Little Red Dots as τ-Toroidal-Horizon Black Holes

We present a categorical account of the JWST-discovered Little Red Dots (LRDs) as τ-toroidal-horizon black holes born at saturation mass via single quasi-isothermal d_top = 1 contraction in atomic-cooling halos at z ≈ 8–15. The seed mass distribution is FLAT in dlogN/dlogM_BH between 10^4.5 and 10^6.5 M_☉ with sharp cutoffs; the upper cutoff at 10^6.5 M_☉ is uniquely τ-distinctive and constitutes the load-bearing operational falsifier (N15). The leading hypothesis (Theorem 3.2) rests on five load-bearing τ-effective registry theorems (V.T109, V.T110, V.R179, V.T40, V.T88) plus a dedicated V.T-LRD-1 birth-condition theorem with sub-claim B (upper cutoff value) Lean-certified at the TauReal level via the post-Phase-0.5 f_iota_TauReal_approx_uniform_convergence (Wave R10-2). Companion v2.3 documented Phase 0.5 closure (sorry 10 → 0 across waves R8b–R8j); v3.0 integrates Wave R10-2/4/5 closures (Cauchy bound tightening, V.T-LRD-1D Lean carrier resync to ≤ 1.5 dex composite, IotaTauTauRealHelpers module promotion). Trust budget: 0 sorries, 3 axioms (programme-wide, none LRD-specific), 0 LRD-relevant native_decide leaves. Companion software: TauLib Lean 4 formalization (v3.0 cites commit e09759d, post-Wave-R10).