Hilbert Space Refactorization Principle and the Intensive Nature of Time

We propose the Hilbert Space Refactorization Principle (HSRP): physical evolution may be equivalently described as a change of subsystem decomposition rather than a change of the global state. This conceptual shift leads to a fundamental redefinition of time in quantum gravity. We formulate the Intensive Time Principle: in systems where time emerges from entanglement structure, physical time is an intensive thermodynamic observable, dual to entanglement entropy. Specifically, if entanglement entropy scales as S ~ N^β and emergent time as τ ~ N^α, then α < β implies that time is intensive. We show that this leads to non-additivity of time: τ(A ∪ B) ≠ τ(A) + τ(B), fundamentally distinguishing temporal emergence from extensive thermodynamic quantities. Numerical analysis yields the scaling law τ ~ S^0.34. The framework provides a natural resolution to the cosmological bounce and the Past Hypothesis, and predicts observable gravitational wave echoes with distinctive logarithmic scaling Δt_echo ∝ M ln(M), distinguishing it from classical horizon models. This is Version 1.1, with corrected PDF encoding to ensure proper text copy-paste functionality. Version 1.0 is available at DOI: 10.5281/zenodo.20751798.