Independent certification of the 0.1787854 candidate

The complete certificate establishes $\Lambda\leq893927/5000000=0.1787854<1/5$ ; CLAIM.md states the exact inequality and falsifier. Both complete finite implementations, all fresh analytic lanes, and the independent certificate assembly have passed.

The candidate is due to Jude Gomila. This folder adds a new complete finite algorithm and an analytic audit. NOTE.md develops the argument, INTERPOLATION.md proves the new finite remainder bound, and ANALYTIC_REVIEW.md records the review of the candidate's analytic transfers. See ATTRIBUTION.md for source and authorship boundaries.

Reproduction

The pinned upstream checkout is required because the analytic source and archived comparison data remain there:

git clone https://github.com/judegomila/dbn-lambda-01787854-candidate-audit.git candidate
git -C candidate checkout a74738deb6d5e0f76887cb36901da08b68dca705

This checks both entire retained finite streams, all coefficient containments, all 883 prism inequalities, and the analytic interfaces. It requires Python 3.11 or later and git:

bash problems/riemann-hypothesis/compute/q2/run_all.sh "$PWD/candidate"

This mode checks the recorded interval computations. To rebuild the programs and regenerate all numerical lanes, supply a new output directory:

bash problems/riemann-hypothesis/compute/q2/run_all.sh "$PWD/candidate" /tmp/rh-q2-new-run

The fresh mode additionally requires a C17 compiler, 64-bit Unix, Rust, FLINT 3 with its Arb headers, and Python packages mpmath, sympy, and python-flint. The completed finite run used GCC 14.2.0, Rust 1.85.0, FLINT 3.1.3, mpmath 1.4.1, SymPy 1.12, and python-flint 0.9.0. Activate the Python environment before running. For a non-system FLINT installation, export FLINT_PREFIX to its prefix containing include/ and lib/ or lib/x86_64-linux-gnu/.

Fresh mode runs one numerical process at a time. Do not start a second fresh run alongside it. Logs are streamed and complete finite outputs occupy about 213 MB before compression. The two finite computations used less than 18 MiB each including their launchers. The historical upstream stored assembly was also checked once, but it buffered about 1 GB; it is excluded from the normal reproduction path because the new stream checks replace it. The reported RSS in its old lane manifest is cumulative across children and must not be read as each later job's memory usage.

What is checked independently

Obligation	First check	Independent check and scope
Every finite index	Original C Taylor producer	Rust positive-sum interpolation over all 3,149,013 indices; shares Arb
Weakest finite index	Original C row	Rust direct convolution without interpolation
Finite implementation regression	Rust update/merge algorithm	Python dictionary convolution on 100 cases
Finite error and infinite tail	Fresh C/Arb enclosures	Python interval calculations; repeated C precision is additional corroboration
Barrier	Fresh coefficient, remainder, derivative, and winding computations	Independent rational parser for all coefficient containments, seams, winding intervals, and prism inequalities
Theorem transfer	Candidate's supplied argument	Source-level analytic review, including the zero-time endpoint; no external human review claimed

check_rejections.py tests 16 malformed-certificate cases, including a wrong finite row with its hash updated to match. Hashes identify the evidence; the content checks enforce coverage and decisive inequalities.

Files

vendor/finite_original.c, regenerate.py: original producer and full streaming replay against the pinned archives.
direct.rs, interpolate.rs, ball.rs, arb_bridge.c: independent finite algorithms. The C bridge provides Arb operations only.
check_small.py, check_rejections.py: mathematical regression and certificate rejection checks.
replay_analytic.py: fresh height, error, tail, and barrier runs.
verify_finite.py, verify_analytic.py: complete transcript checks.
archive_results.py, check_certificate.py: retention and replay of complete evidence. Lane manifests retain claim_certified: false or certifies_claim: false because an individual lane is insufficient.

The complete compressed certificate occupies about 47 MiB. The finite-floor figure, PDF, and exact bin data show the two verified floors; the drawing is not a proof input.

An incomplete range, nonpositive margin, failed interval comparison, altered numerical source, missing analytic input, or unfinished barrier prevents success. A successful diagnostic is not the bound in CLAIM.md.