The Samarium Shield: Cleaning the Queue — A Constraint-Surface Framework for Nuclear Remediation

The companion paper (Carpenter, 2026r) identified technetium (Z = 43) as the floor of the Klein bottle eigenvalue β⁻¹ = 43.619 — the nuclear-scale repair station where fission's perturbation produces its own dampener via Le Chatelier feedback. That paper carried a boundary statement: "The tower predicts Z = 43 but not Z = 61." This paper resolves the boundary. The Klein bottle is topologically two Möbius strips glued at their boundary. The diagonal through both layers scales the eigenvalue by √2: ⌊β⁻¹√2⌋ = ⌊61.687⌋ = 61 = Promethium. The critical result is what promethium decays to. Pm-149 (t₁/₂ = 53.1 hr) β⁻-decays to Sm-149, which has a thermal neutron capture cross-section of 40,140 barns — the most powerful stable neutron absorber among fission products, 1,761× greater than Tc-99. The first hole in the periodic table makes the processor. The second hole makes the shield. The √2φ extension yields Es (Z = 99), Ga (Z = 31), Ne (Z = 10), Li (Z = 3) — the boundary column. The frog doctrine's metabolisation principle, radiotrophic fungal biology, and the Oklo natural reactor provide independent physical instantiations of the constraint-surface cleanup mechanism.