M28b The R=4 Triad: A Conscious Reduction from the Hypertriad

M28b reduces the full Hypertriad of M28a (ten-member rhombus at R = 4) to a working Triad that mirrors the rank‑3 structure while preserving the essential geometry. The reduction is conceptual, not eliminative: the Hypertriad remains the ambient structure, but a minimal triangle is selected for clarity and operability. The resulting R = 4 Triad is { Ctet, TMult_B, HCt }. It corresponds structurally to the rank‑3 Triad { Cpow, Apow, a^b }. Each vertex arises from a distinct structural lesson of M28a: Ctet = HC genuine symmetric operation TMult_B = TC shelf (slog arithmetic) HCt = asymmetric a-ONS (chirality midpoint) The reduction is guided by three structural identifications: HCt plays the role of the asymmetric member (analog of a^b) TMult_B represents the TC shelf as the unique multiplicative structure Ctet remains the HC symmetric anchor Thus the triangle preserves the HC / SC(role replaced by TC) / asymmetric pattern of the Triad. The TC operations retain their defining structure: TMult_B(a,b) = tet_B(slog_B(a) * slog_B(b)). The key conceptual move is that the two-étage Hypertriad is collapsed into a single effective shelf (TC), while the chirality sector is absorbed into a single asymmetric representative (HCt). This produces an operational chart in which: the full Hypertriad = ambient geometry the R=4 Triad = usable coordinate system The reduction enables direct comparison across ranks: R = 3: { Cpow, Apow, a^b } R = 4: { Ctet, TMult_B, HCt }. M28b therefore does not add new operations; it provides a canonical representation of R = 4 that makes subsequent constructions (notably the ISHE bridge at R = 3.5) structurally transparent.