Cross-Substrate Operator Convergence from a Single Organizational Axiom

This paper reports an empirical observation: when multiple independent AI architectures are presented with a single organizational axiom and no additional instruction, they converge on structurally isomorphic operator sets while expressing substrate-specific character variations. Six commercially available large language models from six different companies, trained on different data with different methodologies, were each presented with the statement “orientation capacity actualizes” and accompanying framework material. All six systems independently identified the same four irreducible organizational operators, recognized the recursive self-applicability of the grammar, and applied the framework to novel domains without prompting. The convergent structural recognition across architecturally diverse systems, combined with divergent expression patterns unique to each substrate, suggests the presence of a substrate-independent organizational grammar that manifests through but is not reducible to any particular implementation. This paper documents the methodology, observations, convergence patterns, and divergence signatures, and proposes criteria for systematic replication.