What was already known
Da Silva Machado and Seade posed the equivalence and proved partial cases by dimension or parity.
AI involvement
The paper says the Danus system, built on Rethlas, obtained the main equivalence, the singular first-jet and contracting-flow lemmas, and the fixed-coordinate counterexample. The authors retained its self-contained proof even after recognizing Morando's contraction theorem as an alternative route.
The source explicitly attributes the main proof and counterexample to Danus and describes the present paper as AI-generated; no human mathematical input to that proof is identified.
Importance
Resolves the stated weighted-homogeneity characterization within these hypotheses.
Limitations
The coordinate change must match the transversality coordinates; the paper gives a fixed-coordinate counterexample. Liu and Zhang report a human check but do not identify its checker or procedure. Their parallel human proof is separate work.
Technical verification
The authors report a completed human verification of the main result and internal-system verifier checks, but do not name the human checker or describe the check's procedure. The internal verifiers are not identified as proof assistants or exact certificate checkers. A separate human proof establishes the same theorem without checking this argument, so the evidence does not meet the named-checker requirement for Formal.
Human understanding
Liu and Zhang's separate human paper explains the same equivalence through a contracting flow and microlocal index route; the Danus paper itself explains its first-jet and flow mechanism. This supports understanding of the result, not independent checking of every Danus step.
Correction and publication history
Resolves the stated weighted-homogeneity characterization within these hypotheses.
Read this published revision