What was already known
The planar embedding question asks for one bound independent of graph size; finite experiments cannot establish it.
What changed and why it matters
Resolves the planar L₁ embedding question for the full stated class of weighted planar graphs.
The AI contribution
OpenAI attributes the manuscript to an internal frontier model. This entry does not infer the exact human contribution to this individual result from the release-wide description.
Limitations
The statement concerns planar shortest-path metrics. It does not give the same bound for arbitrary graphs or zero/negative edge weights. Preprint. AIProofWatch reviewed the source statement and scope, not the full proof, and has not independently run a formal checker.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Reported theorem in the pinned manuscript. This records the claim, not an independent proof check.
Accessible artifact / proof
Manuscript proof is accessible. Formalization availability alone is not labelled as successful formal verification.
Correction and publication history
Editorial importance reassessment: rate the scoped impact if correct independently from verification. The claim, limitations, sources, and verification evidence are unchanged.
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