Independent Reproduction and Convergence Analysis of the Connes-Consani-Moscovici Zeta Spectral Triple

Version 2.5. We independently implement the Connes–Consani–Moscovici (CCM) operator construction described in arXiv:2511.22755 in Rust using arbitrary-precision MPFR/GMP arithmetic. This manuscript combines independent reproduction, empirical convergence analysis, and rigorous certification of selected finite CCM configurations. Changes in Version 2.5. This revision adopts Xcelerator Toolkit v0.15.0, incorporates the completed rerun of all 14 individual claim scripts under their documented applicability policies, and extends the first-zero headline to 1495.14 measured matching decimal digits. It adds analytic finite-matrix and root certificates, independent verification programs, refined Critical-N measurements, an exact small-source root census, and controlled matrix-assembly, precision, and prime-response experiments. The accompanying implementation defaults individual claims to Ultra research capture and provides explicit numerical PASS/FAIL summaries. The 1495.14-digit result is obtained at λ² = 1200 and N = 970 with an HP-2000 requested-precision target and 6708 working bits. At the fixed configuration λ² = 1000, N = 800, increasing requested precision from HP-1000 to HP-2000 improves the first-zero match from 1019.0 to 1260.36 digits. This paired experiment separates arithmetic limitation from resolved finite-configuration error. Matching digits use the relative metric Dr = −log10(|νr − γr| / |γr|), comparing a computed finite CCM ordinate νr with the reference Riemann zeta ordinate γr. The direct comparison with the original CCM headline also reports absolute error. Main findings and new verification evidence. Analytic finite ground-state and root certificates. At λ² = 13, N = 10 and 120, analytic interval assembly and two independent inertia calculations certify positive-definite matrices with simple, even ground states. A proved residual-to-gap bound transfers eigenstate uncertainty to the secular roots. All ten positive movable-root brackets at N = 10 and a unique root near the first zeta zero at N = 120 are certified and independently replayed. The latter retains 55.763557879 matching digits. The larger-cutoff root interval checks, including the 1495.14-digit result, certify roots of the exact serialized finite sources. Critical N resolved on integer brackets. Forty additional computations at HP-200 and HP-1000 refine the first-zero accuracy crossings at λ² = 13: 50 digits are first reached within the tested bracket at N = 40, and 55 digits at N = 56. Critical N depends on the requested root, target accuracy, cutoff, and working precision; resolution and saturation are distinguished. Empirical convergence structure. Increasing N produces a smoothly saturating accuracy ramp, approximately linear over the observed early range. The first-zero plateau tracks the Weil-eigenvalue depth −log10|εN| with a finite conversion gap. Across the measured fixed-N cutoff sweep, that gap is approximately 2.7–3.2 digits. Along sampled cutoff-and-basis paths, the eigenvalue depth gains hundreds of digits over the listed prime-count doublings; these measurements do not establish a prime-count-only or asymptotic convergence law. Parity and spectral separation. The unrestricted lowest state is essentially even at every tested configuration above the precision floor, through λ² = 1200 at HP-2000. Positive even–odd and internal even-sector gaps at five headline configurations support numerical simplicity. A residual-to-gap estimate explains the observed parity noise, while the two configurations at λ² = 13 receive rigorous finite certification. Reference-free small-source census and explicit indexing. A 21 × 21 matrix constructed from six primes achieves 21.585 matching digits on the first zeta zero. An exact rational census isolates all ten positive movable roots before comparison with zeta references. The first five movable roots occupy positions 1, 2, 3, 6, and 8 in the full positive spectrum, including the untouched lattice. This makes the beyond-band matches and their spectral indexing explicit. Independent numerical controls. Tanh-sinh integration checks all 441 entries of the λ² = 13, N = 10 matrix at 60 and 90 decimal digits. Nine fixed-matrix entry-precision experiments isolate roundoff effects. At λ² = 13, N = 120, independent perturbation solves verify all nine prime-power response directions at three centered step sizes, with final relative first-root response discrepancies below 1.1 × 10−117. These controls distinguish scalar prime weights from actual local root sensitivity. The rigorous certificates concern finite matrices and finite secular sources. The manuscript does not claim to prove the limiting convergence required for a proof of the Riemann Hypothesis. The accompanying software retains matrices, sector spectra and selected eigenstates, root-conditioning evidence, applicable target diagnostics, prime-power and cutoff-flow responses, and prefix moments and checkpoint diagnostics. Unsupported measurements and numerical limitations are explicitly reported. Supporting code, aggregate evidence, and verification instructions are included in the repository. The reproduction scripts reuse compatible cached artifacts when available and compute locally otherwise. Seeded root refinement and independent finite-root discovery are distinguished; reference ordinates are not substituted into computed results. This work has been shared with the CCM authors and reviewed by the lead author, Professor Alain Connes. Akiva Groskin also reviewed the work, independently reproduced key aspects of the truncated Weil-form computation, and cited earlier versions in his own research. This record archives the Version 2.5 manuscript. A separate Zenodo software deposit archives the source code and reproducibility infrastructure. The exact source revision for this manuscript is identified below. Tagged paper source: v2.5Paper source revision: ecb31a7688f5b3bbb0c33ed77fbdb32bbefc1743Toolkit release: v0.15.0Toolkit revision: 2bea90ec7cb23d4d615448c293c8af0f94e14119