The Zeeman domain is the single most striking cross-instrument result. STRUC-I reports ρ = 0.9585 — the highest structural pressure in the entire physical corpus, deep in the CRITICAL zone, 10× higher than nuclear, with only 4.15% margin before violation. STRUC-PERC reports FULL_PERCOLATION — but at κ_connect = 2–4 × 10⁵, the most extreme connectivity delay of any domain. Both instruments are correct; they are measuring orthogonal structural properties of the same gap architecture. STRUC-I sees: the inversion budget is almost fully exhausted (ν ≈ inv). STRUC-PERC sees: the gap distribution has extreme outlier transitions that require astronomical κ to bridge. The physical mechanism is the same — fine-structure Zeeman splittings produce a small bulk of nearly-equal gaps (high ρ, high mutual connectivity) pierced by a handful of extreme hyperfine transitions (astronomical tail, delayed percolation). The system is simultaneously maximally pressured and fully percolating — the boundary-stabilized state captured from two angles.

Both instruments agree the QT45 ribozyme fitness landscape is admissible. But the granularity of the comparison is revealing. STRUC-PERC sees a flat picture: all 7 biological ladders return FULL_PERCOLATION with very low κ_conn (0.42–2.00) — the most immediately connective physical domain in the corpus. STRUC-I reveals a wide internal spread: substitution ladders ρ ≈ 0.188 (Stable), combined_del ρ = 0.554 (Weak Persistence), deletion ρ = 0.819 (Boundary-Stabilized — the highest-pressure biological result and among the highest in the entire corpus). Both are admissible, but STRUC-I shows that deletion mutations push the fitness landscape to the very edge of the admissibility boundary in the inversion space, while STRUC-PERC finds that the gap structure still percolates easily. The biological system operates near the USL limit not through structural fragmentation but through extreme inversion pressure.

The cosmic web domain produces the strongest qualitative agreement across instruments. STRUC-I observes a dramatic ν-explosion at κ ≈ 0.30: ν jumps 8.7× in a single κ step, ρ collapses from 0.651 to 0.058, and the ρ(κ) profile has the most dramatic cliff in the entire corpus. STRUC-PERC finds that DESI ladders cannot achieve κ_connect at any tested scale — giant ratio plateaus at 0.994, void gaps of ~10⁶ × median dominate the tail, tail dominance = 0.913. Both instruments are detecting the same physical structure: the separation between galaxy filament spacings and void diameters. STRUC-I sees it as a scale transition in the admissibility budget (the cliff). STRUC-PERC sees it as persistent non-connectivity (the isolated void vertices). The joint result establishes this as the most structurally complex domain in the shared corpus — simultaneously highly admissible (Aκ ≈ 1.000) and never fully connected.

The condensed matter domain is the only case of genuine (partial) instrumental divergence. STRUC-I tests TiO₂ as a crystallographic phase chain (rutile/anatase/brookite polymorphs, n=3, ρ = 0.033) — a Stable Structure result with zero pressure. STRUC-PERC tests TiO₂ as a raw density-of-states ladder (HARD_FRAGMENTATION, giant ratio 0.833, Theorem 1 triggered) and as a cleaned spectral peaks ladder (FULL_PERCOLATION at κ_conn = 681). The divergence is not a contradiction — it is a representation sensitivity finding. The instruments are measuring different physical objects derived from the same material. The phase-chain representation (structural parameters across polymorphs) is admissibility-trivial (n=3, all gaps similar). The raw DOS representation reveals genuine structural fragmentation invisible to STRUC-I's phase-chain probe. This is the most important data-representation finding in the corpus.

STRUC-I reports nuclear as a compact, well-behaved domain: mean ρ = 0.197 (2.2× GOE null), all ladders Stable Structure, no Weak Persistence or boundary cases. The instrument sees the nuclear domain as homogeneous. STRUC-PERC disagrees on homogeneity: 10 isotopes return FULL_PERCOLATION (consistent with STRUC-I's Stable verdict) but 4 return TAIL_FRAGMENTATION with tail dominance = 1.000 and astronomical max ratios (10⁹–10¹⁸). The TAIL isotopes — ²³⁸U, ¹⁵⁰Nd, ¹⁰⁰Mo, ⁴⁸Ca — are all nuclei with known structural complexity (deformation, shape coexistence, double β-decay candidacy). STRUC-I's ρ metric averages over all gap pairs and does not flag these isotopes because their extreme tail transitions are rare (small count, small ρ contribution). STRUC-PERC's tail dominance = 1.000 means these single transitions consume 100% of the gap budget — a structural asymmetry STRUC-I cannot resolve. STRUC-PERC provides strictly finer nuclear discrimination.

