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Euler case with source-checked exact quartic address laws, least periods and isometric binary inversion, finite-field Hurwitz mode inversion, and formal logarithmic/Stirling coordinates. Earlier packet, matrix, congruence, Fibonacci and calculus derivations remain. Universal source inputs, written same-assistant proofs and bounded computations are distinguished. No new Lean, independent review, global novelty, exclusive-method, speed or analytic continuation claim. The optimal classical dyadic boundary is extended by exact tail factorization, binary carry minima, sparse-binary all-row valuation laws and a cancellation example. The source preparation theorem is distinguished from the unresolved universal simplicity problem."}