Information Field Dark Matter IV: Planet 9 as Primordial Black Hole — Testable TNO Clustering Beyond the Newtonian Horizon

We model Planet 9 as a 5 M⊕ primordial black hole generating an Information Field with torque ∝ 1/r (vs Newton 1/r²). Predicts sustained TNO clustering R_IF=0.25 at 1000-1600 AU (vs R_N=0.07). Falsifiable by Vera Rubin LSST (science operations since June 2026). * Update 17/10/2026 — Version 2: [ v2 adds the Addendum "Post-Publication Tests, Corrections, and Independent Verification": (1) The April 2026 test on 8 eTNOs (R = 0.830, mean ϖ = 58.2°) with the exact 8-object list published for the first time; (2) The May 2026 test on 76 MPC eTNOs (R = 0.200) with a statistical correction — the reported permutation p = 1.0 was erroneous, the correct value is p ≈ 0.05 (conclusion unchanged: not significant at the 1% level); (3) An independent recomputation from current MPCORB data reproducing R = 0.826 for the 8-object sample; (4) An independent convergence note: Galiazzo & Finch (arXiv:2606.00612, 30 May 2026) propose an aligned Planet 9 at implied ϖ ≈ 55.2°, within 3° of the April 2026 estimate.] * Update 06/05/2026: ( Post-publication test (May 2026): A follow-up test on 76 extreme TNOs from the MPC sample yields a circular mean longitude near 19.2°, but the Rayleigh clustering statistic remains modest (R = 0.200) and is not statistically significant at the 1% level (two-sided p ≈ 0.05; the originally reported p = 1.0 was erroneous — see v2 note above). This suggests the present constraint is preliminary and should be treated as a provisional alignment estimate pending Rubin LSST expansion. ) * Update 06/04/2026: ( Post-publication test (April 2026): 8 canonical eTNOs from Batygin & Brown 2016 show Rayleigh R = 0.830 (strong clustering) at mean varpi = 58.2°. If P9 is aligned with TNO cluster (not anti-aligned), implied P9 position = 58.2° — consistent with Paper IV's own prediction of 40° within ~18° (the 40° value belongs to Paper IV, not to Batygin & Brown). Anti-aligned assumption in original paper may need revision. Full constraint pending Rubin LSST data. ) Extends FhiemDien series: FhiemDien. 2026b, Planet 9 Position Prediction from Black Hole Entropy Gradient Anal-ysis, Zenodo, DOI:10.5281/zenodo.18774095FhiemDien. 2026a, Information Field Dark Matter I: Deriving the Baryonic Tully-FisherRelation from Holographic Black Hole Entropy, Zenodo, DOI:10.5281/zenodo.18779541FhiemDien. 2026c, Information Field Dark Matter II: SPARC 116 Galaxies, Zenodo,DOI:10.5281/zenodo.18785473FhiemDien. 2026d, Information Field Dark Matter III: LITTLE THINGS Dwarfs, Zenodo,DOI:10.5281/zenodo.18830476