Parallel-support transfer and sparse paving quotients in a one-sided Merino–Welsh inequality

This preprint combines a conditional quotient-to-matroid transfer mechanism for the one-sided inequality T_M(0,2) >= b(M), an all-parameter sparse paving quotient application, and a complementary strict corank-two theorem. The transfer uses a quotient girth budget; sparse paving quotients have rank c >= 1 and size m >= 2c. The corank-two theorem assumes the quotient has two disjoint bases. It does not resolve the full Merino–Welsh conjecture or cover all paving quotients or all two-base matroids. It cites and extends the earlier parallel-support corank-at-most-one preprint, DOI 10.5281/zenodo.22296382, without changing that record. Known endpoints and standard recurrences are credited; no global-priority claim is made. Status: v0.1-beta; independently internally audited preprint; external mathematical review and formal peer review pending. Finite original-object controls do not replace proofs. PDF, LaTeX source, Markdown manuscript and a reproducibility ZIP are supplied. Manuscripts and documentation are CC BY 4.0; verification code is MIT. AI-assisted research and writing: AI tools assisted with research, checking, literature comparison, and writing. Carptopus is the sole responsible author.