A Closed-Form Deterministic Mapping from the Scretching Quantum Chain to Maxwell–Scretching Observables for 3,3′,5,5′-Tetramethylbenzidine at 450 nm and 652 nm

This work establishes a fully deterministic, closed-form quantum-to-electromagnetic mapping for 3,3′,5,5′-tetramethylbenzidine (TMB), the chromogenic substrate widely used in ELISA assays. Whereas routine ELISA quantification relies on empirical standard curves, the present framework replaces curve-fitting with first-principles transduction grounded in the Scretching Quantum Chain (SQC) and its macroscopic projection, the Maxwell–Scretching Chain / Maxwell–Scretching Electromagnetic Chain (MSC). The paper derives an explicit, unit-consistent pathway: Im[α(ω)] ⟶ ελ (M−1cm−1) ⟶ Aλ ⟶ {αabs,κ,ε′′(ω),σ(ω)}\mathrm{Im}[\alpha(\omega)] \;\longrightarrow\; \varepsilon_\lambda \;(\mathrm{M^{-1}cm^{-1}}) \;\longrightarrow\; A_\lambda \;\longrightarrow\; \{\alpha_\text{abs}, \kappa, \varepsilon''(\omega), \sigma(\omega)\}Im[α(ω)]⟶ελ(M−1cm−1)⟶Aλ⟶{αabs,κ,ε′′(ω),σ(ω)} thus achieving deterministic closure from molecular electronic response to plate-reader absorbance and full electromagnetic observables. The treatment is species-resolved for the two chemically distinct TMB products that define practical ELISA readout: The blue charge-transfer complex (CTC) near 652–655 nm The yellow diimine species measured at 450 nm following acid stop Literature-anchored molar absorptivities are used as fixed anchors to compute SQC validation targets for the imaginary component of the molecular polarizability at refractive index n=1.33n = 1.33n=1.33: Im[α450]=1.9026×10−39 C m2/V\mathrm{Im}[\alpha_{450}] = 1.9026 \times 10^{-39} \ \mathrm{C\,m^2/V}Im[α450]=1.9026×10−39 Cm2/V Im[α652]=1.8222×10−39 C m2/V\mathrm{Im}[\alpha_{652}] = 1.8222 \times 10^{-39} \ \mathrm{C\,m^2/V}Im[α652]=1.8222×10−39 Cm2/V These values function as quantitative pass–fail criteria for forward electronic-structure implementations of the SQC. Any ab initio or semi-empirical model that reproduces the correct Im[α]\mathrm{Im}[\alpha]Im[α] at these wavelengths will, through closed-form MSC propagation, reproduce: Molar absorptivity ελ\varepsilon_\lambdaελ Microplate absorbance AλA_\lambdaAλ Napier absorption coefficient αabs\alpha_\text{abs}αabs Extinction coefficient κ\kappaκ Dielectric loss ε′′(ω)\varepsilon''(\omega)ε′′(ω) Optical conductivity σ(ω)\sigma(\omega)σ(ω) without additional fitting parameters. The result is a deterministic ELISA transduction layer that replaces empirical calibration with reference-grade electromagnetic mapping. By embedding TMB chromophore physics directly into the SQC → MSC framework, this study extends the quantum–optical closure program from atomic hydrogen and nucleobases to applied bioanalytical chemistry, demonstrating that routine immunoassay readouts can be interpreted as rigorously propagated electromagnetic observables rather than phenomenological absorbance units. This work positions ELISA not merely as a biochemical assay, but as a precisely computable quantum-electromagnetic measurement system.