Harmonic Origin Pulse

The Harmonic Origin Pulse is the quadratic pulse-density law P(n) = (n+1)² that the book makes the generator of all complex spectral structure in BPT. In place of classical linear harmonic progression, the Harmonic Origin Pulse sets quadratic growth as the source of nonlinear frequency spacing that reflects computational depth rather than mechanical resonance. Its scaling is inherited further on: stable forms in the thresholds of recursion have quantized energy levels that follow it directly, through BPT Energy Quantization E_n = ħω⥂ × P(n), and quantum evolution in the recursive substrate follows a Modified Schrödinger Equation with a recursive complexity potential and an effective mass. The formal statement is P(n) = (n + 1)², where P(n) is the pulse density function and n the level index, both [∅]. In the energy law E_n = ħω⥂ × (n + 1)², E_n is the quantized energy at level n [J], ħ the reduced Planck constant [𝕄·𝕃²·𝕋⁻¹] and ω⥂ the pulse frequency [𝕋⁻¹]; the book's check is consistent. It connects to the Harmonic Origin Sequence, Pulse Density, Harmonic Complexity Scaling, Cumulative Complexity Accumulation and Effective Mass.