# Verification of the odd ear complexity manuscript

The five-page English manuscript proves NP-completeness of deciding beta(G)>=k, where beta counts initial odd ears including the first cycle. It covers simple 2-connected 2-degenerate apex-bipartite graphs of arbitrarily large fixed girth. This is a complete complexity classification for OWR-13353-012, not an unconditional separation of P and NP.

The proof uses Lovasz's factor-critical characterization and explicitly credits the Gomes et al. SAT support. The cone identity, two multiplicity forcing inequalities, perfect-matching constraints, polynomial explicit edge-list size and both directions of odd-subdivision invariance have been checked in detail. The manuscript treats k<=0 separately.

Exact finite diagnostics pass: 512 weighted bipartite supports; 97 exhaustive small formula optimizations; 41 direct cone formula instances; 154 formula thresholds, comprising 129 satisfiable and 25 unsatisfiable cases; and 200 subdivision identities. Python's normal and optimized modes agree byte for byte. An unsatisfiable negative control refutes the naive transfer from matching weight to induced edge count. The general theorem rests on the written proof, not on finite computation.

The desktop LaTeX compiler and Tectonic compile successfully. All five final pages were visually inspected, including formulas, references, page boundaries, the name-only author line and the affiliation footnote. The final packaging record binds the portable rebuild and checker replay results to file hashes.

Three primary PDFs and seven complete relevant source pages were reviewed. Third-party PDFs and extracted text are retained privately and excluded from the uploaded archive. This is an originating-researcher self-audit. Independent review, formal verification, maintainer acceptance and absolute priority are not claimed.