Diagnostic correction, not a certificate; see the finite-compression certificate in ../v141/.
The original results.md and zeros.py are preserved as the historical run.
Their sinc-lattice conclusion is withdrawn because the script reconstructs
a different function from the matrix eigenvector.
The actual matrix uses unshifted Fourier modes on [0,L], as stated in
prop:v116-window-positive. Moving their even combinations to [-L/2,L/2]
changes cosine coefficients from v_n to (-1)^n v_n. The old xhat()
uses v_n without that phase. It also rounds L to a float, stops at a small
coefficient, changes precision during evaluation, and replaces failed root
solves by scan-cell midpoints. These cannot certify zero positions.
For unshifted coefficients, the correct exact formula is
ghat(z) = 2 sin(zL/2)/sqrt(L) [v_0/z + sqrt(2) sum_{n=1}^N v_n z/(z^2-omega_n^2)].
At a retained lattice point, its removable-pole value is
ghat(omega_k) = sqrt(L/2) (-1)^k v_k.
A small nonzero coefficient does not make this value zero. Concentration of 90% of the coefficient mass in low modes does not control relative error near transform zeros or imply that off-lattice zeros are absent.
NS-2 now reproduces CCM section 6 Figure 1 at the existing lambda=3, N=120
benchmark. All first eight published discrepancies match their rounding;
the first is approximately 1.582329697193127e-34. The new verifier uses Arb
assembly and isolated eigenpairs at 768/1024 bits, then interval signs and
a nonzero derivative to certify each proposed local root bracket. These
are finite-compression statements; see prop:v141-ccm-lock and its artifacts.
This run uses CCM’s N=120, not the historical NS-14 N=256. It does not silently substitute one cutoff for the other: the exact phase correction applies to both, while the numerical certificate is only for N=120. No certified claim about the complete-ground zero locations at lambda=3 or 4 follows. The old negative diagnostic conclusion supplies no evidence against CCM step (b). Complete-ground transfer and cofinal convergence remain open, as do G2 and RH. No new window was computed.