docs(pacseries): compile v0.3 paper PDFs + harden md_to_tex for XeTeX

Compile all six v0.3 papers to paper.pdf (tectonic/XeTeX), matching the v0.2 gold
standard. md_to_tex.py fixes required for XeTeX: load amssymb before unicode-math (\eth
clash), auto-brace macro sub/superscripts (unicode-math needs _{\mathbb{C}}), and stack
the author/metadata block. paper.tex regenerated for all six.

Author: pgroom2

foundational/docs/preprints/PACSeries/md_to_tex.py

@@ -22,15 +22,19 @@
 
 PREAMBLE = r"""\documentclass[11pt,a4paper]{article}
 \usepackage{iftex}
+\usepackage{amsmath,amsthm}
 \ifPDFTeX
   \usepackage[T1]{fontenc}
   \usepackage[utf8]{inputenc}
   \usepackage{textcomp}
+  \usepackage{amssymb}
 \else
+  %% XeTeX/LuaTeX: amssymb BEFORE unicode-math (unicode-math then overrides it cleanly;
+  %% the reverse order clashes on \eth). Keeps \square, \mathbb, \mathfrak available.
+  \usepackage{amssymb}
   \usepackage{unicode-math}
   \defaultfontfeatures{Scale=MatchLowercase}
 \fi
-\usepackage{amsmath,amssymb,amsthm}
 \usepackage{booktabs}
 \usepackage{longtable}
 \usepackage{array}
@@ -60,6 +64,15 @@
 
 FOOTER = "\n\\end{document}\n"
 
+# Brace a macro (and its single-brace arg) when it's a bare sub/superscript target:
+# `_\mathbb{C}` -> `_{\mathbb{C}}`, `^\top` -> `^{\top}`. Valid in amsmath but unicode-math
+# (XeTeX) requires the braces. Applied to math spans only, so it never touches prose.
+_SUBSUP = re.compile(r'([_^])(\\[a-zA-Z]+(?:\{[^{}]*\})?)')
+
+
+def _norm_math(s):
+    return _SUBSUP.sub(r'\1{\2}', s)
+
 
 def escape_tex(s):
     # s has NO math/code spans (already protected). Escape LaTeX specials.
@@ -82,7 +95,10 @@ def inline(text, store):
     """Protect math/code, escape, then apply md inline formatting, then restore."""
     # 1. protect $$...$$, $...$, `code`
     def protect(pat, m):
-        store.append(m.group(0) if pat != 'code' else '\\texttt{' + escape_tex(m.group(1)) + '}')
+        if pat == 'code':
+            store.append('\\texttt{' + escape_tex(m.group(1)) + '}')
+        else:
+            store.append(_norm_math(m.group(0)))
         return f'\x00{len(store)-1}\x00'
     text = re.sub(r'\$\$.*?\$\$', lambda m: protect('math', m), text, flags=re.S)
     text = re.sub(r'(?<!\\)\$.+?(?<!\\)\$', lambda m: protect('math', m), text)
@@ -163,14 +179,14 @@ def convert(md, title):
 
         # display math block
         if stripped.startswith('$$') and stripped.endswith('$$') and len(stripped) > 3:
-            out.append(r'\[' + stripped[2:-2].strip() + r'\]')
+            out.append(r'\[' + _norm_math(stripped[2:-2].strip()) + r'\]')
             i += 1; continue
         if stripped == '$$':
             i += 1; buf = []
             while i < n and lines[i].strip() != '$$':
                 buf.append(lines[i]); i += 1
             i += 1
-            out.append(r'\[' + '\n'.join(buf) + r'\]')
+            out.append(r'\[' + _norm_math('\n'.join(buf)) + r'\]')
             continue
 
         # headings
@@ -229,7 +245,12 @@ def convert(md, title):
         i += 1
         while i < n and lines[i].strip() != '' and not re.match(r'^(#{1,6}\s|\s*[-*]\s|\s*\d+\.\s|\$\$|```|-{3,}$)', lines[i]) and not ('|' in lines[i] and i+1 < n):
             para.append(lines[i]); i += 1
-        out.append(inline(' '.join(p.strip() for p in para), store))
+        # consecutive bold-only lines are a metadata block (author / paper no. / date /
+        # version) — stack them with LaTeX line breaks instead of flowing into one line
+        if len(para) > 1 and all(re.match(r'^\*\*.+\*\*', p.strip()) for p in para):
+            out.append(' \\\\\n'.join(inline(p.strip(), store) for p in para))
+        else:
+            out.append(inline(' '.join(p.strip() for p in para), store))
 
     return '\n'.join(out)
 

foundational/docs/preprints/PACSeries/v0.3/connection_identity_spacetime/paper.pdf

