What question did this study set out to answer?

The aim is to derive a closed-form T_c expression for superconductivity that incorporates multiple material families and addresses specific unresolved issues.

April 25, 2026Open Access

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

Key Points

The aim is to derive a closed-form T_c expression for superconductivity that incorporates multiple material families and addresses specific unresolved issues.
Developed a closed-form T_c expression calibrated on a subset of five d-metals.
Extended the framework to include cuprates, MgB₂, hydrides, and A15 materials.
Introduced relativistic corrections and new scaling factors to enhance model predictions.
Achieved a master fit yielding r(log T_c) = 0.875 and RMS_log = 0.346.
Structural coefficients κ_TGP ≈ 2.012 and β ≈ 2.527 were derived for various coupling mechanisms.
Predicted five materials, including LuH₁₀ at high pressures, continue to show promise without notable changes.

Abstract

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 Tc 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 Tc) = 0. 875, RMSₗog = 0. 346. Structural coefficients κTGP ≈ 2. 012 (spin-fluctuation coupling), β ≈ 2. 527 (magnetic blocking) and αPB ≈ 0. 2887 μB⁻² (Abrikosov-Gorkov pair-breaking) are reported alongside the cross-sector universal constant cTGP = 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 Af (Z) = Af · sqrt (1 + ηf Z² / 137²), ηf = −1. 308; (ii) introduces a mandatory low-N (EF) stretched-exponential cutoff g (x) = exp−α (1/x − 1) ^β with (α₇. 12, β₇. 12) = (0. 08, 2. 30) to suppress spurious Tc predictions of 7–60 K for non-superconducting metals (Cu, Ag, Au, graphite, insulators) ; (iii) introduces a class-indexed pairing scale ΛENi ≈ ΛEᶜup / 3 for bilayer nickelates; (iv) closes the d-class subset with an empirical Matthias band-filling factor fᵥ (v) plus McMillan prefactor κₑp = 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: superconductivityclosure/ (Tc formula, candidate scans, P6/P7 validation, post-v1 refinement series P7. 5–P7. 12) and liquidᵥiscosity/ (η/s bound recovering the Kovtun-Son-Starinets floor).

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

Key Points

Abstract

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