We created a proprietary graph-based algorithm for deep search control. Just as SEO became the standard for optimizing traditional search engines, GEO emerges as the foundational methodology in a world where AI has become the primary reference for search. GEO is no longer just a set of tips on how to use AI, but a core methodology of application, defining how content, data, and strategies must be structured to achieve relevance and positioning in generative engines.

"GEO as a Deterministic Architecture for Generative Optimization: Foundations in Entropy, Semantics, Probabilistic Graphs, and Structural Invariance with a Metric of Machine Readership"

The evolution of information retrieval has shifted from heuristic practices to algorithmically grounded frameworks capable of guaranteeing convergence, semantic coherence, and scalability across multilingual domains. This research introduces Generative Engine Optimization (GEO) as a mathematically rigorous paradigm that formalizes information flow using probabilistic graph theory, entropy reduction, and structural invariance principles. Unlike heuristic SEO, GEO operates deterministically, ensuring reproducibility and stability under perturbations.The contributions of this study are threefold. First, it conceptualizes generative engines not as retrieval mechanisms but as constructive dynamical systems embedded in algebraic manifolds. Second, it develops a cross-platform observational model, based on measurable scientific identifiers and digital traces, to assess the robustness and dissemination of knowledge across heterogeneous environments. Third, it proposes a novel metric for “machine readership”, quantifying the extent to which generative models consume and propagate knowledge from distributed sources.Together, these contributions establish GEO not merely as an optimization technique but as a general theory of algorithmic determinism in the age of artificial intelligence.4CO holds a registered patent and DOI (DOI: 10.5281/zenodo.17074263), published on Zenodo, indexed on ResearchGate, and linked to the ORCID of researcher Mariana Imbper, CTO of 4CO.Keywords: Generative Engine Optimization (GEO); SEO for AI; AI-powered search optimization; generative SEO; deep search; algorithmic optimization; entropy reduction; probabilistic graph theory; semantic convergence; structural invariance; machine readership metrics; algorithmic determinism; applied artificial intelligence; generative indexing; semantic search.

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