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Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps
Jonathan Washburn, Megan Simons
We recover a shared constitutive generator from equilibrium locations on weighted graphs. For an even log-coordinate potential with positive curvature, the complete two-site…
d'Alembert's Functional Equation and a Globally Convex Free-Action Principle on Positive Paths
Sebastian Pardo-Guerra, Jonathan Washburn
We study the kinetic action that d'Alembert's functional equation induces on positive paths in $\Rplus$, and prove it strongly convex. Calibrated d'Alembert forces the cosh cost $\…
Reciprocal Convex Costs for Ratio Matching: Functional-Equation Characterization and Decision Geometry
Jonathan Washburn, Amir Rahnamai Barghi
We study ratio-induced mismatch costs of the form , built from positive scale maps and and a penalty $J:(0,\infty…
The Coercive Projection Theorem for Canonical Reciprocal Costs
Jonathan Washburn, Amir Rahnamai Barghi
We develop a finite-data framework for certifying \emph{zero-defect} (neutral) configurations of positive vectors under the canonical separable reciprocal cost. We show that this s…