Presentation Independence of Ambient Adjoint Cartier Algebras

Let R=S/I be an integral algebra of finite type over a perfect field of characteristic p>0, with S polynomial and I of height c. We give a direct proof that restriction to R of degree-e Cartier maps with coefficients in I^{c(p^e-1)} is independent of the polynomial presentation, in every degree. A dummy-variable coefficient identity and common graph presentations compare arbitrary polynomial embeddings. Ideal-pair twists are independent of ambient lifts. The resulting Cartier algebras and their test ideals localize and glue without a Q-Gorenstein assumption. We explain the established comparison with Mather-Jacobian multiplier ideals for each fixed rational-exponent pair over an algebraically closed characteristic-zero field, after reduction to sufficiently general closed fibres. Source context: Ishii's Problem 2.15 in the AIM workshop Relating test ideals and multiplier ideals (August 2011), frozen Hugging Face record AIM-ALGEBRAIC_GEOMETRY-0289 in ulamai/UnsolvedMath v1.6.0. The ambient construction and characteristic-zero comparison are prior work of Takagi, Smolkin, Eisenstein and Ein-Ishii-Mustata and are explicitly credited. No pure-Mather theorem, all-small-prime resolution equality, imperfect-base generalization or whole-source closure is claimed. The original source record is not counted as fully resolved. Exact standard-library Python regression code accompanies the written proof. This English preprint is AI-assisted, originating-researcher self-audited and unrefereed. Novelty remains undetermined after bounded primary-source search; no independent human review, proof-assistant verification or absolute-priority claim is made.