John Nader

An explicit coefficient-module proof of Conjecture 3.4(a) in Au's Wilf-Zeilberger seeds paper

K. C. Au, Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds, arXiv:2602.08721v3, conjectures in Conjecture 3.4(a) that the first summand S1(a,b,c,d,e;n) of Example II has coefficient spaces VN(S1) (the Q-span of the sequences n ↦ [ai1···ei5]S1 with...

A finite harmonic closure and assembled proposed proof of the eta(2tau)^12 eighth-power supercongruence

Start here: The finite harmonic congruence proof (PDF) contains the closing congruence T + H[N]S₃ ≡ 2U (mod p), for primes p > 5. The accompanying one-page, three-line reading guide (PDF) explains its last three steps in plain language with selectable symbols. For the assembled e...

A sharp tail lemma, a valuation census, and a collapse of the remaining obligation for the eta(2tau)^12 eighth-power supercongruence

The conjecture. For the newform η(2τ)12 = ∑ c(n)qn (weight 6, level 4, LMFDB 4.6.a.a) and tk = binom(2k,k)/22k, @multiple_zeta conjectured (10 July 2023) that for every prime p ≠ 2, 5, Σp = ∑k<p(4k+1)tk8 ≡ p·c(p) (mod p6). It is open; the proved uniform record is the same congrue...

A reduction: no finite Hankel prefix certifies the Riemann Hypothesis without Xi-specific input, and the exact rank at which a hidden pair appears

A reduction, displayed in the Frey–Ribet–Wiles style. The Riemann Hypothesis is equivalent, through the square-variable function GΞ(w) = Ξ(√w)/Ξ(0) and its logarithmic moments σn, to positive semidefiniteness of the single Hankel tower Hr = [σi+j+1] at every rank r (self-weighted...

Two mathematical defects in the IT³ "Perez Hourglass" architecture (Zenodo 21792530): a metric signature change at the poles, and failure of the stated O_h invariance

Comment on V. Logvinovich, “The Macroscopic Vacuum Architecture: Perez Hourglass Topology, Counter-Rotating Bowls, and m=6⊕12 Fractal Superposition in the Solar System (IT3 Framework v6.0)”, Zenodo, 2026-08-04, doi:10.5281/zenodo.21792530. Two equations displayed in the target ma...

Two mathematical defects in the IT³ "Perez Hourglass" architecture (Zenodo 21792530): a metric signature change at the poles, and failure of the stated O_h invariance

Comment on V. Logvinovich, “The Macroscopic Vacuum Architecture: Perez Hourglass Topology, Counter-Rotating Bowls, and m=6⊕12 Fractal Superposition in the Solar System (IT3 Framework v6.0)”, Zenodo, 2026-08-04, doi:10.5281/zenodo.21792530. Two equations displayed in the target ma...