Errata and Dimensional Self-Consistency: Corrected α–κ Coupling Relation in the Cognitive Phase Space Unified Theory

This manuscript formally resolves a dimensional inconsistency present in the cross-scale coupling relation originally postulated in the founding framework of the Cognitive Phase Space Unified Theory. The naive reciprocal relation α = κ⁻¹ is mathematically invalid due to a fundamental dimension mismatch: the microscopic cognitive-quantum coupling κ carries physical dimensions [E·L·Info⁻¹], while the macroscopic cosmological cognitive-gravitational coupling α is required to be dimensionless. Through rigorous Kaluza–Klein dimensional reduction over the five Planck-scale compactified internal cognitive dimensions of the nine-dimensional cognitive fiber bundle, this work derives the unique dimensionally closed correction: α = κ/(ℏc). The product ℏc = E_P·l_P constitutes the only fundamental dimension-[E·L] universal invariant available in quantum-gravitational physics to mediate cross-scale dimensional normalization. The corrected relation fully preserves the core physical intuition of the original framework while eliminating the only formal mathematical inconsistency in the axiomatic system. Order-of-magnitude numerical evaluation yields α ∼ 3×10⁻⁵, consistent with astrophysical dark energy observational bounds.