BT‑PEC Ontological Theory: Ternary Coupling Topological Axiom System with One Hundred Falsifiable Scientific Predictions

This paper presents BT-PEC ontological theory, a ternary coupling topological axiom system built upon the core complex-valued conservation axiom Ω = tr(BT) − tr(PEC) = 0. This framework applies SL(3,ℤ) modular group symmetry and persistent homology topological data analysis, constructing computable matrix operators for matter topology, spacetime geometry, energy dynamics, topological information and global conservation constraints. General relativity, quantum field theory and topological matter states are interpreted as low-energy effective approximations emerging when topological information degrees of freedom are frozen. This work provides one hundred quantitatively falsifiable scientific predictions. Each prediction includes physical mechanism, experimental detection scheme, 5 σ quantitative threshold, exclusivity analysis against classical theories, expected observation and Ω residual calculation procedure linking the core axiom to experiments. These predictions span Planck-scale vacuum, black-hole physics, cosmology, quantum decoherence and measurement, topological condensed matter, particle excitations, life and complex systems, as well as engineering physics. This work establishes a new cross-scale research paradigm for topological information-matter coupling.