QSG-String - Time as Existence - QSG State as Fundamental Mathematics

Time is not a primitive background parameter but a theorem of existence. This work develops the Quantum State Geometry (QSG) framework, showing that distinguishability of quantum states in projective Hilbert space generates temporal succession, finite bounds, and spacetime structure. By linking Fubini–Study curvature to emergent causality, we derive minimum time, maximum speed, and worldsheet dynamics as Jacobi bundles of histories. The Existence Postulate (RFs > 0) provides a universal cost of distinguishability, with anomaly selection pointing to CP4 superstring (10D) and CP11 bosonic string (26D). This extends QSG toward a unified quantum gravity picture without assuming Einstein–Hilbert action, connecting Fisher equilibrium to emergent Einstein equations.