\\documentclass[11pt]{article}
\\usepackage[margin=1in]{geometry}
\\usepackage{hyperref}
\\title{The Thirteen-Bill Closure Pattern of Integer Factoring (2024--2026)}
\\author{Kevin Russell \\\\ ProjectForty2}
\\date{May 2026}

\\begin{document}
\\maketitle

\\begin{abstract}
The factorization ledger audits 504 papers from 2024--2026 on integer-factoring claims spanning quantum, classical, and learning-style approaches. The harness consists of thirteen bills, six meta-costs, and three escape gates. Three bills are predicted empty: Bill 6, Bill 7, and Bill 8. Across the 504-paper batch, Bills 6 and 7 receive zero triggers, while Bill 8 receives one marginal candidate with zero clean frontier-gate crossings.
\\end{abstract}

\\section{Main Claim}

Any frontier integer-factoring claim must pay at least one closure bill before it can count as a clean breach. The empty-space hypothesis predicts that the most important unclaimed space is not a missing implementation detail, but a structural closure gap: no paper in the audited corpus supplies the exact-point, cross-Frobenius, and cross-regime evidence required to move from suggestive construction to frontier breach.

\\section{Method}

The public receipt layer is available at ProjectForty2:
\\begin{itemize}
  \\item \\texttt{data/factorization/bills\\_draft.md}
  \\item \\texttt{data/factorization/corpus\\_synthesis.json}
  \\item \\texttt{data/factorization/audit\\_scripts.md}
  \\item \\texttt{atlas.html}
\\end{itemize}

\\section{Status}

This TeX export is the lightweight public receipt paired with \\texttt{eprint.html}. The canonical public evidence remains the static ProjectForty2 ledger and data bundle.

\\end{document}