Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 089. Bounded-distortion L 1 embeddings of planar and bounded-treewidth graphs
Family claims › Convex and metric geometry · lines 706–711
OpenAI@2026-10-07#rem:oai-089
Resolves the planar and bounded-treewidth cases of the Gupta–Newman–Rabinovich–Sinclair conjecture. Shortest-path metrics of finite connected graphs with arbitrary positive edge lengths embed into real with universal distortion for planar graphs, and distortion depending only on treewidth for bounded-treewidth graphs. The corresponding multicommodity flow–cut gaps are uniformly bounded.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 087. The Mahler conjectures and symplectic width
- remark: Remark: Family 088. Petty's projection-volume conjecture and simplex counterexamples
- remark: Remark: Family 090. Universal optimality of the triangular lattice
- remark: Remark: Family 091. The logarithmic Brunn–Minkowski conjecture
- remark: Remark: Family 092. The optimal order of convex-body covering density
- remark: Remark: Family 093. Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
- remark: Remark: Family 094. Subpolynomial dimension reduction in L p
- remark: Remark: Family 095. Hyperbolicity cones without semidefinite lifts