# Abstract and publication identity

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**Abstract.**

Which configuration probabilities can be assigned to a wavefunction consistently across different physical controls? We consider a single projective density assignment in nonrelativistic Bohmian mechanics, with twice continuously differentiable dependence on the wavefunction in a specified Schwartz-space sense. We prove that consistency with Schrödinger evolution and the guidance current for local one-body scalar potentials forces this assignment to be the Born density when the fixed pair interactions connect the particles and have nonzero mixed spatial derivatives. The argument extracts statistical identities from coordinate conjugations of the fixed interaction; it does not require implementing additional many-body potentials. All translates of one real Schwartz profile with nonzero integral suffice for each particle. We also give an effective-spin extension, a sector-preserving identical-particle refinement, and a separate characterization from binary-flag heredity. Weak continuity under specified state approximations extends the results across nodes. The theorem makes precise a previously proposed universal-equivariance characterization and reduces its control requirements. Its statistical consistency premise is explicit. Consequences for apparatus records are obtained under the usual joint-preparation and implemented-coupling assumptions. 



**Keywords:** quantum equilibrium; Bohmian mechanics; control consistency; probability assignments; interacting systems; conditional probabilities.