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 ~ S⁰. 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 Δtₑcho ∝ 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.