Only 1 of 81 runs (TiO₂ density, giant ratio 0.8333) triggers Theorem 1, confirming a USL violation. All remaining 80 domains return verdicts consistent with structural admissibility. This is the central result of the corpus: at the current κ-grid range, real physical ladders are overwhelmingly admissible or inconclusive, with true structural failure appearing only in the one known pathological case.

The corpus cleanly partitions into three structural regimes distinguished by their κ_connect scale:
— Immediate percolation (κ_conn ≤ 2): biological fitness landscapes, atmospheric wind fields, adversarial baselines, some condensed-matter.
— Moderate delayed percolation (κ_conn = 10–8000): condensed matter solids (FeO, KSiO, Cu, VO), CMB spectra (230–2389), GPS crustal displacement.
— Extreme delayed / tail-dominated percolation (κ_conn = 10⁴–4×10⁵): nuclear γ-level schemes, atomic spectra (Na, He-II, Li). These connect only at κ far exceeding the main grid, driven by astronomical gap ratios (max ratio up to 4×10⁵) yet structurally consistent.

All 7 biological runs (QT45 ribozyme fitness landscape) return FULL_PERCOLATION with κ_conn in the range 0.42 – 2.00 — the lowest of any physical domain. This means the fitness landscape gap structure is the most locally homogeneous in Δ-space of all systems tested. The result is consistent with the published biological extension article at unns.tech and confirms the earlier STRUC-BIO-I findings.

The four TAIL_FRAGMENTATION nuclei are ²³⁸U, ¹⁵⁰Nd, ¹⁰⁰Mo, ⁴⁸Ca — all isotopes with known structural anomalies (deformed nuclei, shape coexistence, or collectivity transitions). Giant ratios range from 0.976 to 0.988, with tail dominance = 1.000 and astronomically large max ratios (up to 2×10¹⁸). These outliers are single extreme-energy γ-transitions far above the bulk level scheme. Theorem 1 does not apply (TAIL verdict), but the pattern is physically interpretable: structural irregularity in the level scheme produces outlier gaps that resist global connectivity at the tested κ scale.

All 5 cosmic web runs (2MRS, DESI synthetic, DESI sample, SDSS) return GIANT or TAIL verdicts with no κ_connect on the main grid and no adaptive extension result. Giant ratios are tightly clustered at 0.994–0.999. This is structurally different from the nuclear tail cases: the cosmic web ladders have isolated vertices at maximum κ that extension cannot resolve within the tested range, reflecting genuine large-scale void structure in the galaxy distribution. The 3 TAIL cases have tail dominance 0.913, driven by a max ratio of ~10⁶.

All three CMB spectra (TT, TE, EE) return FULL_PERCOLATION after adaptive extension, but with dramatically different connectivity scales: TE connects at κ ≈ 230, TT at κ ≈ 322, EE at κ ≈ 2389. The large κ required reflects the multi-scale power spectrum structure — acoustic peaks create local gap homogeneity at specific scales, but the overall spectrum is too heterogeneous to bridge within κ ≤ 1. EE polarization requiring 10× larger κ than TE is a new discriminative result consistent with the different noise properties of these spectra.

The tio2_density_ladder (cleaned dataset) returns HARD_FRAGMENTATION with giant ratio 0.8333 — the only run triggering Theorem 1. The companion tio2_cleaned_dataset run returns FULL_PERCOLATION at κ_conn = 681, showing that the raw density representation produces genuine structural fragmentation while the cleaned spectral dataset is admissible. This split is scientifically significant: it demonstrates that data pre-processing choice directly affects PRP verdict for the same physical system.

Six molecular species (H₂O, NH₃, CO₂, CH₄, O₃, CO) and all four gravity field models (Earth EIGEN-6C4, Mars JGM85, Moon AIUB-GRL350A, Earth spatial 2°) return GIANT_COMPONENT_PERCOLATION with giant ratios 0.997–0.9997, but no κ_connect on the main grid and no adaptive extension. This is the most structurally coherent GIANT cluster in the corpus: persistent near-complete connectivity without a small number of extreme outliers preventing closure. It suggests these systems are structurally admissible at scale but have isolated tail gaps that resist connection even at κ = 1.