Correcting the back referencing from bibliography

Question

I am writing lecture notes where the title page numbering is set to gobble, the toc pages are in roman and the lectures pages are in arabic.

The problem is specifically on the 1st lecture page. I have a citation on the page. But its bib item on the bibliography section is back-referencing to the title page. The other citations that are not on the 1st page are not having this issue.

Here's the MWE of my lecture notes:

\documentclass[a4paper]{report}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \input{setup/preamble}
% basics
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage{url}
\usepackage{hyperref}
\hypersetup{
    colorlinks,
    linkcolor={black},
    citecolor={black},
    urlcolor={blue!80!black},
    % backref=true, 
    % pagebackref=true
}
% Page Margins
\usepackage[
    margin=2.8cm, 
    % top=2.8cm, bottom=2.8cm,
    % left=1in, right=1in, 
    % headheight=14.5pt
    ]{geometry}
% \usepackage{graphicx}
% \usepackage{float}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{lipsum}
% bibliography
\usepackage[
    backend=biber, 
    backref=true, 
    style=numeric, 
    sortcites=true, 
    sorting=none, 
    defernumbers=true
]{biblatex}       % bibliography  % https://www.overleaf.com/learn/latex/bibliography_management_with_biblatex
\usepackage{xurl}                % handling the urls in bib file and it should be loaded after loading biblatex
%% Change formatting of back references % https://tex.stackexchange.com/a/606518/114006
\DefineBibliographyStrings{english}{
   backrefpage={p.},
  % backrefpage={},
   backrefpages={pp.}
  % backrefpages={
}
\renewcommand*{\finentrypunct}{}
\usepackage{xpatch}
% \DeclareFieldFormat{backrefparens}{\mkbibparens{#1\addperiod}}
\DeclareFieldFormat{backrefparens}{\raisebox{-4pt}{\scriptsize{\mkbibparens{#1}}}}
\xpatchbibmacro{pageref}{parens}{backrefparens}{}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{filecontents}{ref.bib}
@book{arnold2013mathematical,
  title = {Mathematical {{Methods}} of {{Classical Mechanics}}},
  author = {Arnold, Vladimir I},
  date = {2013},
  series = {Graduate {{Texts}} in {{Mathematics}}},
  volume = {60},
  publisher = {{Springer Science & Business Media}}
}
@article{yang1954conservation,
  title = {Conservation of {{Isotopic Spin}} and {{Isotopic Gauge Invariance}}},
  author = {Yang, Chen N and Mills, Robert L},
  date = {1954-10-01},
  journaltitle = {Physical Review},
  shortjournal = {Phys. Rev.},
  volume = {96},
  number = {1},
  pages = {191--195},
  doi = {10.1103/PhysRev.96.191}
}
\end{filecontents}
\addbibresource{ref.bib}
\title{Lecture Notes}
\author{me}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\maketitle
\pagenumbering{gobble}
% \input{preface}
\newpage
\pagenumbering{roman}
\pdfbookmark{\contentsname}{toc}

\setcounter{tocdepth}{0}
\tableofcontents
\newpage
\pagenumbering{arabic}
% start lectures
\chapter{Sat, Mar 18, 2023}
\lipsum[1] \cite{arnold2013mathematical} 
\lipsum \cite{yang1954conservation}
% \intput{endpage}
% Bibliography
\printbibheading[heading=bibintoc, title={\protect\numberline{}Recommended Resources}] % https://tex.stackexchange.com/a/222961/114006
\printbibliography[type=book,heading=subbibliography,title={Books}] % https://www.overleaf.com/learn/latex/Articles/Getting_started_with_BibLaTeX
\printbibliography[nottype=book,heading=subbibliography,title={Others}]
\end{document}

Answer 1

This is probably a hack (and Ulrike will scold me for that ) but if you remove the \pagenumbering{gobble} and add, before \maketitle:

\pagenumbering{roman}
\setcounter{page}{-1}\thispagestyle{empty}
\maketile
[...]

(and obviously remove the other \pagenumbering{roman} below) the backlink of the bibliography seems to work.

I didn't try your full example (this one is already on the big side for an MWE...), but probably the only trick is to find the correct negative number to start with...

The other option, as suggested by Ulrike in a comment, is to change the "name" of the page; something on the line of changing the title part like that:

% make a full copy of the current \thepage
\NewCommandCopy{\savethepage}{\thepage}
\pagenumbering{gobble}
\renewcommand{\thepage}{Title-Preface-\arabic{page}}
\maketitle
% \input{preface}
\newpage
% reset back the page name
\RenewCommandCopy{\thepage}{\savethepage}
\pagenumbering{roman}

...so you should have different anchor names even if there are more than one title-preface unnumbered pages.

Using the full expl3 copies is probably too much, and a \let should suffice in this case. But you never know if \thepage will change in the future...

Or even easier, as suggested again by Ulrike (thanks!)

\pagenumbering{gobble}
% this is reset back by \pagenumbering
\gdef\thepage{Title-Preface-\arabic{page}}
\maketitle
% \input{preface}
\newpage
% \pagestyle{plain}
\pagenumbering{roman}