What was already known
Earlier work characterized threshold-graph Hansen polytopes as Hanner and established related bounds for split, unconditional or locally anti-blocking classes, without these three all-cograph statements.
AI involvement
Jeremy Parker set the project and wrote or repaired portions by hand. GPT-5.6 Sol and Terra sessions designed the overall proof structure and proved sections. Jonathan Ho’s separately authored analytic Lean work supplies supporting infrastructure; a completed human check of all final theorems is not documented.
AI sessions supplied the overall proof design and individual central sections, with Parker's manual contributions and Ho's upstream infrastructure separately credited.
Importance
Proves three sharp inequalities and their equality cases for Hansen polytopes of cographs.
Limitations
The formalized class excludes the null graph; these results do not settle the analogous conjectures for all centrally symmetric polytopes.
Technical verification
The six Solution declarations are reported proved in Lean with no proof-side admits or custom axioms. The six Challenge holes are deliberate statement placeholders; this review did not rerun the kernel.
Formal checking
Lean compilation of the six proved cograph statements and a permitted-axiom audit.
- Checker
- Lean 4 kernel
- Scope
- The six Mahler, face, flag and threshold-equality declarations for nonempty cotree cographs
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Manual edits and a literature explanation are documented, but no named human explanation of all three central proof mechanisms is established; Few is the evidence-gap default.
Correction and publication history
Proves three sharp inequalities and their equality cases for Hansen polytopes of cographs.
Read this published revision