A Formal Mathematical Theory of Triadic Structural Closure

A Formal Mathematical Theory of Triadic Structural Closure This record contains the formal mathematical companion to the empirical PETU atlas, together with a separated preregistration-oriented document of strong predictions and test criteria. The mathematical companion formalizes support (H), structure (S), linkage (L), closure/coherence (Φ), unity, balance, dominance, fragility, co-inherence, perturbative response, multi-scale closure, categorical structural equivalence, tensorial extension, variational stability and law-candidate criteria. The strong-predictions companion converts the PETU framework into preregistered empirical test classes, including baseline hierarchies, null models, thresholds, domain templates, falsification criteria and reporting requirements. Scientific status This package is a theoretical and preregistration-oriented companion to the empirical PETU atlas. It presents PETU as a candidate cross-domain structural principle. It does not claim that PETU is a completed universal law, a theory of everything, a replacement for domain sciences, a metaphysical proof or a theological proof. Included files PETU_Mathematical_Theory_Formal_Companion_v1.pdf PETU_Strong_Predictions_Preregistered_Tests_v1.pdf PETU_Theory_and_Strong_Predictions_Public_Package_v1.zip The ZIP archive includes PDF, LaTeX and Markdown sources, README files and audit materials. Public related records Empirical PETU preprint:https://doi.org/10.5281/zenodo.20821557 PETU repository/data-code archive:https://doi.org/10.5281/zenodo.20820252 GitHub repository:https://github.com/hector-eag85/petu-triadic-structural-closure-atlas Claim boundary The package should be cited as a formal mathematical companion and prediction framework. It does not replace independent empirical validation, adversarial null testing or preregistered replication. Citation Álvarez García, H. E. (2026). A Formal Mathematical Theory of Triadic Structural Closure: Support, Structure, Linkage, Coherence, Unity and Fragility in the PETU Framework. Zenodo.