SAM and the Riemann Hypothesis

The Substrate Accumulation Model supplies a route from a normalized accumulationcoordinate to logarithmic translation. In that coordinate, reciprocal translation energy,prime-power weights and the archimedean completion of the Riemann zeta function can bewritten in one exact form. The canonical value A0 = 1/(12π) fixes the additive normalizationwhen the translation kernel and Gamma convention are held fixed. We derive that identityand place it on the endpoint-annihilating test class of the Weil positivity criterion. A pairedscale difference factors through the same endpoint operator, giving an explicit Mellin/Parsevalbridge. An independent divisor reference has exact trace π8/9216, a positive conservedreservoir, and coupled coefficient allowance below 1.061680773A0. Prime attenuation hasa sharp recovery threshold at γ = 1/2. We then construct one global increment of theobserved principal-band source: shifted arguments cross every internal band boundary withtheir exact prime-source corrections, leaving only the global terminal region [Y /4, Y ]. Theknown initial seed supplies uniform increment recovery; critical attenuation costs O(log Y )in norm. The coherent/local projection has positive local defect at most 128 log Y . Asubpower upper bound for the retained coherent moment would imply RH by an explicitenergy-to-holomorphy argument. That coherent estimate remains open; the identities,component bounds and conditional completion mechanism are stated separately.