Paper 125G: The Riemann–Holosphere Component Map Signed Assembly, Closure, Visibility, and the Boundaries of Transfer

This paper consolidates the Holosphere-inspired constructions that produced concrete mathe-matical results in the author’s Riemann program. The retained connections are signed assemblybefore a quadratic measurement, complete boundary accounting, separate prime-factor packets,bright–dark response coordinates, moving-window observability, common real Gram features, andresponse-preserving elimination. In the arithmetic applications, these constructions give exact blockand channel identities, completed-packet cancellation, an explicit factor-count observation matrix,and recovery of smooth Möbius tests. The observation construction leads to the single-scale andAbel–Hardy criteria of Papers 125E–125F. In the operator branch, the contact calculation suppliesa common positive feature space and a trace-complete Schur reduction; the complete responding-tail method is also used in the source-reported odd Weil-form certificate at support radius two.Each retained connection names both its source and its accomplished mathematical output. Therole-separated packet construction is credited as a successful translation of an organizing idea, notas a physical identification of primes with constituents. The paper is a synthesis of establishedconstructions and explicitly scoped source results. The global arithmetic energy bound and theidentification of the contact response with the Riemann theta response remain separate requirements,rather than conclusions of these mappings.