@@ -1,14 +1,18 @@
 \documentclass[11pt,a4paper]{article}
 \usepackage{iftex}
+\usepackage{amsmath,amsthm}
 \ifPDFTeX
   \usepackage[T1]{fontenc}
   \usepackage[utf8]{inputenc}
   \usepackage{textcomp}
+  \usepackage{amssymb}
 \else
+  % XeTeX/LuaTeX: amssymb BEFORE unicode-math (unicode-math then overrides it cleanly;
+  % the reverse order clashes on \eth). Keeps \square, \mathbb, \mathfrak available.
+  \usepackage{amssymb}
   \usepackage{unicode-math}
   \defaultfontfeatures{Scale=MatchLowercase}
 \fi
-\usepackage{amsmath,amssymb,amsthm}
 \usepackage{booktabs}
 \usepackage{longtable}
 \usepackage{array}
@@ -37,7 +41,10 @@
 
 \subsection*{On deriving the Lorentz group, invariant interval, and speed of light from ADE graph structure and SEC complexification}
 
-\textbf{Peter Groom, Dawn Field Institute} \textbf{PACSeries Paper 10} \textbf{Date}: May 2026 \textbf{Version}: 1.0 (Draft)
+\textbf{Peter Groom, Dawn Field Institute} \\
+\textbf{PACSeries Paper 10} \\
+\textbf{Date}: May 2026 \\
+\textbf{Version}: 1.0 (Draft)
 
 \begin{center}\rule{0.5\linewidth}{0.4pt}\end{center}
 
@@ -119,7 +126,7 @@ \subsection*{3.1 Convergence, not imposition}
 
 The relaxation ratios between force depths follow $\varphi^{d_2 - d_1}$:
 \begin{itemize}\tightlist
-\item Strong/EM ratio: $\varphi^{13-3} = \varphi^{10} \approx 122.99$ (vs observed $\alpha_\text{EM}/\alpha_s \sim 130$)
+\item Strong/EM ratio: $\varphi^{13-3} = \varphi^{10} \approx 122.99$ (vs observed $\alpha_{\text{EM}}/\alpha_s \sim 130$)
 \item EM/weak ratio: $\varphi^{7-13}$ (inverse Fibonacci depth ordering)
 \end{itemize}
 
@@ -145,7 +152,7 @@ \subsection*{4.1 The derivation}
 \begin{enumerate}\tightlist
 \item $A_1$ has Lie algebra $\mathfrak{su}(2)$ (3 generators: rotations)
 \item SEC promotes real parameters to complex: $\theta \to \theta + i\eta$
-\item Complexification: $\mathfrak{su}(2)_\mathbb{C} = \mathfrak{sl}(2, \mathbb{C})$
+\item Complexification: $\mathfrak{su}(2)_{\mathbb{C}} = \mathfrak{sl}(2, \mathbb{C})$
 \item Real form: $\mathfrak{sl}(2, \mathbb{C}) \cong \mathfrak{so}(3,1)$ (Lorentz algebra)
 \end{enumerate}
 
@@ -205,7 +212,7 @@ \subsection*{6.3 The invariant interval}
 
 \[ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2\]
 
-The metric signature is not chosen; it is forced by the Killing form of the complexified $A_1$ algebra. On the 6-dimensional real algebra the Killing form has signature $(3,3)$ (rotations positive, boosts negative); restricted to the 4-dimensional vector representation it has signature $(1,3)$, the Minkowski metric (M13 exp\_09). The interval $s^2 = x^\top\eta\,x$ is preserved across 135 Lorentz transforms (maximum relative error $2.9\times10^{-6}$, growing with rapidity up to $\eta=10$), and the invariant form is unique: the space of symmetric bilinear forms preserved by all $\mathfrak{so}(3,1)$ generators is one-dimensional (Schur's lemma), so the metric is a consequence of the algebra rather than a choice.
+The metric signature is not chosen; it is forced by the Killing form of the complexified $A_1$ algebra. On the 6-dimensional real algebra the Killing form has signature $(3,3)$ (rotations positive, boosts negative); restricted to the 4-dimensional vector representation it has signature $(1,3)$, the Minkowski metric (M13 exp\_09). The interval $s^2 = x^{\top}\eta\,x$ is preserved across 135 Lorentz transforms (maximum relative error $2.9\times10^{-6}$, growing with rapidity up to $\eta=10$), and the invariant form is unique: the space of symmetric bilinear forms preserved by all $\mathfrak{so}(3,1)$ generators is one-dimensional (Schur's lemma), so the metric is a consequence of the algebra rather than a choice.
 
 \begin{center}\rule{0.5\linewidth}{0.4pt}\end{center}