Paper FBW-B: Cosmological Origin of Quantum Mechanical Axioms: Derivation of the Born Rule from FSC Four-Sector Structure

We demonstrate that the axioms of quantum mechanics -- superposition, the Born rule, and the projection postulate -- are not independent assumptions but theorems derivable from the Four-Sector Cosmological (FSC) structure. Sector-II, the dark matter sector, acts as a universal environment: tracing it out from the global FSC state generates the mixed density matrix of Sector-I (baryonic matter), from which quantum probabilities emerge as Schmidt coefficients (Theorems 3.1-3.4). The Schmidt coefficient spectrum is determined within the FSC modular framework: the ratio R = Omega_DM/Omega_b = 5.4 (Planck 2018) fixes the FSC parameter p = -6 ln R/pi = -3.221, and the S-transformation of the partition function Z_I(tau) = |eta(tau)|⁻²ᵖ mathematically derives Omega_Lambda/Omega_b = <|tau|⁻ᵖ>_F = 13.6, yielding Omega_b = 1/20 = 0.05 in agreement with Planck 2018 observations (1.4% accuracy, Theorem 4.5). A number-theoretic observation emerges: 1/Omega_b = 20 = c_Monster - |Z_4| = 24-4, connecting the baryonic density to the Monster moonshine central charge and the FSC Z_4 symmetry (Corollary 4.5.1). The monotonic increase of entanglement entropy S_ent(t) reproduces the arrow of time consistent with Paper E (Theorem 5.1). Five open questions for future work are identified (OQ-1 through OQ-5). This paper initiates the FSC & Baryon World (FBW) series, focusing on the interface between FSC cosmological structure and quantum information.