What question did this study set out to answer?

This research aims to establish a formal arithmetic system that preserves provenance in arithmetic operations.

February 10, 20260 citationsOpen Access

Provenance-Preserving Arithmetic

Key Points

This research aims to establish a formal arithmetic system that preserves provenance in arithmetic operations.
Developed a formal arithmetic system using Laurent polynomial algebra.
Implemented operations that maintain full information retention during calculations.
Created a Python library (composite_lib.py) to facilitate the arithmetic and its applications.
Introduced a universal calculus machine enabling exact symbolic differentiation and integration.
Showed that all operations are reversible, avoiding information loss during calculations.
Provided machine learning demos and a comprehensive test suite validating over 175 tests.

Abstract

Composite Calculus is a formal arithmetic system built on Laurent polynomial algebra where every operation preserves full provenance — no information is ever lost, even in traditionally destructive operations. The system models numbers as coefficient-carrying objects across a dimensional scale, enabling reversible computation and exact symbolic differentiation, integration, and multivariate calculus through simple algebraic manipulation. Includes a Python library compositeₗib. py, a comprehensive test suite (175+ tests), machine learning demos (MNIST and Transformer learning-rate finders), and foundational papers. Key features: Provenance-preserving arithmetic with full reversibility Universal calculus machine via dimensional coefficient algebra Constructive infinitesimal system — fully computable, no abstract foundations required Multivariate extensions for partial derivatives and PDEs Repository: https: //github. com/tmilovan/composite-machine

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