Local-to-Global Invertibility Challenge
S16
smale derived
smale derived
External: externally open
τ response: further investigation
If a polynomial map over a characteristic-zero field has constant nonzero Jacobian determinant, must it have a polynomial inverse?
Current τ response
See the paired Local-to-Global Invertibility Challenge — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.
Current status: further investigation.
Challenge statement
If a polynomial map over a characteristic-zero field has constant nonzero Jacobian determinant, must it have a polynomial inverse?
Why this challenge is in the ledger
Excellent fit for τ-holomorphy, regularity, continuation, invertibility, and local-to-global structure.
τ-facing burden
Show whether τ-holomorphic or address-theoretic structure can detect when local invertibility extends to global polynomial inverse structure.
First reviewer questions
- Does τ produce a genuine attack on the Jacobian conjecture?
- Is τ-local nondegeneracy equivalent to the classical Jacobian condition?
- Does τ introduce extra assumptions that make the result easier but non-equivalent?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.