High-Precision Galerkin Experiments on the Connes–van Suijlekom Truncated Weil Form, with an Out-of-Sample Empirical Test at c=100

The Connes–van Suijlekom truncated Weil quadratic form, indexed by a cutoff parameter c that controls the primes p ≤ c entering the operator, produces a ground state whose Fourier–Mellin zeros provably lie on the critical line; whether they converge to the Riemann zeros as c → ∞ is open (Connes 2026; Connes–Consani–Moscovici 2025). We present, to our knowledge, the first independent public implementation of the Connes–van Suijlekom Galerkin matrix at sixteen cutoffs (c = 13 through 67, plus c = 100). Across the in-sample window c = 13 through c = 67 at N = 100, the first-zero absolute error |γ1 − γ1Riemann| shrinks monotonically from ∼2×10−55 to ∼1. 5×10−168 — a 113-OOM convergence across fifteen cutoffs. The smallest-positive even-sector eigenvalue λmineven separately reaches ∼10−334 at c = 100, N = 250 (275-OOM span from c = 13). Out-of-sample test at c = 100. On the four-point N-sweep N ∈ 100, 150, 200, 250 at dps = 500, consecutive first-difference ratios 0. 837 and 0. 836 match to two decimal places. Aitken-Δ2 on the two overlapping triples yields log10|λ∞even| ≈ −536. 8 and ≈ −533. 7, approaching the Connes 2026 §6. 4 heuristic prediction (≈ −530. 4) monotonically with N (6. 4 and 3. 3 OOM gaps out of |x∞| ∼ 530). The same eigenvector recovers γ1, …, γ10 to 307–329 matching digits at N = 250, dps = 500. Under the unitary equivalence with Connes–Consani–Moscovici Lemma 5. 1, this is the deepest such Galerkin-truncation recovery in the public Connes–van Suijlekom / Connes–Consani–Moscovici literature, subject to a hypothesis-status caveat: the raw finite-N matrix carries a small block of dps-stable negative-sign eigenvalues, so we report the smallest-positive branch (continuum positivity of QWλ is RH-equivalent and is not assumed at λ = √100). The fit |log10 λmin| ≈ 13. 24 c0. 634 on c ≤ 67 at N = 100 is shown to be a finite-N rate, falsified at c = 100, N = 200 by 49 OOM in the direction of faster decay. Structural observations include approximate eigenvector c-invariance (overlap ≥ 0. 9498 on all 105 cutoff pairs despite eigenvalues differing by 113 OOM), multi-zero convergence universality (all ten detectable zeros within 3. 8% of each other), an empirical Galerkin-convergence exponent s (c) ≈ 55 log c − 128, un-rescaled Galerkin bulk-spectrum Poisson statistics (β < 0. 05; this is a structural diagnostic of the truncated operator, not a test of Montgomery's conjecture, which applies to locally-rescaled zero spacings), and tight bulk invariants log|det Qc| ≈ −65. 6 c + 542 (R2 = 0. 997). We make no claim of proof; the contribution is reproducible numerical data and its careful interpretation under the existing CvS / CCM framework. All code, data, and ancillary files are publicly available.