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This research note aims to consolidate findings from previous papers into a cohesive separation theorem related to the SCT critical sector.

March 28, 2026Open Access

The Carrier–Extractor Separation Theorem for the SCT Critical Sector

Key Points

This research note aims to consolidate findings from previous papers into a cohesive separation theorem related to the SCT critical sector.
Synthesis of results from Papers 38–40 and Research Notes 9–11.
Development of a single separation theorem.
Analysis of the interaction between Archimedean carriers and Hecke-type obstacles.
Establishment of a spectrally locked Archimedean carrier in the SCT critical sector.
Identification of six Hecke-type kills that obstruct native extraction.
Confirmation that abstract KMS recursion functions in an enlarged algebra.

Abstract

Research Note 12 in the Geometry of the Critical Line programme. Synthesizes results from Papers 38–40 and Research Notes 9–11 into a single separation theorem: the SCT critical sector carries a spectrally locked Archimedean carrier (isolated, shaped, spectrally excluded, logarithmically dense) from which native extraction is obstructed by six proved Hecke-type kills. The abstract KMS recursion survives only in an enlarged algebra. The SCT–Connes dictionary is the structurally indicated resolution.

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