The Law of Recursion as Foundational Cosmology: Nucleosynthetic Necessity and the Material Identity of the Triadic Minimum

Paper 1 of 8: The Law of Recursion Applied Across Domains — Don L. Gaconnet, LifePillar Institute for Recursive Sciences

This paper applies the Law of Recursion to cosmology and demonstrates that the nucleosynthetic sequence Hydrogen → Carbon → Oxygen is not a historical contingency but a thermodynamic necessity. The triadic minimum required for any recursive architecture demands exactly three functional roles: medium (relational ground), structure (scaffold), and boundary (selective membrane). Only three elements fulfill these roles: Hydrogen as medium, Carbon as structure, and Oxygen as boundary.

The argument proceeds in four stages: (1) the triadic minimum of the Echo-Excess Principle requires exactly three functional components; (2) these functional roles map uniquely onto material elements; (3) stellar nucleosynthesis necessarily produces these elements in the required sequence; (4) no alternative elemental triad satisfies the functional requirements.

The universe does not merely permit recursive architecture — it requires it. The material conditions for life are structural necessities derivable from first principles.
Author: Don L. Gaconnet | ORCID: 0009-0001-6174-8384 | DOI: 10.17605/OSF.IO/MVYZT

Keywords:

law of recursion, nucleosynthesis, cosmology, triadic minimum, hydrogen, carbon, oxygen, cosmological necessity, Echo-Excess Principle, material identity, stellar nucleosynthesis, Big Bang, triple-alpha process, recursive sciences, Don Gaconnet

Categories:
Cosmology, Theoretical Physics, Philosophy of Science, Astrophysics