The Relational Calculus for Green AI

Abstract

This project is the public home of Relational Calculus, a meta‑mathematical framework that replaces the brute‑force logic of absolute‑scale computation with dimension‑less, capacity‑anchored blueprints. At its heart lies a simple but radical axiom: every system possesses an intrinsic maximum—a “North Star”—and by expressing all observations as fractions of that limit, complexity collapses, efficiency soars, and transfer across domains becomes automatic. The collection gathers the complete stack: the foundational theoretical paper, a ready‑to‑run Relational Decoder (an open‑source algorithm that probes any black‑box function and extracts its dimensionless template), and five applied case studies that prove the principle in wildly different arenas—number theory (deterministic prime pair lattices), symbolic artificial intelligence (a geometric chess engine that exhibits emergent strategy with zero domain knowledge, gaining 90%+ efficiency), high‑energy physics (scale‑invariant jet tagging that transfers zero‑shot across collision energies with +14.5% AUC), quantum chemistry (80% error reduction in cross‑molecule transfer), and precision oncology (a lightweight XGBoost that achieves 98.4% cross‑species diagnostic accuracy under a 70% hardware‑signal collapse, completely erasing batch effects). A companion paper extends the logic to large language models, proposing Relational‑CoT as a drop‑in replacement for resource‑intensive chain‑of‑thought reasoning. Every work converges on the same empirical signature: >90% reduction in computational cost, genuine zero‑shot generalization across scales and species, and the proof that Green AI is not an aspiration but an engineering reality. An integrated STEM curriculum for ages 10–14 ensures that the relational lens is taught before the continuous one, inoculating the next generation against the wasteful “math of deviation.” All code, data, and executable papers are open‑source. The project is intended not as a scholarly gesture but as an enablement instrument for the industrial shift from the Age of Fire—where more compute meant more extraction—to the Era of Relation, where measuring how full a system is replaces the endless pursuit of how much.