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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18774109 |
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Table of Contents:
- <h1>THE SCRETCHING SUPERCONDUCTOR CHAIN (SSC)</h1> <p><strong>Stiffness-Centered Reorganization of Canonical Theory with Empirical Scaling Relations and Algebraic Invariants</strong> <em>Corrected Edition with Full Numerical Validation</em></p> <h2>Description</h2> <p>This work presents a systematic reorganization of canonical superconducting electrodynamics around a single electromagnetic primitive — the <strong>superconducting stiffness</strong> f_SC ≡ 1/(μ₀λ²) = n_s e²/m_e — designated the Scretching Superconductor Chain (SSC). Rather than introducing new fundamental physics, the SSC framework recasts the five landmark theoretical frameworks of superconductivity (London, Ginzburg-Landau, BCS, Abrikosov, and Josephson) into a unified stiffness-centered algebraic structure, exposing scaling relationships and invariant identities not previously consolidated across the literature.</p> <p>The work is motivated by recent stability analyses demonstrating that <strong>phase rigidity</strong>, not pairing energy alone, is the binding constraint on achievable critical temperatures — a finding that privileges stiffness as the natural organizing quantity for superconductor classification and comparison.</p> <h2>Key Contributions</h2> <p><strong>Algebraic Invariants.</strong> The SSC chain yields several exact identities — including f_SC ξ² κ² = 1/μ₀ and f_SC · ξ = 1/(μ₀κλ) — that follow by construction from the definitions of f_SC and the Ginzburg-Landau parameter κ. These are verified at 0.00% deviation across all twelve benchmark materials, serving as rigorous internal consistency checks on the entire framework.</p> <p><strong>Empirical Scaling Relation.</strong> The product f_SC · ξ · T_c ≈ (2.78 ± 0.25) × 10¹⁴ K·A²s²kg⁻¹m⁻² is demonstrated to hold within 9% for four conventional Type I superconductors (Sn, In, Pb, Hg), consistent with the BCS structural result n_s ∝ 1/v_F. The analysis is transparent about the empirical character of this relation and the dataset scope required to establish it as a general invariant.</p> <p><strong>Gap Correlation.</strong> The dataset relation Δ(0) ∝ C·√f_SC·F(λ_ep) is validated to 1.3% for Pb with explicit strong-coupling correction applied, and is correctly characterized as a fit to conventional superconductors rather than a microscopically derived result.</p> <h2>Methods and Validation</h2> <p>Material parameters — penetration depth λ, coherence length ξ, and critical temperature T_c — were compiled from authoritative sources including Tinkham (1996), Orlando & Delin (1991), Basov & Timusk (2005), and Buzea & Robbie (2005), supplemented by NIST CODATA 2018 fundamental constants throughout. Full uncertainty propagation was carried forward using the dominant relation δf_SC/f_SC = 2δλ/λ, yielding realistic propagated errors of 15–35% reflecting the precision limits of tabulated experimental parameters. Every derived relation was independently verified by triple-checking dimensional analysis and cross-validation against primary experimental literature.</p> <h2>Significance</h2> <p>The SSC framework provides the field with a <strong>unified classification metric</strong> for comparing superconductors across elemental and alloy systems, a <strong>transparent uncertainty accounting</strong> methodology, and a structured map of where stiffness-centered relations hold predictively and where they require correction — particularly in exotic, unconventional, or strongly-correlated materials systems. The corrected edition strengthens the work's intellectual honesty by precisely delineating algebraic identities (which hold by definition), empirical scaling relations (which hold within stated uncertainty for the tested dataset), and microscopically derived results (which require explicit coupling corrections).</p> <p><em>Published by Scretching Quantum Press LLC, Wyoming, USA | DOI: 10.5281/zenodo.18774109 | ORCID: 0009-0008-9586-2717</em> <em>Submitted: February 24, 2026</em></p>