G3 × Condensed Matter: Elastic-Mechanical Resolution of Quantum Critical Phenomena

The strongly coupled gapless states emerging at continuous quantum phase transitions constitute a central problem in condensed matter physics that has long resisted a first-principles resolution. No low-energy effective theory can be written for these states; why the gap closes at the critical point, why the order parameter deviates from the Landau paradigm, and where generalised symmetries come from — these questions have been attributed in modern theories to statistical effects of quantum fluctuations or to the algebraic structure of topological order, yet their physical roots have remained unrevealed. The G3 series provides a unified answer within the framework of the Gluon Elastic Lattice Theory (GELT): space is a nonlinear elastic medium whose constitutive relation K(ρ)=K₀1+ηθ produces a stiffness softening at the critical density, with the hardening coefficient η=0.573, driving all the core phenomena of gapless states. The series consists of four papers — G3.1 proves that gap closure is a direct mechanical consequence of stiffness softening; G3.2 proves that the order parameter jumps from a scalar to a tensor, because the softest modes near the critical point are shear–compression mixing rather than pure compression; G3.3 proves that generalised symmetries (1-form symmetries, conserved 2-form currents) are an algebraic necessity of the liberation of the shear degrees of freedom at the stiffness zero; and G3.4 explicitly verifies the correspondence between the conserved 2-form current and elastic vortex rings in the Kitaev model on a cubic lattice. All four papers emerge from one and the same nonlinear elastic constitutive relation, requiring neither a quantum-fluctuation hypothesis nor any free parameters.