Spectral Manifold Dynamics III: Critical Percolation Thresholds, Dynamic Intervention Scaling, and Cosmological Seed Bounds

While topological phase transitions near the 4D bond percolation threshold (pc ≈ 0.1601) govern algebraic connectivity, resolving parameter degeneracy requires mapping local graph pruning directly to global observables. Under calibrated dynamic starvation filtering (S0 = 0.025, γstarve ∈ [0.3, 0.9]), local 66.7% node pruning establishes an ensemble-averaged dy- namic scaling exponent of αdyn = 1.7924. By linking the discrete Graph Laplacian spectral gap λ2(L) ∼ L −αdyn to field variance via heat kernel two-point correlations, we derive three overconstrained observational scaling relations: a primordial gravitational wave spectral index nT = 3 − αdyn = 1.2076, a tabletop optomechanical quantum decoherence gap expo- nent αdyn/2 = 0.8962, and an un-accreted primordial seed black hole mass function slope M−1+αdyn/4 = M−0.5519. Reaching observed high-redshift active galactic nuclei envelopes (M−0.7 to M−1.1 ) requires a subsequent steepening of ∆γ ≈ 0.15 − 0.55 via post-formation baryonic accretion, a magnitude consistent with standard early growth models.