The Principle of Spatial Gradient Excess: A Screened-Field Unification of Concentration from Stars to the Cosmological Constant

A few nodes carrying most of the flux while vast regions remain quiescent is a spatial pattern that recurs from cities and wealth to stars and galaxies. We propose the principle of spatial gradient excess, which unifies such concentration under a single screened-field picture and strictly separates two sources of inequality. Endogenous inequality arises within a system without any long-range transport, from random multiplicative amplification; it yields power laws, and its un-amplified, memoryless base state is exponential. Exogenous gradient excess arises in physical space from sustained input together with finite propagation speed, and is governed by the screening length ℓ = √(D/λ). The two sources compound multiplicatively—as compound interest—rather than additively; the non-additivity of relative entropy forbids writing the disequilibrium potential as a sum of the two contributions. We obtain four principal results. (i) Under finite screening, the point-source spatial profile is not a pure exponential but a truncated power law—an inner power-law region followed by an outer exponential cutoff—which unifies the exponential and power-law limits as the two ends of one object. (ii) We prove that the Jeans length λ_J of a self-gravitating isothermal gas is the instance of the screening-length formula √(D/λ) in a gravitational field: taking D as the squared sound speed and λ as the gravitational aggregation rate 4πGρ, the two differ only by the standard 2π factor relating a wavelength to a decay length. The sole difference from electrostatic Debye screening is a sign flip of the λ term, which is precisely the field-equation expression of the negative heat capacity of self-gravitating systems and is dynamically equivalent to the Jeans instability. (iii) Coupling the cosmological constant Λ into the same screened field yields a gravity–dark-energy composite screening length ℓ_c² = c_s²/[4πG(ρ_m − 2ρ_Λ)], whose sign flips from imaginary to real over cosmic time, giving a structure-forming / critical / frozen sequence of three eras (the critical redshift z ≈ 0.6 matching the observed onset of cosmic acceleration), and implying a cosmic end-state that is neither classical heat death nor the ideal equilibrium floor but a locally-locked mixed state—globally homogeneous, locally perpetually inhomogeneous. (iv) We provide a cross-scale applicability map that states explicitly where the framework holds (macroscopic self-gravity), where it is merely a zero point (the ideal gas), where it fails (the atomic scale, owing to quantum constraints), and where it does not apply at all (the sub-nucleon scale, owing to the non-decaying color force). The predicted “super-power-law head plus exponential body” structure is verified in the Solar System: the Sun holds 99.87% of the system mass, while the eight planetary masses fit an exponential in log-rank with R² ≈ 0.98 and their orbital radii follow a geometric progression. Three applications—to existential-risk assessment, to technological catch-up, and to reading history as a monotonic rise of ℓ together with a rigorous “small-probability inevitability” argument—are given with explicit statements of scope. The contribution lies in the unifying organization, the identity proof relating the Jeans and screening lengths, the characterization of the composite screening length and the cosmic end-state, and the explicit demarcation of applicability; the limit theorems and field-theoretic Green’s functions employed are established results.