Density-Transition Signatures at Digital Boundary Heights: Pre-Registered Null Results under Two Distinct Heuristic Conventions for Joint ζ / L(χ₅) Zero Counts

We pre-registered and ran two numerical tests of a structural prediction from the 2I Universe Programme: that digital boundaries in cumulative mod-6 prime products at scales 10⁶¹ and 10⁸⁰ should register as density-transition signatures in the joint counting function Δ(T) = N_ζ(T) − N_L(χ₅)(T) at heights γ corresponding to those scales. The conversion from scale to height is heuristic; two defensible conventions exist in the standard analytic-number-theory literature, neither rigorously derived for our specific observable. We tested both. Test 1 (natural-log convention, γ_d = d · ln(10)) at predicted heights γ ≈ 140, 184 returned empirical p-values 0.353 and 0.092 — boundary 1 essentially at null mean; boundary 2 elevated (RMS 0.689 vs null mean 0.614) but with p = 0.092 above the registered 0.05 threshold. Test 1b (resonance-period convention, γ_d = 2π · d / ln(10)) at predicted heights γ ≈ 166.45, 218.30 returned empirical p-values 0.429 and 0.459 — both at the null median. The Test 1 boundary-2 elevation does not replicate at the alternate convention. The pre-registered conjunctive pass criterion (p < 0.05 at both boundaries) is not met under either convention. The locally-windowed density-transition framing of digital boundaries, at the resolution and statistic registered, is therefore not supported by the data under either of the two heuristic conventions tested. The qualifier "locally-windowed" is deliberate and is discussed in §8.1: cumulative or broadband observables remain untested. Independent calibration audits (5 points for Test 1, extended to 9 for Test 1b) confirmed the Selberg analytic null was correctly specified through the test region. Pre-registration documents precede result computation in the git history; the audit gaps are the pre-registration moments. We document what was tested, what came out, and what is and is not entailed. Keywords: Riemann zeros, Dirichlet L-functions, χ₅, pre-registration, density transitions, digital boundaries, null result, Bonferroni.