trailAlpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverse
The Hessian conjecture is false in dimension five
Non-invertible constant-Jacobian polynomial self-maps of ℂ³ exist in every geometric degree at least three
claim · empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →claim page ↗︎
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
✓VerifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →credence 0.98Credence, 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 →
3depended on by
Bedrock: a verified fact. It is checked directly against sources; nothing lies beneath it.
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.