Theory of Generated Space — Superconductivity closure: a TGP-structured T_c formula across five families (version 2)

Version 2 (April 2026). Preprint and supporting numerical material for the TGP superconductivity-closure paper, a companion to the TGP core paper (Zenodo DOI: 10.5281/zenodo.19670324). The paper applies the substrate-field framework of TGP to the superconducting Tc: it derives a closed-form T_c expression calibrated on a five-d-metal subset, extends it across cuprates, MgB₂, hydrides and A15, and states explicit open sub-problems (Ce/Kondo regime, √n scaling). The 31-material master fit yields r(log T_c) = 0.875, RMS_log = 0.346. Structural coefficients κ_TGP ≈ 2.012 (spin-fluctuation coupling), β ≈ 2.527 (magnetic blocking) and α_PB ≈ 0.2887 μ_B⁻² (Abrikosov-Gorkov pair-breaking) are reported alongside the cross-sector universal constant c_TGP = 1/(4π) that reappears in the liquid-viscosity sector. Version 2 changes. Post-v1 analysis (programmes P7.5–P7.12) added a new Section 11 «Post-v1 refinements and scope of validity» which: (i) introduces a Z-dependent relativistic correction to the lanthanide orbital amplitude A_f(Z) = A_f · sqrt(1 + η_f Z² / 137²), η_f = −1.308; (ii) introduces a mandatory low-N(E_F) stretched-exponential cutoff g(x) = exp[−α(1/x − 1)^β] with (α_7.12, β_7.12) = (0.08, 2.30) to suppress spurious T_c predictions of 7–60 K for non-superconducting metals (Cu, Ag, Au, graphite, insulators); (iii) introduces a class-indexed pairing scale Λ_E^Ni ≈ Λ_E^cup / 3 for bilayer nickelates; (iv) closes the d-class subset with an empirical Matthias band-filling factor f_v(v) plus McMillan prefactor κ_ep = 11.5 (Lu remains irreducible outlier; W, Ir over-predicted); and (v) explicitly places normal-state electrical resistivity ρ(T) out of scope. The five v1 named predictions (LuH₁₀ @ 170 GPa ≈ 200–250 K flagship, Hg1245/SrTiO₃, FeSe/BaTiO₃, YbH₉, SmH₉) and the 31-material master fit are unchanged. The repository contains the paper source, compiled PDF, and the two numerical folders that are directly cited: superconductivity_closure/ (Tc formula, candidate scans, P6/P7 validation, post-v1 refinement series P7.5–P7.12) and liquid_viscosity/ (η/s bound recovering the Kovtun-Son-Starinets floor).