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 three 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 λJ 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) 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. Two applications—to existential-risk assessment and to technological catch-up—are given with explicit statements of scope. The contribution lies in the unifying organization, the identity proof relating the Jeans and screening lengths, and the explicit demarcation of applicability; the limit theorems and field-theoretic Green’s functions employed are established results.
Qinfu Li (Sat,) studied this question.