What question did this study set out to answer?

To explore a numerical mechanism for stabilizing the transport ratio in the context of the critical line.

March 31, 2026Open Access

Real Contractive Linearisation of the SCT Projective Transport Residual

Key Points

To explore a numerical mechanism for stabilizing the transport ratio in the context of the critical line.
Derived an exact lambda variation identity with corrected sign.
Inferred a positive-real linearisation coefficient in a specific testing window.
Analyzed contractive flow behavior toward a target variable without phase twists.
The linearisation coefficient was consistently found to be positive-real.
Results support contractive flow towards ρ(m) with no observed phase twist.
Findings are part of a broader research agenda on the critical line.

Abstract

Research Note 17 in the "Geometry of the Critical Line" programme. This note proposes a numerically supported mechanism for the high-energy stabilisation of the transport ratio R (λ, m) = M₂₁/M₁₁. An exact λ-variation identity is derived with a corrected sign, and the numerically inferred linearisation coefficient a (λ, m): = −∂_λR/ (R − ρ) is found to be positive-real (arg a < 0. 02 rad) in the tested window. This is consistent with contractive flow toward ρ (m) without phase twist. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme. The programme does not claim to prove the Riemann Hypothesis.

Real Contractive Linearisation of the SCT Projective Transport Residual

Key Points

Abstract

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