Spectral anomalies in metals from the pentachoron: Cooper-pair mass, London moment, band renormalisation, and parity violation

Four anomalies in metallic and superconducting systems — spanning four decades — are addressed from a single theorem of the K₅ pentachoric framework.

(i) Cooper-pair mass excess (Tate et al., PRB 42, 7885, 1990): unexplained for 35 years. The 9 Hilbert–Schmidt-orthogonal scattering channels of the electron vertex (P2 Theorem), perturbed by the Fermi kinetic energy, give Δm/m = (9/2)(v_F/c)². For Nb: 9.40 × 10⁻⁵, measured 9.2 × 10⁻⁵, deviation 2.1%. The coupling α* cancels identically.

(ii) London moment: all rotating superconductors yield m' = mₑ, contradicting the BCS prediction m' = m*. The K₅ correction (~10⁻⁴) falls below the 1% precision of London experiments. In K₅, the London moment probes the vertex mass mₑ = m₀ u⁹, not the lattice-dressed m*.

(iii) Band renormalisation in iron-based superconductors: the universal factor ≈ 3 near the Fermi level is n_e = dim(V₁) = 3 — the same integer, seen in the propagation space V₁ (vectors, Matthiessen scattering) rather than the scattering space End(V₁) (operators, logarithmic derivative).

(iv) Tajmar parity violation: the CW/CCW ratio u¹⁶ = 4.23 matches the lowest-ratio material YBCO (4.42, 4%) and equals the up-quark mass ratio of P2. The material-dependent excess in Nb, Al, and Pb is an open problem.

All four results derive from the spectral filtration of K₅ with dim V₁ = 3 and dim End(V₁) = 9, the Hilbert–Schmidt orthogonality of scattering channels, and the multiplicative mass formula mₑ = m₀ u⁹ (P2). No adjustable parameter enters any formula. The integer 9 = n_e² is the same that generates the nine fermion masses (P2, mean 2.4%), the Higgs-to-W ratio u⁵ (P3, 0.73%), and Newton's constant via Σn_k² = 50 (P2, 0.29%). Predictions for Al, Pb, Sn, YBCO, and Cu are given; the ratio of anomalies between any two metals depends only on (v_F)² and is independent of the coefficient 9/2.

Companion script: P16_companion_v2.py (108 tests, 0 failures).