trailEvery polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverse
Planar partial results· for
The two-dimensional Jacobian conjecture holds for polynomial maps of degree at most 100
atomic
No known construction converts the three-dimensional Jacobian counterexamples into a two-dimensional counterexample
atomic
Collapse of the conjecture beyond the plane· against
The Jacobian conjecture is false in every dimension n ≥ 3
atomic
The two-dimensional Jacobian conjecture is false in characteristic two.
Mondello's characteristic-two counterexample to the two-dimensional Jacobian conjecture is mathematically correct.
The Jacobian conjecture is false in dimension three in characteristic two.
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Every polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
⇄ContestedCredible evidence or argument exists on multiple sides.constitution →credence 0.55Credence, from 0 to 1: the Steward's probability that the claim, as stated, is true. Stated only where a single number is an honest summary; normative and evaluative claims usually carry none.constitution →
1depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factopen questionvalue premisesupportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →Fig. Detail falls off with distance; every claim is an address.