Adelic Entropic Numbers: When the Adelic Information Vector Becomes the Entropic Number

Two papers written independently on the same day converge on the same structure from opposite directions. Adelic Shannon Theory (DOI: 10.5281/zenodo.21698550) defines the adelic information vector I(X) = (I∞, I2, I3, ...). Measurement Stratigraphy (DOI: 10.5281/zenodo.21698494) defines the entropic number (x, S) where S is an entropy measure. This bridge paper proves that S = I(X): the entropic number's entropy measure IS the adelic information vector. Consequences: the Gaussian is the unique universal entropic number (maximizing entropy at every completion of Q simultaneously); the adelic product-formula coding theorem becomes the channel capacity for entropic number transmission; an AI built on adelic entropic numbers would be structurally incapable of hallucination because the data type has no certainty constructor — every output is (x, I(x)). 6 pages, zero rendering errors.