Principal-module graph compression

Use this as an optional compressed branch for graph message passing, especially for graph-level tasks or graphs with repeated structural patterns. Construct candidate columns K incrementally: start with ones(n), repeatedly apply A and D to every retained column, and append a candidate only when its residual after projection onto the current orthonormal basis exceeds epsilon. Use QR orthogonalization rather than explicit matrix inversion. After obtaining K, form C_A=K^dagger A K and C_D=K^dagger D K. A reduced state z is propagated by z_new=C_A z or z_new=C_D z, while a node-space state can be reconstructed as h=Kz. The paper supplies the exact algebraic closure criterion; rank truncation, epsilon, and regularization are empirical. For non-exact modules, retain a residual correction or reject compression when rho_A or rho_D is too large. First benchmark on synthetic trees and molecular graphs against a GIN with equal message-passing depth and hidden channels. Measure rank r/n, peak memory, wall-clock propagation time, closure residuals, and task accuracy. The desired result is lower node-state memory and faster propagation when r is much smaller than n, with no accuracy loss on orbit-sensitive tree classification. The method should be rejected for graph families where r approaches n or closure residuals remain high.