Number-Theoretic Scheduling for Diffusion Language Models: Void Descent, Digital-Root Cycles, and Commit Gating

A number-theoretic denoise schedule: φ-geometric noise, an 18-level void descent with resistance peaked at level 9, a logistic commit gate, and the digital-root cycle ⟨2⟩=(ℤ/9ℤ)ˣ={1,2,4,8,7,5}. This revision adds a Reference Implementation & Verification note to Data Availability: the paper's falsifiable claims are now numerically verified in the open-source harmonic-engine package (tests/test_new_math.py, passing on CPU). The schedule primitives are verified in harmonic_engine/schedule.py.