Directed Acyclic Graph Information in Living Systems: Validation of Triadic and Higher-Order Metrics on Acute Myeloid Leukemia Networks

Context: This manuscript represents the empirical biology validation track of the Directed Acyclic Graph Interpretation (DAGI) research program at Whytics. It serves as a macroscopic biological counterpart to our previous noisy intermediate-scale quantum (NISQ) hardware validations, proving that the multiscale informational primitives of DAGI (Möbius cumulants and O-information) are domain-agnostic and robust enough to extract mechanistic structure from real-world living systems. Abstract: The Directed Acyclic Graph Informational (DAGI) framework proposes a Möbius-based decomposition of multivariate information that treats higher-order correlations as real, composable resources. While previously stress-tested on synthetic models and quantum hardware experiments inspired by Quantum Darwinism, here we test DAGI on highly noisy biological data by combining it with the TRIM algorithm for mining triadic interactions in gene regulatory networks. Using Acute Myeloid Leukemia (AML) transcriptomic data, we show that DAGI's irreducible triadic information (f₃) reproduces TRIM's information-centric statistics while remaining orthogonal to network topology, both in the heavily selected triads of the original run and in new robustness analyses on an independent AML cohort (TCGA-LAML). Moving beyond three variables, we define a practical reliability frontier for finite biological data: the higher-order raw Möbius terms f₄ and f₅ fail to discriminate biologically meaningful structure at current sample sizes, whereas aggregate O-information (Ω) reliably separates tetrads and pentads that differ in construction scheme, underlying triadic significance, and regulatory class. Regulators stratified by their mean Ω form three informational archetypes whose target modules are indistinguishable in Gene Ontology space but differ systematically in internal mutual information and protein-protein interaction (PPI) density. Finally, focusing on HOX/TALE transcription factors, we derive a "Disruption Index" built from conditional mutual informations that almost perfectly predicts four-body synergy, identify a strongly directional MEIS1-HOXA9 partnership, and demonstrate an Ω-minimisation procedure that reliably grows universally synergistic pentads from synergistic tetrads. Taken together, these results provide a biology-domain analogue of earlier Quantum Darwinism validations, delineate a practical reliability frontier for DAGI metrics in finite data, and introduce new analytical tools with immediate applications to other macroscopic complex systems. Key Experimental Highlights: Cross-Domain Universality: Proves that the exact same DAGI informational mathematics used to benchmark quantum entanglement can successfully decode macroscopic gene regulatory networks. Robustness of f₃: Demonstrates that DAGI's irreducible triadic information isolates true regulatory dependence independent of structural network topology or background correlations. The Finite Data Frontier: Establishes that while raw higher-order Möbius atoms (f₄, f₅) are fragile under finite biological sampling, aggregate O-information (Ω) successfully discriminates "structural complexes" from "informational relays." The Disruption Index: Introduces a novel, DAGI-native metric that almost perfectly predicts four-body synergy based on the directional addition of a genetic cofactor. Mechanistic Assembly: Proves that algorithmic Ω-minimization can be utilized as a generative tool to actively build functionally synergistic gene clusters (pentads) from smaller topological seeds.