A Cost-Model Auditor for Structural Semiprime Defects: Placing Anchored Sparse-Offset Screening Among Known Factoring Methods

We formalise a cost-model auditor that places the anchored sparse-offset ("dyadic-shell") screen of the preprint series on a common footing with the standard integer-factoring methods. The auditor separates an unconditional baseline (GNFS, ECM, Pollard rho, Lehman) from conditional costs that are low only under an explicit structural assumption on the semiprime's generation. Generator defects are modelled as independent, co-occurring features (seven axes A-G), not mutually exclusive classes. Within this model the dyadic-shell screen is shown, analytically and by proof-of-concept experiment, to give a conditional advantage over the baseline in exactly one feature - a sparse arithmetic centre at large prime gap - while being dominated by Fermat, Coppersmith, or ECM in the others. The result is stated as a conditional, not an exclusivity, claim; the principal open problem (multi-block lattice methods against a sparse centre) is recorded. Companion paper to the dyadic-shell preprint series (series concept DOI 10.5281/zenodo.20306132). Use of AI-assisted tools. AI-assisted tools were used in the preparation of this work (drafting and editing, literature triage, and numerical experiments); all definitions, derivations, experiments, and conclusions were reviewed and verified by the author, who takes sole responsibility for the content. Note on origin. This work grew out of follow-up reflections prompted by Anthropic's October 2026 report "Claude reveals ECDSA curve origins"; the connection is thematic (the provenance of structured parameters), not technical.