Adopting the normalized d'Alembert degree-two closure (RCL) to induce real-valued costs X_ω = J(r_ω), multinomial counting and convex duality recover the finite-state Gibbs weights together with the identity F_R(q) - F_R(p) = T_R D_KL(q || p).
American Mathematical Society, 2000
2 Pith papers cite this work. Polarity classification is still indexing.
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For heterogeneous power-p pseudospherical scoring rules with d ≤ 4, the True-KL0 property R(M,p,d) < 1 holds for all M > 1, establishing unconditional DSIC via a Prekopa-based log-concavity argument on the loss integral.
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A Finite-State Gibbs Construction from a Recognition Cost
Adopting the normalized d'Alembert degree-two closure (RCL) to induce real-valued costs X_ω = J(r_ω), multinomial counting and convex duality recover the finite-state Gibbs weights together with the identity F_R(q) - F_R(p) = T_R D_KL(q || p).
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Honest Reporting in Scored Oversight: True-KL0 Property via the Prekopa Principle
For heterogeneous power-p pseudospherical scoring rules with d ≤ 4, the True-KL0 property R(M,p,d) < 1 holds for all M > 1, establishing unconditional DSIC via a Prekopa-based log-concavity argument on the loss integral.