Numerical Evidence for Entanglement Time: Scaling Laws and the Past Hypothesis

We present numerical evidence for the Hilbert Space Refactorization Principle and the Intensive Time Principle proposed in Ref. [1]. Using spin-chain simulations with Heisenberg XXX interaction, we demonstrate three key results: (1) Past Hypothesis without fine-tuning: Refactorization of Hilbert space from (8+2) to (9+1) spin bipartition reduces the effective entropy of the daughter subsystem by a factor of ~5 (ratio S_daughter/S_before ≈ 0.19). (2) Modular time deviation: For N=8 spins initialized in the Néel state, the entanglement time deviates from proper time by Δτ ≈ 1.82 (18% reduction) over t = 10, correlating with the rate of entanglement growth. (3) Scaling laws: Systematic simulations for N = 6, 8, 10, 12 reveal that entanglement entropy scales extensively (ΔS ~ N^0.80), while entanglement time scales sub-extensively (Δτ ~ N^0.27), yielding the non-linear relation Δτ ~ (ΔS)^0.34. This provides numerical confirmation of the Intensive Time Principle: time is an intensive thermodynamic observable, fundamentally distinct from extensive quantities like entropy. These results establish entanglement time as a robust physical effect that survives the thermodynamic limit, supporting the conceptual framework of Ref. [1]. This is Part II of a trilogy. Part I presents the conceptual framework (DOI: 10.5281/zenodo.20760213). Part III will derive observational predictions for gravitational wave detectors.