Riemann hypothesis: independent verification campaign

The certificate establishes $\Lambda\leq893927/5000000=0.1787854<1/5$, compared with the published Platt–Trudgian upper bound $1/5$. The number and candidate construction are due to Jude Gomila. This campaign completes the finite regeneration and analytic review left by the earlier notebook run. Both complete finite algorithms and all fresh analytic lanes passed, including the entire closed barrier and independent rational assembly.

Work lives in compute/q2/. The model is GPT-6 Astra, 2026-09-08. The exact user prompt is preserved in prompt.md. No other problem's claim was changed and covering was left untouched.

Both complete finite calculations have finished. The original C program regenerated all 3,149,013 rows in 23 sequential segments and matched the candidate archives exactly. A new Rust algorithm interpolates positive Dirichlet sums at eight nodes, with a proved derivative remainder and exact cutoff updates. It independently checks every index and reaches the same minimum floor $791366/10^{12}$ at $N=690988$. The C run took 4265.578 seconds; the Rust interpolation runs took 600.144 seconds. A separate Rust direct convolution at the weakest row took 73.064 seconds.

The finite error allowance is $233494905212337849/10^{24}$, leaving the exact margin $557871094787662151/10^{24}>0$. Python dictionary convolutions checked 100 small cases. Sixteen deliberate certificate corruptions were rejected, including corruptions with matching updated hashes.

The analytic review reads the pinned source against the actual published theorems. It checks the native convolution's normalization and conjugation, the Dini derivative at coefficient zeros, all-window and all-height directions, cap monotonicity in the infinite tail, and the barrier homotopy. It supplies the compact dominated-convergence argument needed to include $t=0$. The coefficient generator's old quadrature is used only to select a matrix size; the separate factorial remainder is the required proof of truncation accuracy.

Fresh C/Arb error and tail runs at 256 and 512 bits have passed, as have the 180/256-bit height-transfer runs, the correction/normalizer checks, and the Python interval tail. The whole barrier completed in 1153.983 seconds, including coefficient regeneration. All 7,688 components fit their serialization balls, all 883 closed prisms passed, and the minimum independently recomputed margin exceeds $0.5198$. The uniform error is less than $0.000356523011600040<1/800$.

The complete compressed evidence occupies about 47 MiB. The retained certificate verifier checks both full finite streams and every closed prism with exact rational parsing. Its initial generic failure-word check mistook the historical summary PASS: 30 FAIL: 0 for a failure; the parser now recognizes that exact zero-failure form and still rejects a nonzero failure count. No numerical inequality was weakened.

The final run_all.sh certificate replay exited 0. Its output is retained in compute/q2/run_all_result.txt. Fresh arithmetic was run through the individual sequential component drivers; the two-argument orchestration was not repeated after those successful full runs. Shell syntax and the component commands were checked. A final diff audit confirmed that every other README claim and every other problem folder remained unchanged.

The two main finite programs use little memory and ran sequentially under an exclusive lock. The historical stored assembly unexpectedly buffered about 1 GB; it passed after a compiler include-path repair, and was then removed from the normal replay path. Its work is redundant with the new streaming certificate assembly. Dependency installation remained under /tmp; package downloads and the upstream clone used the granted network approvals. No publication, merge, or external mathematical endorsement is implied by the local computations.