Four certified results in analytic number theory: a refined bound for simple zeta zeros on the critical line, C > 3.14279 for the Montgomery–Vaughan constant, the sharp odd Robin threshold, and a refuted Epstein zeta conjecture. Interval-arithmetic certificates, reproduction code, Lean 4 proofs.

interval-arithmetic formal-verification arb mathlib riemann-hypothesis analytic-number-theory lean4 critical-line riemann-zeta-function python-flint hilbert-inequality epstein-zeta-function

• Updated Nov 11, 2026
• HTML

Three results in analytic number theory with interval-arithmetic certificates and a Lean 4 core: the log log Q in Wolke's prime-moduli large sieve is necessary; Λ is unbounded on a family sharing L(s,χ₋₇)'s functional equation; Λ > 0.23 for the Davenport–Heilbronn function. Unrefereed.

interval-arithmetic formal-verification arb mathlib mpmath analytic-number-theory lean4 l-functions de-bruijn-newman-constant python-flint davenport-heilbronn large-sieve proofmap

• Updated Nov 11, 2026
• HTML

Arbitrary precision floating / ball arithmetic (interval arithmetic) dtype in NumPy / array API

numpy arbitrary-precision flint acb interval-arithmetic arb mpmath array-api python-flint

• Updated Nov 8, 2026
• Python

Bernstein's constant to ten rigorously certified digits: beta = 0.2801694990, proved in interval arithmetic (Arb) where the 1985 Varga-Carpenter rigorous enclosure gives five. OEIS A073001. Every number re-derivable from the shipped data in exact arithmetic.

reproducible-research open-data oeis interval-arithmetic arb numerical-analysis approximation-theory computer-assisted-proof chebyshev-approximation rigorous-numerics best-uniform-approximation mathematical-constants certified-computation python-flint bernstein-constant

• Updated Sep 3, 2026
• Python

Adaptive Precision Search algorithm.

math algorithms computational-mathematics arbitrary-precision number-theory lattice-basis-reduction mpmath lll-reduction pslq python-flint

• Updated Oct 7, 2026
• Python

OMEGA Framework: certified interval-arithmetic enclosures of the Guinand-Weil matrix (Arb LDL^T, N=400 and N=800 positive definite, ball arithmetic, python-flint). Matrix-constraint verification -- not a proof of the Riemann Hypothesis.

reproducible-research mathematics arbitrary-precision spectral-analysis numerical-linear-algebra mpmath ball-arithmetic certified-computation python-flint guinand-weil ramanujan-pft positive-definiteness ldl-t eigenvalue-bounds

• Updated Oct 15, 2026
• Python

Anonymous CC0 unrefereed candidate on exact low-length Recht–Ré inequalities, with replayable certificates, six-factor balanced families, and a reshuffling metric reversal.

python reproducible-research sympy semidefinite-programming sum-of-squares computer-assisted-proof exact-arithmetic random-reshuffling noncommutative-algebra python-flint matrix-inequalities

• Updated Aug 21, 2026
• Python

Rigorous ball-arithmetic certification of the Riemann zeta function, Dirichlet L-functions and Guinand-Weil spectra: certified interval enclosures, sealed hash-chained ledgers, CI-guarded reproducibility.

reproducible-research interval-arithmetic spectral-analysis random-matrix-theory computational-number-theory rigorous-numerics lean4 riemann-zeta-function ball-arithmetic certified-computation python-flint dirichlet-l-functions guinand-weil interval-newton

• Updated Nov 3, 2026
• Python

Independent verification of the published certificates of rigorous lower bounds for the truncated Weil form in Arb ball arithmetic (python-flint).

interval-arithmetic arb computer-assisted-proof computer-assisted-proofs rigorous-numerics explicit-formula python-flint weil-form

• Updated Nov 5, 2026
• Python

Arb-certified local descent near regular projective-response levels in quantum control.

interval-arithmetic chebyshev quantum-control geometric-control computer-assisted-proof python-flint validated-numerics

• Updated Aug 18, 2026
• Python