The OMARWA-E8 Correspondence: A Research Program Connecting Modular Periodicity to Exceptional Lie Structure

A research program preprint exploring the numerical correspondences between the OMARWA sequence T_k = 6*2^k + 1 (OEIS A004119) and the exceptional Lie algebra E_8. Documents 17 observations connecting modular periodicity to E_8 structure: the super-period L=30 equals the Coxeter number h(E_8), the Weyl exponents {1,7,11,13,17,19,23,29} are exactly the OMARWA primitive periods, the root count |Delta|=240=8*30 follows from the period structure, and the P622 crystallographic space group (IT #177) connects to the 354-channel OMARWA cycle. All number-theoretic results are formally verified in Lean 4 (956 theorems, 0 sorry). Epistemic classification [A]/[B]/[C] is applied throughout. Experimental predictions at BSM scale ~1.35 TeV and falsification criteria are provided. 13 pages, 17 references.