Riemann hypothesis, first computation

Outcome

The published explicit de Bruijn–Newman window remains

This folder has three replayable pieces:

1. Exact arithmetic for the Polymath 15 / Platt–Trudgian parameters. The printed decimals in Polymath Table 1 give $0.19999966445$, but the table is rounded and Platt–Trudgian prove the stated bound $0.2$. The extra digits are therefore diagnostic only.
2. A resource-light audit of the off-arXiv $0.1787854$ candidate at commit a74738deb6d5e0f76887cb36901da08b68dca705. The upstream stored assembly parsed all 3,149,013 finite rows. Fresh Arb runs at 256 and 512 bits checked the Proposition 4.10 error bound and the infinite tail; a fresh barrier run checked 883 consecutive prisms and all 7,688 stored-sum components. A fresh producer run matched the sealed first finite row at $N=690988$. The full finite range was not freshly regenerated, and the analytic bridge was not independently reviewed, so this is residue and not a new upper bound.
3. The printed Saouter–Gourdon–Demichel Lehmer-pair arithmetic, including $G<379.1995$ and the historical $\Lambda>-1.14541\cdot10^{-11}$. That lower bound is now dominated by Rodgers–Tao's $\Lambda\geq0$.

Replay

From any directory:

problems/riemann-hypothesis/compute/q1/run_all.sh

The local replay needs Python 3 and a C compiler, uses no network, and finishes in well under a second. It checks the fresh-log hashes, exact rational identities, all decisive log markers, the 883-prism sequence, and the Lehmer formula through independent Python Decimal and C long double paths.

What the retained logs mean

The files under fresh/ were regenerated sequentially from the candidate repository with GCC 14 and FLINT/Arb 3.1.3. The two precision lanes agree, and the finite producer's first canonical row agrees exactly with the sealed row. barrier_target_closed.log took about 55 minutes wall time while another campaign was already using the machine; the remaining fresh numerical lanes were short. The candidate source and its archived certificates are not copied here. Its repository is judegomila/dbn-lambda-01787854-candidate-audit.

The scope note in uniform_error.log is important: analytic justification at $t=0$ remains external. Hashing a successful log authenticates this replay; it does not supply a missing theorem.