Endpoint Renormalization of the SCT Transport Ratio
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866902091782422528 |
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| author | Kramarenko-Byrd, Pavel |
| author_facet | Kramarenko-Byrd, Pavel |
| contents | <p>Research Note 18 in the "Geometry of the Critical Line" programme.</p> <p>Paper 42 reported numerical stabilisation of the SCT transport ratio R(λ,m) = M₂₁/M₁₁ on the real axis. Subsequent large-λ scans appeared to show a slow secular drift, raising the question of whether the putative fitted transport limit ρ(m) actually exists in the present extraction scheme.</p> <p>This note resolves that tension. The drift is a cutoff artifact of the raw Frobenius extraction at the right endpoint. The key diagnostic finding: M₂₁ is cutoff-stable to 0.04% across a 250× range of the regularisation parameter η, while M₁₁ carries an endpoint normalization factor of order η^{−p} with p ≈ 1, varying by factor ~220× over the same range. The extraction pathology lies entirely in M₁₁, not in the propagated dynamics.</p> <p>After empirical endpoint renormalization, the transport ratio becomes much more nearly λ-independent, with stability improving rapidly with winding number. The Paper 42 transport-constant picture survives as a renormalized transport observable, not as the literal raw Frobenius-truncation ratio. This diagnosis directly motivates the jet conditioning theorem of RN23, which identifies the exact truncation exponent, and Paper 45, which shows what survives after the contamination is accounted for.</p> <p>No arithmetic interpretation is claimed.</p> <p>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 + e^{iπ − 1/Φ} = 0.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19319849 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Endpoint Renormalization of the SCT Transport Ratio Kramarenko-Byrd, Pavel endpoint extraction cutoff dependence renormalization Frobenius truncation connection matrix Evans function SCT manifold chiral operator Spectral Theory Numerical analysis <p>Research Note 18 in the "Geometry of the Critical Line" programme.</p> <p>Paper 42 reported numerical stabilisation of the SCT transport ratio R(λ,m) = M₂₁/M₁₁ on the real axis. Subsequent large-λ scans appeared to show a slow secular drift, raising the question of whether the putative fitted transport limit ρ(m) actually exists in the present extraction scheme.</p> <p>This note resolves that tension. The drift is a cutoff artifact of the raw Frobenius extraction at the right endpoint. The key diagnostic finding: M₂₁ is cutoff-stable to 0.04% across a 250× range of the regularisation parameter η, while M₁₁ carries an endpoint normalization factor of order η^{−p} with p ≈ 1, varying by factor ~220× over the same range. The extraction pathology lies entirely in M₁₁, not in the propagated dynamics.</p> <p>After empirical endpoint renormalization, the transport ratio becomes much more nearly λ-independent, with stability improving rapidly with winding number. The Paper 42 transport-constant picture survives as a renormalized transport observable, not as the literal raw Frobenius-truncation ratio. This diagnosis directly motivates the jet conditioning theorem of RN23, which identifies the exact truncation exponent, and Paper 45, which shows what survives after the contamination is accounted for.</p> <p>No arithmetic interpretation is claimed.</p> <p>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 + e^{iπ − 1/Φ} = 0.</p> |
| title | Endpoint Renormalization of the SCT Transport Ratio |
| topic | endpoint extraction cutoff dependence renormalization Frobenius truncation connection matrix Evans function SCT manifold chiral operator Spectral Theory Numerical analysis |
| url | https://doi.org/10.5281/zenodo.19319849 |