STRUC-I shows GOE as the null baseline: ρ = 0.087–0.101 across n=100, 200, 500, the most relaxed structural state of any tested object, below even Earth's gravity field. This is the expected RMT result — level repulsion produces locally uniform spacing (small ρ, minimal inversion pressure). STRUC-PERC finds GIANT_COMPONENT_PERCOLATION rather than FULL, with GR = 0.9960, no κ_connect on the main grid or via extension. This is a new observation: GOE level repulsion creates a nearly-but-not-quite globally connected graph. The isolated vertices correspond to rare large eigenvalue gaps (the tail of the GOE bulk spacing distribution). Both instruments agree the GOE is structurally benign; STRUC-PERC adds that even the most relaxed known ordered structure cannot achieve perfect percolation within the tested κ range.

The solar domain is where both instruments agree most concisely on internal differentiation. STRUC-I shows F10.7 coronal flux at ρ = 0.022 (most relaxed solar measurement, below GOE), solar dynamo at ρ = 0.376 (Weak Persistence, distributed Aκ deficits), and flare flux at ρ_peak = 0.806 (Weak Persistence, sharpest ν-cliff in the corpus, 46× jump at κ ≈ 0.052). STRUC-PERC tests the GOES-XRS 2014 solar flare record (flux-type ladder) and finds TAIL_FRAGMENTATION with GR = 0.982, tail dominance = 1.000, max ratio = 3.2×10¹⁰. The 10¹⁰ × median outlier in STRUC-PERC is the physical flare spike — the same structural feature that creates STRUC-I's 46× ν cliff. The instruments independently identify the same solar flare energy as the dominant structural anomaly.

STRUC-I distinguishes planetary bodies dramatically: Earth ρ = 0.073 (below GOE, most ordered), Mars ρ = 0.277, Moon absS ρ = 0.640 (near-random — "statistically indistinguishable from a synthetic random field" for S-coefficient ordering). STRUC-PERC collapses this hierarchy: all four gravity field ladders (Earth EIGEN-6C4, Mars JGM85, Moon AIUB-GRL350A, Earth spatial 2°) return GIANT with GR = 0.997–1.000, no κ_connect. The STRUC-PERC result is informationally poorer here — it cannot distinguish Earth's extraordinary geometric regularity from the Moon's near-random coefficient ordering. STRUC-I provides strictly richer discrimination in this domain. This is the most significant case where STRUC-I outperforms STRUC-PERC.

Across all shared domains, no run produces a physical contradiction between the two instruments. Where STRUC-I finds Stable Structure, STRUC-PERC finds FULL or GIANT percolation. Where STRUC-I finds Weak Persistence or Boundary-Stabilized, STRUC-PERC finds FULL percolation at large κ or TAIL (inconclusive). The single HARD_FRAGMENTATION case (TiO₂ raw DOS) tests a representation not covered by STRUC-I's phase-chain probe — not a contradiction but a representation-sensitivity finding. The two instruments are consistent with each other everywhere they overlap.

The Zeeman domain demonstrates the boundary-stabilized state from two independent angles simultaneously. STRUC-I: ρ = 0.9585 (CRITICAL, 4.15% margin). STRUC-PERC: FULL at κ = 2–4×10⁵ (extreme delay). A system can simultaneously be at maximum structural pressure (STRUC-I) and fully percolating at large scale (STRUC-PERC). This is not a paradox — it reflects two orthogonal structural properties of the same gap architecture. The physical system is sitting at the edge of the admissibility boundary from the inversion direction while being globally connected in the percolation graph. Both measurements are required to fully characterise the boundary-stabilized state.

Individually, STRUC-I classifies by pressure zone (4 levels) and STRUC-PERC by percolation tier (4 levels). Together, the joint matrix identifies five empirically distinct structural states in this corpus: (1) Relaxed-Connected (low ρ, FULL/GIANT, low κ) — biological, atmosphere; (2) Moderate-Connected (medium ρ, FULL, moderate κ) — nuclear, condensed matter; (3) Relaxed-Tail (low ρ, GIANT, no conn) — molecular, geoid, GOE; (4) Stressed-Extreme (high ρ, FULL at extreme κ) — Zeeman; (5) Stressed-Fragmented (high ρ, TAIL, no conn) — cosmic web peak, solar flare. No physical system falls in the (high ρ, HARD) cell — the only HARD case is TiO₂ raw DOS, a data representation issue not arising from the physical system itself.