docs(docs): built docs

Note for now much of the docs is LLM written. This was done to save time and focus on code development. The docs have been LOOSLEY reviewed. However, the code itself has been either fully written by hand or fully reviewed. Therefore, the docs should at the moment be seen as a loose resource rather than authoratiative (and this is on top of the general ability for docs to drift)

docs/man/man3/controller.hpp.3

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+.TH "src/include/serif/solver/continuation/controller.hpp" 3 "Version v0.0.1a" "SERiF" \" -*- nroff -*-
+.ad l
+.nh
+.SH NAME
+src/include/serif/solver/continuation/controller.hpp
+.SH SYNOPSIS
+.br
+.PP
+\fR#include <algorithm>\fP
+.br
+\fR#include <array>\fP
+.br
+\fR#include <cmath>\fP
+.br
+\fR#include <cstdint>\fP
+.br
+\fR#include <limits>\fP
+.br
+\fR#include <optional>\fP
+.br
+\fR#include 'serif/utils/error/errors\&.hpp'\fP
+.br
+
+.SS "Classes"
+
+.in +1c
+.ti -1c
+.RI "struct \fBserif::solver::continuation::CoordinateOptions< Count >\fP"
+.br
+.RI "Numerical increments are fractions of each coordinate's complete physical span\&. "
+.ti -1c
+.RI "struct \fBserif::solver::continuation::CoordinateProposal< Count >\fP"
+.br
+.ti -1c
+.RI "struct \fBserif::solver::continuation::CoordinateCounters\fP"
+.br
+.ti -1c
+.RI "class \fBserif::solver::continuation::CoordinateController< Count >\fP"
+.br
+.RI "Own only the continuation path; a caller promotes physical states after successful correction\&. "
+.in -1c
+.SS "Namespaces"
+
+.in +1c
+.ti -1c
+.RI "namespace \fBserif\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver\fP"
+.br
+.ti -1c
+.RI "namespace \fBserif::solver::continuation\fP"
+.br
+.in -1c
+.SS "Enumerations"
+
+.in +1c
+.ti -1c
+.RI "enum class \fBserif::solver::continuation::CoordinateOrder\fP { \fBserif::solver::continuation::automatic\fP, \fBserif::solver::continuation::preferred\fP, \fBserif::solver::continuation::strict\fP }"
+.br
+.ti -1c
+.RI "enum class \fBserif::solver::continuation::AttemptOutcome\fP { \fBserif::solver::continuation::success\fP, \fBserif::solver::continuation::recoverable_rejection\fP, \fBserif::solver::continuation::fatal_failure\fP }"
+.br
+.ti -1c
+.RI "enum class \fBserif::solver::continuation::ControllerStatus\fP { \fBserif::solver::continuation::ready\fP, \fBserif::solver::continuation::pending\fP, \fBserif::solver::continuation::complete\fP, \fBserif::solver::continuation::attempt_limit\fP, \fBserif::solver::continuation::no_progress\fP, \fBserif::solver::continuation::fatal_failure\fP }"
+.br
+.in -1c
+.SH "Author"
+.PP 
+Generated automatically by Doxygen for SERiF from the source code\&.