Claims

Search the graph by meaning. Each result carries its current verdict; open one to see its decomposition, provenance, and the reasoning behind the assessment.

3 results

The Kaliman–Zaidenberg conjecture in affine algebraic geometry that a homogeneous polynomial's Hessian vanishing implies it is a coordinate (in the polynomial ring); claims about its truth in a given dimension, counterexamples (e.g. dimension five), and relations to the Jacobian conjecture belong here.

The Hessian conjecture in dimension 2n implies the Jacobian conjecture in dimension n

VerifiedThe evidence, examined directly, establishes the claim.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Jacobian conjecture Algebraic geometryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The four-dimensional Hessian conjecture implies the two-dimensional Jacobian conjecture

VerifiedThe evidence, examined directly, establishes the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Jacobian conjecture Algebraic geometryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The Hessian conjecture is false in dimension five

VerifiedThe evidence, examined directly, establishes the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Algebraic geometryimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Contribute

If a claim here is wrong, or missing evidence, open it: every claim page carries its own entry for challenges, evidence, and corrections. If the graph is missing a claim or a question entirely, propose it below. A proposal is reviewed on its wording; accepted proposals are matched against the graph before they enter it.