas, and packages the profile through Fitting ideals and transverse-slice dimensions. Exact verification scripts and machine-readable summaries accompany the paper. Research methodology and AI assistance:This work was developed using the CARMA-Math research workflow, a cumulative AI-assisted mathematical research methodology using persistent research archives, literature and prior-art investigation, iterative proof exploration, and verification procedures. Generative AI (ChatGPT) was used extensively for mathematical exploration, proof development, computational reasoning, literature research, and manuscript preparation.
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations