Inverse-Square Critical Coverage and Constant Saturation Depth from an Exact Interval Theorem

The auto-calibrated saturation depth n₁(q) for BFS on Heis₃(Z/qZ) — the central asymptotic variable of the O25–O28 window calibration — converges in probability to the constant n_* = 22 under uniform generic block sampling, and the critical coverage x₁(q) = B_n₁/q² obeys the inverse-square law x₁(q) q⁻². The mechanism is an exact algebraic reduction. Every implemented three-step Weil fingerprint is a non-zero scalar multiple of a single Fourier character, so the cumulative rank is a sumset cardinality, \[ r_c(n) = {T'_c} + C\,Iₙ₊₁ , {T'_c} = \{(c_2+c_3)η_2 + c_3η_3: η_i ∈ \{-1,0,1\}\}, \] with C = c₁+c₂+c₃ and Iₘ the reduction of $[-m,m]$; the shellwise novelty obeys the universal deterministic ceiling Δ rc(n) ≤ 2T'c ≤ 18. Exact sphere counts of the infinite discrete Heisenberg group give the strict threshold crossing s₂₂ = 16,934 < 18/εₛₐₜ = 18,000 < s₂₃ = 19,412. Deterministically, for every prime q ≥ 311 and every admissible block sequence, n₁(q) ≤ 22 and 5/q² ≤ x₁(q) ≤ 99,689/q²; under uniform generic block sampling, n₁(q) → 22 and q²\,x₁(q) → B₂₂ = 99,689 in probability. The measured depths (n₁ = 14 at $q=211$, $19$ at $q=601$) sit in a transitional regime governed by block resonances, whose deficits produce the observed effective exponent ≈ -0.76 en route to the exact asymptotic $-2$. A structural corollary is that the implemented auto-calibrated fitting window closes deterministically for q > 937,024. As interpretation (structural reading, not a result): the finite Weil–BFS observable has a finite novelty horizon — beyond a fixed relational depth, independent of the arithmetic size of the substrate, exploration creates no above-threshold spectral novelty per vertex — so shellwise novelty is a local combinatorial phenomenon, and no continuum-scaling channel opens from this observable.