η-Invariant Conservation and RFB = ∞ Irreducibility from Bordism Duality

We establish five interconnected results for the 4-dimensional Pin⁺ bordism group Ω4Pin+=Z16, unified by the interpretation of the reduced ηˉ-invariant as a topological information carrier: (1) the tangent-normal Pin duality—TM admits Pin⁺ iff ν admits Pin⁻, proved in three lines from the Whitney sum; (2) domain wall duality with dimension shift Δd=2; (3) RFB=∞ from the non-splitting of 0→Z2→Z16→Z8→0, classified by Ext1(Z8,Z2)=Z2; (4) η-invariant conservation as a topological charge and information carrier, with ηˉ taking values in 161Z—the non-splitting guarantees this “hyperfine quantization” precision of 4 bits, irreducible by Ext1; (5) 4D uniqueness reinforcement via a triple blockade—Ω5Pin+=0, Ω4Pin−=0, KO−3(pt)=0—rendering Z16 a non-extendable structure. We identify Z8 with Bott periodicity in Clifford algebra classification, where 48↔Cl4=H(2)≅Cl(1,3). Physical implications for dark energy, strong CP, measurement, and the Swampland Cobordism Conjecture are discussed through the lens of ηˉ as information carrier.