Octomorphic III_ The Registry and the Spectral Sieve.pdf

The Octomorphic Framework — Chapter 3: Spectral Sieve and Mode-Lock Dynamics Builds the operational machinery of the framework. Defines mode sets, overlap fractions, and the spectral sieve that filters stable configurations. Demonstrates how triality-lawful gating reproduces observed shell closures, magic numbers, and elemental periodicities without adjustable parameters. Presents the deterministic “registry → spectrum” pathway that bridges microscopic geometry to macroscopic matter stability. ---