A Localized Primordial Power Excess Confronts the Lyman-α Forest: Early-Structure Amplification, Compressed-Statistic Blindness, and a Multi-Model Constraint on the y⁴ Acoustic-Island Branch of General Coherence Field Theory

We confront a model-derived localized primordial power excess of General Coherence Field Theory (GCFT) — the y⁴ acoustic-island source, A(y)=y⁴exp(−βy²) with y=k/k_peak — with cosmological data, focusing on its single binding test: the small-scale Lyman-α forest 1D flux power spectrum. The source amplifies the high-redshift halo mass function (factors of 89–243× at z=25 for the retained tiers) while remaining negligible at the pivots probed by broad summaries, leaving it Planck-invisible and quiet in σ8 and z=0 halos. We show that the standard compressed Lyman-α statistics are structurally blind to it (the trained CH24/LaCE emulator shifts its prediction by ≤0.05%), then apply five treatments that can resolve the feature: a linear FGPA projection against the DESI DR1 P1D full covariance (Δχ²=165 conservative, 419 aggressive), an anisotropic nonlinear flux model, and a bounded lognormal–FGPA skewer mock — both of which increase the tension — plus a mapping onto the k_peak axis of a published full-hydrodynamic primordial-magnetic-field analysis, which places the excess (peak k≈13–16 Mpc⁻¹) inside its >3σ-disfavored region. Safety would require gas pressure filtering 2–3× stronger than any calibrated simulation, and the tension localizes at z≈2.8–3.0. Every treatment that resolves the feature disfavors it; only the feature-blind statistics call it safe. An independent JWST/DS-3 cosmic-dawn discriminator is offered. We report the branch as broadly viable but Lyman-α proxy- and analogue-disfavored, with a bespoke hydrodynamic likelihood the sole route to a formal verdict. The source is model/toy-derived; this is not a formal exclusion.