Demonstrates Wronskian cancellation and derives a geometric transport limit in SCT connectors, revealing geometrical insights.
Paper 45 in the "Geometry of the Critical Line" programme. The SCT transport ratio R(λ,m) = M₂₁/M₁₁ is extracted at the right endpoint using a leading-term Frobenius basis. RN23 showed that the extracted M₁₁ is contaminated by truncation at exact exponent p = 2 Re r₁ − 2. This paper proves what survives that contamination. The leading-extractor quotient law: the renormalised ratio satisfies |R(λ,m;η)|/ηᵖ⁽ᵐ⁾ = (|r₁ − r₂|/|c₁(r₂)|)(1 + O(η)) as η → 0, where r₁, r₂ are the Frobenius exponents and c₁(r₂) is the first correction coefficient of the singular branch. The proof is a Wronskian cancellation at the right endpoint; it does not rely on WKB or Whittaker asymptotics. Using large-m scaling of the Frobenius data from the indicial recurrence, the paper derives the geometric transport limit: limm→∞ |r₁ − r₂|/|c₁(r₂)| = 2/k = 16/π, where k = π/8 is the SCT metric constant. A numerically supported candidate subleading correction +49π/(32m²) is obtained under a numerically confirmed recurrence coefficient. Finite-cutoff numerical data for m = 2 to 50 are consistent with the quotient law, with agreement within 0.04% for m ≥ 20. This is the centrepiece of the extraction-pathology arc: RN23 showed why the extraction fails; this paper shows what survives. The quotient |r₁ − r₂|/|c₁(r₂)| depends only on local endpoint geometry and converges to a purely geometric constant encoding the SCT metric. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line, anchored by the SCT 5-Manifold and the cover equation Φ + eiπ − 1/Φ = 0.
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Pavel Kramarenko-Byrd (2026) studied this question.
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