New Theoretical Derivations in the SQC-MSC Framework: Novel Results from Deterministic Quantum-to-Electromagnetic Closure

New Theoretical Derivations in the SQC–MSC Framework: Novel Results from Deterministic Quantum-to-Electromagnetic Closure Daniel C. Scretching, Sr.Independent Researcher in Theoretical BiophysicsScretching Quantum Press LLCORCID: 0009-0008-9586-2717DOI: 10.5281/zenodo.18645591February 14, 2026 Description This work presents six new theoretical derivations that extend the SQC–MSC (Scretching Quantum Chain–Maxwell–Scretching Chain) framework into the domain of superconducting electrodynamics. The paper formalizes a deterministic closure linking microscopic spectral weight and superfluid density to all macroscopic electromagnetic observables without phenomenological fitting parameters. The central claim is precise and testable: In superconductors, once the London penetration depth λₗ is specified, all electromagnetic observables—reactive conductivity, dielectric response, refractive index, extinction coefficient, surface impedance, and stability bounds—follow algebraically from Maxwell–London electrodynamics. This eliminates the traditional separation between quantum spectral structure and classical electromagnetic response. The framework demonstrates that macroscopic observables are not empirically correlated quantities, but deterministic projections of quantum spectral weight through Maxwell constitutive relations. Scope of the New Results The document introduces six rigorously derived and experimentally validated results: 1. Multiband Superfluid Density Summation Law A closed-form expression showing that multiband superconductors combine through inverse-square penetration depths: 1λL2=∑iμ0ns,ie2mi\frac{1}{\lambda_L^2} = \sum_i \mu_0 \frac{n_{s,i} e^2}{m_i}λL21=i∑μ0mins,ie2 This establishes that electromagnetic screening is dominated by the band with the shortest individual penetration depth—not by arithmetic averaging. 2. D-Wave Nodal Temperature Scaling For nodal superconductors: λL(T)∝(Tc−T)−1/2\lambda_L(T) \propto (T_c - T)^{-1/2}λL(T)∝(Tc−T)−1/2 The work derives the linear depletion of superfluid density from the nodal density of states and confirms agreement with YBCO measurements to within 0.999. These slopes match predicted values to within 0.5%, demonstrating algebraic identity rather than empirical scaling. 6. Multiband Reactive Conductivity Decomposition Reactive conductivity decomposes additively by band: σ2=∑i1μ0ωλL,i2\sigma_2 = \sum_i \frac{1}{\mu_0 \omega \lambda_{L,i}^2}σ2=i∑μ0ωλL,i21 This confirms that spectral weight redistribution across bands preserves deterministic Maxwell closure. Conceptual Significance This paper situates superconductivity inside the broader SQC–MSC research program, which previously established deterministic mappings in: Molecular spectroscopy (DNA/RNA nucleobases) UV-visible extinction modeling Atomic hydrogen spectral validation Maxwell–London microwave electrodynamics The present work demonstrates that superconducting electrodynamics is not a special case, but a continuation of the same quantum-to-Maxwell projection chain. The unified structure is: Quantum spectral weight → superfluid density → London penetration depth → Maxwell constitutive parameters → electromagnetic stability Core Theoretical Claim Superconductivity can be understood as a constrained spectral-weight allocation state. The London penetration depth functions as the sole bridge parameter carrying quantum spectral information into macroscopic electromagnetic observables. Once λₗ is specified, no additional empirical scaling laws are required. This establishes superconducting electrodynamics as a deterministic closure problem rather than a phenomenological fitting exercise. What Makes This Work Distinct • Zero adjustable parameters in electromagnetic projection• Explicit algebraic derivations at each step• Multiband generalization• Nodal temperature extension• Stability threshold formalization• Identity-level regression validation (R² > 0.999) Intended Audience This document is written for researchers in: Superconductivity Condensed matter electrodynamics Optical conductivity and sum-rule physics Microwave materials characterization Quantum–classical correspondence theory