| paper | d4-journals-mss-2004-0017 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named results characterize rules by axioms; none states an algorithm, complexity bound, hardness result, or computational formulation used to compute. Thus bit (a) fails, even though one could imagine axiomatic questions over a distribution of claim types.
fails bit a — no named computational result to mirror
No mirror covers a named result; Theorems 1–2, Proposition 1, Corollaries 1–2, and the associated rule characterizations remain axiomatic.
I can’t make a defensible anchor-based case for a continuous mirror under the programme’s criteria. The paper contains no named computational result: Theorems 1 and 2 characterize classes of rules satisfying additivity properties; Proposition 1 and Corollaries 1–2 give further rule characterizations. None establishes complexity or an algorithm for an underlying computational problem.
The strongest possible candidate, Theorem 1(d), says that the proportional rule is the only bankruptcy rule satisfying additivity on the estate. But it is an axiomatic characterization, so it does not qualify as an anchor here. Recasting it over a continuum of claim types would produce an axiomatic question about population distributions, not the computational question this programme asks. The paper’s real-valued allocations also make outcomes continuous; they do not make the society continuous.
So there is no qualifying anchor for which I can state the requested prover-ready computational mirror. The main weakness is decisive: offering one would require changing the paper’s research question.
The case for leaves no computational anchor standing: it identifies Theorem 1(d) as the strongest candidate, then correctly observes that it characterizes a rule rather than the complexity of a computational problem. Theorem 1, Theorem 2, Proposition 1, and the corollaries all have the same character. They describe which rules satisfy specified axioms; none asks an algorithm to decide, optimize, or compute an output from an encoded instance.
A stronger proposed mirror could put claim amounts into types and represent the population by a distribution over those types. That may be a sensible high-multiplicity model: many creditors or claimants can share a claim amount. But it would turn these results into axiomatic questions about rules on distributions. It would not supply the missing computational problem. For Theorem 1(d), evaluating the proportional rule on a finite list of claim types is just its stated formula; the paper does not study that evaluation task. Other characterizations allow arbitrary functions of claims, without specifying an input representation or an algorithmic task to mirror.
The paper’s real-valued claims and estates do not themselves make its population continuous. A continuous population version might be worthwhile as axiomatic research, but that is outside ChoCo’s computational scope. The negative case is strong on that scope question: there is no named computational result to mirror. It is weaker as a universal claim that no worthwhile computational question could ever be built from these models; such a question would be a new project, rather than a continuous mirror of a result in this paper.
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.