BT-PEC: An Emergent Unified Theory from SL(3,Z) Modular Topology

This is the first paper of a five-preprint series on BT-PEC (Berry-Topological PEC emergent cosmology). We propose BT-PEC, an emergent unified theoretical framework built upon five fundamental axioms: relational ontology, SL(3,Z) modular symmetry, spin double cover, topological action quantization, and spherical propagator structure. Starting from integer winding vector r ∈ ℤ³, the framework derives the Standard Model gauge structure, CKM and PMNS mixing matrices, electroweak couplings, Higgs mass radiative corrections, and the cosmological constant from first principles without fitting free parameters. We further extend the model to the full T0–T∞ dimension spectrum, identifying T3 as the unique cognitive habitable band where classical observers and stable matter can emerge. Quantum decoherence is incorporated to explain multiple classical branches within the relational topological landscape. Numerical self-consistency checks are performed with an autonomous derivation engine. Remaining open issues and future work are discussed.