Source code for the paper "On Bruner's Open Questions: Secondary Ext of the Fiber of $\Sq^n$ via Explicit Secondary Adem Tracks"

This repository contains the Python source code and supplementary data used for the computer-aided verification in the paper: "On Bruner's Open Questions: Secondary Ext of the Fiber of $\Sq^n$ via Explicit Secondary Adem Tracks". The code provides an unconditional reproducible certificate for the low-degree Adem reduction calculations and syzygy verification presented in Appendix A of the manuscript. Key functionalities in secondary_adem_tracks.py: Implementation of the tracked Adem reduction algorithm in the Nassau pair-algebra model. Verification of the formal mod-2 boundaries for the listed secondary Adem tracks, including the explicit insertion of mu_0 cancellation terms. Calculation of the kernel of the row matrix for the mapping-fiber complexes through total degree 8. Automated resolution of the finite triangular systems for syzygy verification, confirming the existence (and non-existence for powers-of-two) of triangular syzygies. Requirements: Python 3.x Standard libraries (no external dependencies required). Usage: To run the verification routine and reproduce the results recorded in the paper, execute the following command in the terminal: python3 secondary_adem_tracks.py Interpretation of Output: The script will output the verification results for the low-degree syzygies, the kernel dimension quotient through degree 8, and the solution to the finite triangular systems. All computed values are consistent with the data displayed in the paper's appendix.