The Coercive Projection Theorem for Canonical Reciprocal Costs
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arXiv
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| Format: | Preprint |
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2026
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| author | Washburn, Jonathan Barghi, Amir Rahnamai |
| author_facet | Washburn, Jonathan Barghi, Amir Rahnamai |
| contents | 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 scalar cost is characterized among non-constant continuous costs by the Recognition Composition Law together with a local quadratic calibration at balance; in particular, reciprocity symmetry and the normalization at the neutral point follow from the composition law. Under a conservation constraint and short-window observations of a rational (finite--state) signal class, we construct a canonical decision procedure that is \emph{locally maximal on the identifiability locus} among all sound procedures: any sound rule that resolves a datum must agree with the canonical output, and cannot resolve strictly more cases.
The method is organized as $Φ^\ast=A\circ B\circ P$: the projection/coercivity core is forced by the canonical-cost axioms, while the aggregation/reconstruction step is specified on a non-degenerate identifiability locus (e.g.\ a Hankel invertibility condition). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Coercive Projection Theorem for Canonical Reciprocal Costs Washburn, Jonathan Barghi, Amir Rahnamai Optimization and Control Primary 90C25, Secondary 47H05, 94A12 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 scalar cost is characterized among non-constant continuous costs by the Recognition Composition Law together with a local quadratic calibration at balance; in particular, reciprocity symmetry and the normalization at the neutral point follow from the composition law. Under a conservation constraint and short-window observations of a rational (finite--state) signal class, we construct a canonical decision procedure that is \emph{locally maximal on the identifiability locus} among all sound procedures: any sound rule that resolves a datum must agree with the canonical output, and cannot resolve strictly more cases. The method is organized as $Φ^\ast=A\circ B\circ P$: the projection/coercivity core is forced by the canonical-cost axioms, while the aggregation/reconstruction step is specified on a non-degenerate identifiability locus (e.g.\ a Hankel invertibility condition). |
| title | The Coercive Projection Theorem for Canonical Reciprocal Costs |
| topic | Optimization and Control Primary 90C25, Secondary 47H05, 94A12 |
| url | https://arxiv.org/abs/2603.20205 |