OpenAI · 168-01 · 2026-09-24 · Combinatorics
Combinatorial invariance of Kazhdan–Lusztig polynomials
preprints/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026
Family 168. Combinatorial invariance of Kazhdan–Lusztig polynomials.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the full combinatorial invariance conjecture: isomorphic Bruhat intervals in arbitrary Coxeter systems have identical equal-parameter Kazhdan–Lusztig polynomials. Thus the abstract order of the interval determines the polynomial, even across different Coxeter systems.
We prove that an isomorphism of Bruhat intervals in arbitrary Coxeter systems preserves their equal-parameter Kazhdan–Lusztig polynomials. This resolves the full combinatorial invariance conjecture positively.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 168: Combinatorial invariance of Kazhdan–Lusztig polynomials. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.