Architectural Constraints for Ethical AI: The Cartesian Calculus

Axiomatic mathematical framework establishing ethical constraints for AI systems at the architectural level. Version 1-2 (November 2025) introduced three foundational axioms, the MIU formula, consciousness weighting methodology, and stated the Carter Stewardship Theorem as a conjecture. Version 3.1 (March 2026) advances the framework with updated canonical terminology (SAI replacing MIU), a four-step proof chain from computational complexity to physical energy cost via the Complexity Tax Theorem, the Contradiction Interaction Lemma (machine-checked in Lean 4, eleven theorems, zero sorries), the Erasure-Rate Lemma, and the Landauer-Carter Inequality. The Carter Convergence Theorem is proved via three independent methods.