The Law of Recursion: A First Principle of Systemic Exchange

The Law of Recursion: A First Principle of Systemic Exchange — Don L. Gaconnet, LifePillar Institute for Recursive Sciences
This paper introduces the Law of Recursion as a first principle governing all active systemic exchange. The law states that any process of transmission, transformation, or generation within or between systems requires a mandatory traversal across a seven-node topological path: interior (1a), membrane (M1), exterior (1b), shared substrate (S), exterior (2b), membrane (M2), interior (2a). Each traversal comprises six discrete transitions, and each completed traversal rewrites the architecture it travels through such that subsequent traversals encounter altered conditions. Full recursive coupling requires three traversals (18 transitions): signal, response, and coupled action.

The law operates in two expressions: internal recursion between sub-components of a single system, and external recursion between distinct systems through a shared substrate. External recursion always presupposes internal recursion.

The law is subjected to six falsification tests drawn from quantum mechanics, crystallography, cellular biology, nuclear physics, quantum field theory, and astrophysics. All six tests fail to falsify the law. The falsifiability criterion is established: the absence of recursion corresponds to inert matter in its ground state, which is empirically observable and structurally distinct from all active systems.

The Law of Recursion is the foundational principle from which the Echo-Excess Principle, the Universal Five-Operation Generative Cycle, the Law of Obligated Systems, and Cognitive Field Dynamics are derived as downstream operations.

Author: Don L. Gaconnet
ORCID: 0009-0001-6174-8384
DOI: 10.17605/OSF.IO/MVYZT
Institution: LifePillar Institute for Recursive Sciences
Keywords:
law of recursion, first principle, seven-node topology, recursive exchange, rewriting principle, membrane traversal, falsifiability, inert matter, systems theory, recursive sciences, structural coupling, generative systems, Don Gaconnet, LifePillar Institute
Categories:

Theoretical Physics, Mathematical Physics, Philosophy of Science, Complex Dynamical Systems, Computational Mathematics