Charge and Spin Response of One-Dimensional Electron Delocalization Relation Networks: Theoretical Prediction, Independent Verification, and Boundary Correction Based on Relation Networks

This paper reports a complete theory-test-correction cycle for the Electron Delocalization Relation Network (EDRN) framework, together with a cross-framework independent verification collaboration. Starting from a relation-network perspective, one-dimensional conjugated molecules are defined as EDRNs. Under a critical-regime assumption the framework predicts a charge-compressibility scaling exponent α = 1.75 with chain length L. Density matrix renormalization group (DMRG) calculations on the one-dimensional half-filled Hubbard model (L = 20 to 200), using a two-sector compressibility scheme based on particle-hole symmetry, instead show the charge gap tending to a constant ΔE ≈ 1.35t and a fitted exponent α ≈ -0.03: the original charge-sector prediction fails, and the system is identified as a Mott insulator whose charge degree of freedom is frozen by the gap. The critical behaviour is relocated to the spin sector, where the spin gap Δs is found to decay as 1/L (fitted exponent -1.05 ± 0.03, R² = 0.996), confirming gapless critical behaviour. Three predictions are then tested. Prediction 1 (an A(C) relation) is withdrawn after Drahos identified variable confounding between C and L on a linear chain, and awaits a fixed-L multi-topology retest. Prediction 2 is shown by a decisive L-scan to be a finite-size effect. Prediction 3, αcharge + αspin = -1, is supported by four U-scan datasets and one L-scan and is confirmed as the numerical manifestation of spin-charge separation in the Mott insulator, with an exact Bethe-ansatz correlation-length estimate ξc ≈ 380 at U = 1. Sultanov's independent TAT-Defense blind test detects a structural anchor consistent with the DMRG convergence boundary and passes a U = 2 positive control. Three independent diagnostic frameworks (independent DMRG, exact-solution anchors, TAT diagnostics) converge without pre-set conclusions. An open collaboration between the authors; final technical review by R. Drahos.