\documentclass[12pt,oneside,openany]{book} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath,amssymb,amsthm,mathtools,mathrsfs} \DeclareFontFamily{U}{rsfs}{\skewchar\font127 } \DeclareFontShape{U}{rsfs}{m}{n}{<-6.5>rsfs5<6.5-7.5>rsfs7<7.5->rsfs10}{} \usepackage{booktabs,array} \usepackage[numbers,sort&compress]{natbib} \usepackage{imakeidx}% \usepackage{environ} \PassOptionsToPackage{hypertexnames=false}{hyperref} \input{shared/trilogy-style}% \usepackage{xurl}% \usepackage[nameinlink,capitalize,noabbrev]{cleveref} \usepackage{aliascnt} \hypersetup{pdftitle={Dynamics of the spherical Sherrington--Kirkpatrick model},pdfauthor={P. M. 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We have taken care to supervise this writing to ensure that the proofs meet a minimum standard of readability and that previous literature is appropriately cited. However, the resulting document remains lacking in exposition and overall coherence. We are nonetheless releasing this manuscript on Hexagon to disseminate the result as quickly as possible, because we believe it may be of interest to the mathematics and physics communities. We welcome suggestions concerning mathematical corrections, omitted citations, and attribution of ideas. For publication, the manuscript is divided into two volumes: \emph{Part I: Foundations and tools} (Sections~1--12) and \emph{Part II: Mixing profiles and critical dynamics} (Sections~13--21). Section, theorem, equation, and citation numbers are shared across the volumes, and each volume includes the complete bibliography. P.L.\ was partially supported by NSF grant DMS-2450004. \end{authorsnote} \begin{abstractpage} \input{abstract} \end{abstractpage} \tableofcontents \mainmatter \setcounter{chapter}{12} \setcounter{part}{2} \part{High temperature}\label{part:hot} \input{sections/13-hot-fixed} \input{sections/14-hot-meso} \input{sections/15-infinite} \part{Low temperature}\label{part:cold} \input{sections/16-cold-fixed} \input{sections/17-cold-meso} \part{The critical window}\label{part:critical} \input{sections/18-crit-process} \input{sections/19-crit-profile} \input{sections/20-outer-hot} \input{sections/21-outer-cold} \backmatter \setlength{\bibsep}{3pt plus 1pt minus 1pt} \input{references} \end{document}