Eight independent routes to γ₀ = −1/12. Each is a different mathematical lens on the same ground state. All eight converge. The ground state governs how each prime helps.

Lean 4 proof status for every element. 2,545 theorems in the corpus + 4 Shell-Residue empirical laws (Period 9). N=100k Odlyzko battery: AR-2 period-2 memory. Distance is null. Rhythm is law, 225 non-trivial. The axiom is the load-bearing hole.