| paper | d4-journals-mss-2025-0028 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper’s numbered results characterize the core through axioms or minimality; none states an algorithm, computational hardness result, or computational formulation. A type-based NTU-core problem would require a new input representation and task, so it would not mirror a result in this paper.
fails bit a — no named computational result to mirror
Theorem 1, Theorem 2, and Theorem 3 provide axiomatic characterizations or minimality results; none has a computational mirror anchored in this paper.
I can’t make an anchored positive case under your rules: this paper has no named computational result.
Theorem 1, proved here, characterizes the core as the unique solution satisfying PO, NESPG, SSC and CSSC. Theorem 2, also proved here, gives a different characterization on \(\Gamma\), plus a two-player result under non-levelness. Theorem 3 gives a minimality characterization. These are axiomatic claims; none asserts that a problem is tractable, hard, or has an algorithm. The lemmas support those proofs, and the paper does not formulate a computational problem.
A continuum-agent core problem could be sensible in another project. But here each game has a finite player set \(N\), even though the universe \(U\) may be infinite. Replacing finite players and coalitions with masses and measurable coalitions would introduce a new model and a new computational question. It would not mirror a computational result in this paper, and axiomatic continuization is outside ChoCo’s stated scope. So there are no eligible anchors for which to write a prover-ready continuous problem or give a complexity prediction.
The negative case is unusually strong because it does not depend on whether a high-multiplicity NTU game is sensible. The paper has no computational result to mirror. Theorem 1 and Theorem 2 characterize the core through axioms; Theorem 3 gives a minimality characterization. None studies an algorithm, complexity, or approximation problem. So there are no computational anchors for the proponent to leave standing or for me to rebut.
The best candidate for a new project would be a type-based NTU game: coalition possibilities depend on the masses of finitely many player types, the payoff sets have a finite encoding such as rational polyhedra, and the task is to find a core allocation or decide whether one exists. That could be worthwhile. But the paper neither defines such an input representation nor asks that computational question. Its domain \(\Gamma\) allows arbitrary closed comprehensive payoff sets; boundedness of individually rational payoffs does not give them a finite encoding. Turning the candidate into a computational problem therefore requires adding a population model, an encoding, and a task. It is a new project, not a mirror of any theorem here.
A direct continuization of the paper’s results would instead ask for axiomatic characterizations on a continuum of players, which is outside ChoCo’s computational scope. The honest limit of the negative case is that I cannot establish that *no* continuous NTU-core problem would be worthwhile. I can make the narrower case that this paper supplies no worthwhile computational mirror for the programme.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.