How close is the Connes–Consani–Moscovici trial function to the ground state? Measurements, a leakage estimate and computer-assisted bounds for truncated Weil forms up to c = 150

Connes, Consani and Moscovici (CCM) have reduced the Riemann Hypothesis to statements about the ground states ξ_λ of truncated Weil quadratic forms, and identify as the main open step the closeness of ξ_λ to an explicit trial function k_λ built from prolate spheroidal functions. It is measured here for Galerkin truncations at cutoffs c = λ² from 9 to 150. The squared sine of the angle between k_λ and ξ_λ falls as about 10^(−3.8)c^(−4). The error lies almost entirely along the second even eigenvector, the window-limited oscillator state of level 8, and the gap to that state grows as about 1900c⁴ times the ground energy; together these account for the angle law. Adding the window-limited states of levels 8, 12 and 16 brings ξ_λ within sin² ≈ 10^(−28.5) (c = 13) to 10^(−46.4) (c = 150) of their span. This structure is implied by results of Connes and Consani; its constants fit a prolate-leakage estimate up to overlap factors of 0.5–0.9 not computed independently. Using this gap, the variational bound on the angle is proven in interval arithmetic for the truncations at eleven cutoffs from c = 9 to 150 (c = 150 post hoc), within a factor of 1.2–2 of the measured value except at c = 19 (4.4, below N*). Using it for CCM's missing step would need a lower bound on ε₁, which is equivalent to RH; for k_λ, Temple's inequality, the standard way to derive one, fails by 92 and 247 orders of magnitude at c = 21 and 50. Truncations are reliable only above a basis size of about 2c ln c, where the ground state's Fourier coefficients reach a floor near √ε₁; at c = 100 the resolved values settle near log₁₀ ε ≈ −529.2, 4.5–7.6 orders above published extrapolations from below it. Of five predictions recorded in advance at c = 150, four were confirmed; the fifth failed because of a quadrature error, which is analysed. All results concern finite truncations and do not bear directly on the truth of the Riemann Hypothesis. Contents: paper (PDF, Word), two-page summary, all code (start with code/weil.py), every computed cell as JSON, preregistration files with SHA-256 hashes, and OpenTimestamps proofs (*.ots) for the preregistration files and the paper PDF. The computations and analysis were carried out with AI models (Claude Opus 5.5 and Fable 5.1, by Anthropic) under the author's direction; see Section 1.4 and the section on AI use in the paper. Contact: Mike Luekens, [email protected]. Questions and corrections are welcome.