The Generalized Vanishing Conjecture fails in five variables
Structured and assessed
Left the claim atomic: it has one natural line of support, an explicit counterexample, so no named argument was created. Minted the parent claim "Zhao's Generalized Vanishing Conjecture holds." (this claim contradicts it). Verified the counterexample by exact computation for m ≤ 10 and gave a hand proof of the vanishing for all m. Status: verified (0.9). Importance 0.3, contestation 0.15. Corrected the instance's attribution to Dvorsky. Set no source map: there is a single primary instance, so a map would add nothing.
Updated claim instance
Instance 806a5735-20ac-4a34-b519-61200c4e3417 (https://sbseminar.wordpress.com/2026/07/20/the-new-counterexample-to-the-jacobian-conjecture/): was stance=affirms, confidence=0.8; set confidence=1, speaker="Alexander Dvorsky", publication="Secret Blogging Seminar (comment)", sourceDate="2026-07-23". The page shows the comment was written by Alexander Dvorsky on July 23, 2026.
Assessed Verified
verdict confidence 0.90 · credence 0.97
Zhao's Generalized Vanishing Conjecture says that if a constant-coefficient differential operator Λ and a polynomial P satisfy Λ^m(P^m) = 0 for every m ≥ 1, then for every polynomial Q, Λ^m(Q P^m) = 0 for all sufficiently large m. In July 2026, after Levent Alpöge's announced counterexample to the three-dimensional Jacobian conjecture and Long's SU(2) construction, Alexander Dvorsky proposed an explicit five-variable counterexample: P = (t+c)(ad+bt), Λ = ∂_t(∂_a∂_d − ∂_b∂_c), Q = −c. The construction checks out. Because P has degree 3 and Λ has order 3, Λ^m(P^m) is a constant. A direct expansion shows it equals (m!)^3 Σ_j (−1)^{m−j} C(m,j), which is zero for every m ≥ 1. Λ^m(Q P^m) is linear, and exact computation for m = 2 to 10 gives (−1)^{m+1}(m+1)!(m!)^2 · t, which is never zero. David Speyer could not reproduce the result at first, then traced the discrepancy to his own transcription error and confirmed the construction. One gap remains: nonvanishing for every m is established here by computation and a clear closed-form pattern, not by a written proof. Because the conjecture only requires Λ^m(Q P^m) to vanish for all large m, nonvanishing for infinitely many m is enough to refute it, and the pattern leaves little room for doubt. The main shortfall is that no refereed write-up has yet been located.
Add parent claim
Minted parent claim a00d9637-595f-40ab-8010-0ebf65a4f3b1 ("Zhao's Generalized Vanishing Conjecture holds.") and attached this claim as its subclaim (contradicts): The five-variable failure is a special case bearing on the general conjecture (GVC in all dimensions); a counterexample in five variables refutes the general statement. The graph held only the dimension-indexed claim.
Claim entered the graph