fix(paper): repair authblk stub so author affiliation marks render correctly

The committed authblk.sty is a local stub (system has no real authblk).
It ignored the [n] optional arg on \author (all authors got mark 1) and
overwrote earlier \affil entries (Black Box affiliation vanished, marks
collapsed). Rewrote it to honor explicit marks and accumulate affils,
expanding each mark at storage time via \xdef. Now renders:
Ingram^1, Dyer^2, Shaw^2 with ^1 Black Box / ^2 OCC.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01TdCZM5sFZ3foQPBvshMKUp

Author: ImmortalDemonGod

paper/authblk.sty

@@ -1,5 +1,10 @@
 %% authblk.sty - minimal local stub providing \author, \affil, \Authfont, \Affilfont
-%% Based on the authblk package by Patrick W. Daly
+%% Based on the authblk package by Patrick W. Daly.
+%% Honors explicit optional-argument affiliation marks, e.g. \author[2]{Name}
+%% and \affil[2]{Address}; falls back to sequential auto-numbering when the
+%% optional argument is omitted. Each mark is expanded at storage time (via
+%% \xdef) so it is fixed per author/affil; multiple \affil entries accumulate
+%% (each on its own line) rather than overwriting one another.
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesPackage{authblk}[2001/02/27 1.3 (PWD)]
 \newcommand\Authfont{\normalfont}
@@ -10,35 +15,28 @@
 \newcounter{auth}
 \newcounter{affil}
 \newlength{\affilsep}\setlength{\affilsep}{1.5em}
-\newif\ifnewaffil \newaffiltrue
-\let\AB@authold\author
+\gdef\AB@authors{}
+\gdef\AB@affillist{}
 \renewcommand\author[2][]{%
-  \ifnewaffil\addtocounter{affil}{1}%
-    \edef\AB@affilnote{\theaffil}\newaffilfalse
-  \fi
-  \addtocounter{auth}{1}%
+  \stepcounter{auth}%
+  \edef\AB@mark{#1}%
+  \ifx\AB@mark\@empty\edef\AB@mark{\arabic{auth}}\fi
   \ifnum\theauth=1\relax
-    \gdef\AB@authors{{\Authfont #2}\textsuperscript{\AB@affilnote}}%
+    \xdef\AB@authors{\unexpanded{{\Authfont #2}}\noexpand\textsuperscript{\AB@mark}}%
   \else
-    \g@addto@macro\AB@authors{, {\Authfont #2}\textsuperscript{\AB@affilnote}}%
+    \xdef\AB@authors{\unexpanded\expandafter{\AB@authors}, \unexpanded{{\Authfont #2}}\noexpand\textsuperscript{\AB@mark}}%
   \fi
 }
 \newcommand\affil[2][]{%
-  \newaffiltrue
-  \ifx\\#1\\%
-    \addtocounter{affil}{1}%
-    \edef\AB@note{\theaffil}%
-  \else
-    \def\AB@note{#1}%
-  \fi
+  \stepcounter{affil}%
+  \edef\AB@note{#1}%
+  \ifx\AB@note\@empty\edef\AB@note{\arabic{affil}}\fi
   \ifnum\theaffil=1\relax
-    \gdef\AB@affillist{\textsuperscript{\AB@note}{\Affilfont #2}}%
+    \xdef\AB@affillist{\noexpand\textsuperscript{\AB@note}\unexpanded{{\Affilfont #2}}}%
   \else
-    \g@addto@macro\AB@affillist{\\[0.3ex]\textsuperscript{\AB@note}{\Affilfont #2}}%
+    \xdef\AB@affillist{\unexpanded\expandafter{\AB@affillist}\unexpanded{\\[0.3ex]}\noexpand\textsuperscript{\AB@note}\unexpanded{{\Affilfont #2}}}%
   \fi
 }
-\gdef\AB@authors{}
-\gdef\AB@affillist{}
 \renewcommand\@author{%
   \AB@authors\\[1ex]\AB@affillist
 }