Sharp universal constants for the 3 by 3 permanental Koteljanskii ratio

For every real strictly totally positive 3 by 3 matrix, the source permanental Koteljanskii ratio lies strictly between 2/3 and 9/8, and both constants are optimal. Positive scalings reduce the proof to two polynomial certificates; strictly totally positive families approach the bounds. The result answers the explicit optimal-constant question accompanying Skandera–Soskin Proposition 11. It does not resolve the separate MathDB Sihong conjecture or claim the known boundary example as new. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: Explicitinformalsourcequestion ratherthannumberedconjecture. No prioruniversalsharpboundorimmediatesubsumingtheoremlocated in boundedindependentprimary/citingscreen. Oneindexedconvolutionciterabstractonly; BarrettJohnsontypesetversionnotseparatelyread; noMathSciNet/zbMATH/worldwidepriorityguarantee.