Baris Basaran

Faruk Alpay, Baris Basaran

We study the observation congruences induced by rational polyhedral cones on vector-valued quantitative languages. The extreme rays of the dual cone define intrinsic covectors, and these covectors classify every incremental residual future by a finite sign cell: negative, tight, or positive along each extremal Farkas direction. The resulting carrier is the right-stable carrier of this cone-induced observation family, whose source is canonical: the restricted covector geometry of the order cone on the residual span of the language. We organize this construction through an observation-refinement correspondence, a cone-refinement calculus, and a separation between the qualitative conic observation quotient and the numerical residual carrier needed for potential certificates. A bounded-horizon fragment is fully computable by enumeration of accumulated futures, and reproducible evaluation runs show how the conic layer detects qualitative obstruction cells before numerical refinement.

Faruk Alpay, Baris Basaran

Biprofile deviation logic models strategic social choice states as pairs $(R,P)$, where $R$ is the true profile used for welfare comparisons and $P$ is the submitted report profile used by the rule. Coalition modalities replace only the reports of the coalition, and their relations satisfy the fixed law $E_C \circ E_D = E_{C \cup D}$. The paper proves soundness and completeness of $H_{\mathrm{bp}}$ for the abstract frame class $\mathrm{Dev}(N)$, with the reverse-composition midpoint displayed inside the canonical proof. It then separates abstract $\mathrm{Dev}(N)$-components from genuine report-coordinate products by coordinate separation. On the social-choice side, the classical facts supply the source notions; the paper-specific contribution is the audit layer for representation changes: typed manipulation witnesses, a boundary-row theorem for off-domain extensions, and a factor-closure criterion for public deletions. The ancillary material contains the input formats, an executable certificate checker, Lean and Alloy companions for the finite relational lemmas and update patterns, recorded run logs, and checksums.