A single mathematical operator can derive every rule of formal logic and the core mechanics of calculus at the same time.
April 29, 2026
Original Paper
Propagation Logic: A Single-Operator Foundation for Logic and Calculus
SSRN · 6443722
The Takeaway
Formal logic and continuous calculus have traditionally lived in separate worlds with different rules. Relational propagation unifies these fields by showing they are both special cases of one underlying dynamical mechanism. This single operator handles propositional, modal, and probabilistic logic without needing separate frameworks for each. It simplifies the foundation of mathematics into a unified theory of how information travels. This discovery could allow for a new type of computer architecture that handles discrete logic and continuous physics with the same hardware.
From the abstract
Propagation Logic (PL) is a formal system built on a single dynamical mechanism: as relational patternings propagate they accumulate a loaded history relative to the gradient fields available in their context, and this loaded history sets the gradient demands for all further propagation. Patterns with less loaded history-simpler structures maximally supported by available gradients-propagate faster. As complexity builds through propagation it generates relational drag: the gradient demands of co