Soft and Active Matter Physics: Amorphous Constraint Networks Near Jamming and Their Non-Equilibrium Active Response

Soft and active matter --- from rubber, gels, and colloidal glasses to bacterial suspensions, cytoskeletal networks, and molecular motors --- constitute the two frontier domains of "soft condensed matter physics" and "active matter physics." Standard physics treats them as distinct systems, each with its own models (polymer statistical mechanics, mode-coupling theory, Toner--Tu equations, Vicsek models). Energy-Efficiency Theory (EET) provides a unified constitutional answer rooted in the constraint-network framework. Soft matter is an amorphous constraint network with vertex density φ approaching but below the jamming threshold φ_J. All characteristic soft-matter phenomena --- weak elasticity, extremely slow relaxation, giant fluctuations, nonlinear response --- arise from the critical slowing-down of constraint-network dynamics as the spectral gap λ₁ → 0. Constitutionally, this is a dual-path crossover (kinetic η ≪ 1 + geometric φ → φ_J), not the traditional single-axis "jamming → glass" paradigm. Active matter is the same constraint network maintained far from equilibrium by sustained external energy injection, operating as a non-equilibrium steady state (NESS). Each active unit consumes externally supplied free-state energy, converting it into directed Arrhenius constraint transitions (self-propulsion), sustaining the network in perpetual oscillation between the η > 1 (Se) and η < 1 (Ben) phases. Active matter is pre-life physics --- it possesses active maintenance but lacks informational template inheritance, reproduction, and Adjudicate budget auditing. Seven constitutional propositions anchor the entire field: P1: Soft matter is a constraint network near jamming --- the η-φ two-dimensional phase space replaces single-axis jamming. P2: Elasticity is constraint-network elastic inertia --- entropic elasticity arises from the thermodynamics of constraint-edge-weight distributions, with a first-principles derivation of G' = ν kT directly from Arrhenius transition microphysics. P3: Viscoplasticity is plastic inertia accumulation --- yield, creep, and aging are different manifestations of the monotonic growth of ζ(t), with the constitutional clarification that rejuvenation restores I_elastic, not reverses C(t). P4: The glass transition is constraint jamming --- a continuous kinetic arrest (λ₁ → 0 but λ₁ > 0 always), not a thermodynamic phase transition, with the Kauzmann paradox constitutionally resolved through the extrapolated-zero nature of T_K, and Angell fragility derived as the sub-linear cooperative amplification of Arrhenius energy barriers. P5: Gelation is the percolation transition of the constraint graph --- the L_rw spectral gap λ₁^rw jumps from zero to a positive value, with Capture as the dominant microscopic operation and the full-cost inverse-entropy accounting table constitutionalizing the irreducible cost of every crosslink formation. P6: Active matter is the NESS of a constraint network under external energy injection --- the constitutional distinction between wet and dry active matter (Ξ_wet criterion) unifies generalized Navier--Stokes and Toner--Tu descriptions under a single framework. P7: Motility-induced phase separation (MIPS) is Ben--Se active-density coupling --- the Ben--Se phase diagram in the η_active-φ plane provides a constitutional framework for active phase separation. This REAL covers: the constraint-network first-principles derivation of G' = ν kT; the unified constraint-network form of eight classical viscoelastic constitutive models; gelation percolation scaling laws with the Capture-dominance operational criterion; the five-channel complete signature tables for six core phenomena; the Angell fragility classification derived from cooperative Arrhenius amplification; the five-component full-cost inverse-entropy accounting of crosslink formation; the active stress tensor and generalized Navier--Stokes equations; the wet/dry active matter constitutional bifurcation; the Toner--Tu equation in constraint-network correspondence; active nematic topological defects and SOC active criticality; active turbulence scaling laws and non-Kolmogorov cascades; MIPS Ben--Se active-density coupling; active viscoelasticity and complex fluids; biolubrication and cytoskeletal constraint-network mapping; the constitutional measurement framework for eight core experimental techniques; and the EET constraint-network resolution of approximately twenty core controversies in soft and active matter physics --- all as structural consequences of constraint-network dynamics. This REAL is drafted simultaneously with Fluid Mechanics REAL v1.0, with which it shares M&F v3.2 and Space v3.3 as direct upstream sources. Cross-REAL alignment is ensured in the active stress modification of Navier--Stokes, active turbulence scaling laws, viscoelastic parametrization, and gel--fluid transition regions. Keywords: Soft matter physics; Active matter physics; Constraint networks; Jamming transition; Self-organized criticality (SOC); Arrhenius kinetics; Non-equilibrium steady states (NESS); Glass transition; Gelation; Active turbulence; Motility-induced phase separation (MIPS); Topological defects; Viscoelasticity; Energy Efficiency Theory (EET)