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/qualification.hpp.3

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+.TH "src/include/serif/solver/nonlinear/qualification.hpp" 3 "Version v0.0.1a" "SERiF" \" -*- nroff -*-
+.ad l
+.nh
+.SH NAME
+src/include/serif/solver/nonlinear/qualification.hpp
+.SH SYNOPSIS
+.br
+.PP
+\fR#include <algorithm>\fP
+.br
+\fR#include <cmath>\fP
+.br
+\fR#include <expected>\fP
+.br
+\fR#include <span>\fP
+.br
+\fR#include 'serif/solver/nonlinear/result\&.hpp'\fP
+.br
+\fR#include 'serif/utils/error/errors\&.hpp'\fP
+.br
+
+.SS "Classes"
+
+.in +1c
+.ti -1c
+.RI "struct \fBserif::solver::detail::NewtonFailure\fP"
+.br
+.RI "Explain why a candidate cannot provide a usable nonlinear metric\&. "
+.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::detail\fP"
+.br
+.in -1c
+.SS "Functions"
+
+.in +1c
+.ti -1c
+.RI "std::optional< std::string > \fBserif::solver::detail::preparation_rejection\fP (const auto &problem, const auto &evaluation)"
+.br
+.RI "Preserve numerical preparation failures while propagating invalid physical configurations\&. "
+.ti -1c
+.RI "std::expected< \fBMetricEvaluation\fP, \fBNewtonFailure\fP > \fBserif::solver::detail::qualify_candidate\fP (auto &problem, const auto &state, const auto &evaluation, auto &metric_function, auto &strategy, \fBTrialAssessment\fP assessment={})"
+.br
+.RI "Qualify one already evaluated candidate through the same physical and metric gates everywhere\&. "
+.ti -1c
+.RI "bool \fBserif::solver::detail::finite_correction\fP (std::span< const double > correction, const int expected_size)"
+.br
+.RI "Every custom backend must preserve the correction dimensions and finite coefficients\&. "
+.in -1c
+.SH "Author"
+.PP 
+Generated automatically by Doxygen for SERiF from the source code\&.