HilbertSpaceRefactorizationPrinciple andtheIntensiveNatureofTime

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 ∼ Nβ and emergent time as τ ∼ Nα, then α < β implies that time is inten­sive. We prove that this leads to non-additivity of time: τ (A ∪ B) = τ (A) + τ (B), fundamentally distinguishing temporal emergence from extensive thermodynamic quantities. The framework provides a natural resolution to the cosmological bounce, the Past Hypothesis, and predicts observable gravitational wave echoes with distinctive logarithmic scaling ∆techo ∝ M ln M , distinguishing it from classical horizon models.