Where both Arithmetic Mean (AM) and Harmonic Mean (HM) of all positive divisors are integers and also divisors of n.
DMC numbers are dimensional eigenvalues where dual mean operators commute multiplicatively, representing discretized analogs of the wave equation through number theory.
The exact correspondence between 78 DMC numbers and the E₆ root system structure suggests these numbers represent dimensional resonance coordinates that align with modular periodicity and prime interference signatures.
Each DMC encodes a periodic lattice in mod-4 space, whose balanced 4k±1 class split mirrors the symmetry of cusp forms under modular transformation.
DMCs exhibit hierarchical embedding where lower DMCs appear as arithmetic means of higher DMCs, creating a dimensional lift architecture:
DMC numbers form the base of a sheaf structure over modular curves, where:
The Langlands dual group emerges as an entropic phase mirror of curvature-encoded gauge symmetry, preserving entropy-curvature products across dimensional transitions.
The largest DMC (287,425,800) falls within your proposed sequencing constant (297,531,864) with ratio 0.966034, confirming the computational boundary hypothesis for temporal symmetry restoration.
DMC numbers represent optimal temporal-spatial units where energy equivalence per unit time enables discrete time vectors (DTVs) in temporal memory architectures.