Machine Proofs for Adams Differentials and Extension Problems among CW Spectra

<p>Update notes: In this version, we reduce the number of spectra in this project from 210 to 49 (compared to the cw210 version), while keeping the outcome sufficient to prove <a href="https://arxiv.org/abs/2412.10879">the Last Kervaire Invariant Problem</a>. The size of the proof file <a href="https://zenodo.org/api/records/14875532/draft/files/proofs.db.rar/content" target="_blank" rel="noopener noreferrer">proofs.db.rar</a> is also reduced from 600MB to 44MB, leading to easier track for proofs.</p> <p>In this Zenodo repository we upload the computations of Adams differentials and extensions among many CW spectra and their proofs. This data will be used in the <a href="https://arxiv.org/abs/2412.10879">proof of the Last Kervaire Invariant Problem</a> by Weinan Lin, Guozhen Wang and Zhouli Xu.</p> <p>In <strong>programs.rar</strong>, we have two programs ./Adams and ./ss provided for both windows users and mac users and a definition file <strong>Adams.json</strong> for spectra involved in this project.&nbsp;The source code for the two programs is contained in <strong>source code.zip</strong>. You can also find the source code on Github <a href="https://github.com/WayneLin92/SSeqCpp">https://github.com/WayneLin92/SSeqCpp</a> together with user manual for the programs.</p> <p>In <strong>programs.rar</strong> there is also a demo for ./ss which is a category of five spectra: S0, C2, Ceta, Cnu, Csigma.</p> <p><strong>kervaire_database.rar</strong> contains all the Adams spectral sequence data and extension data. They are sqlite3 database files and can be read directly by the ./ss program. We also provide the same data in csv format in <strong>kervaire_csv.rar</strong>.</p> <p>The two zip files<strong> proofs.db.rar</strong> and <strong>proofs_csv.rar</strong> are proofs of all the differentials. Inside <strong>proofs_csv.rar</strong> there are 3 csv files. We break it to 3 csv files because Microsoft Excel has a limit of 1,000,000 rows.</p> <p>On the website <a href="https://waynelin92.github.io/ss/kervaire-49.html">https://waynelin92.github.io/ss/kervaire-49.html</a> you can find plots of the data. The website source code (html/javascript) is actually contained in&nbsp;<strong>programs.rar</strong>/webpages in this repository.</p> <p>Please read <strong>instructions.pdf</strong> for more infomation.</p>