| paper | d4-conf-aaai-2011-0244 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | unclear |
Theorem 1 is the strongest named candidate and gives the paper computational character through a recursive decomposition used for enumeration. But the proponent states no continuous question, and the opponent's type-composition reconstruction changes arbitrary named-agent values and constraints into a symmetric fractional model, so no anchor-specific mirror survives.
fails bit b-changes — the continuum limit changes the question
Theorem 1's recursive enumeration is the closest candidate; Proposition 1 and Lemmas 1–2 support the finite algorithms, while the experiments remain empirical. No continuous question in the cases covers these results.
I find no result that meets your anchor rule. The paper has numbered propositions, theorems, and lemmas, but none asserts a complexity classification or a named algorithmic guarantee for a computational problem.
The closest candidate is Theorem 1, proved here. It gives a recursive identity that splits the feasible coalitions according to whether they contain a selected agent. Algorithm 1 uses that identity, but the theorem does not establish a running-time bound or tractability result. Proposition 1 is a characterization of which constraint systems are propositionally definable; Lemma 1 and Lemma 2 support the algorithms. The paper’s performance claims come from experiments, not a numbered complexity result.
So I can’t honestly provide an anchor-specific continuous problem under the requested rules. A type-based welfare-maximization model might be a plausible extension, but it would be my construction rather than a mirror anchored in a qualifying result of this paper.
There is no anchor to defeat: the case for names none. Its central point is right under the requested standard. Proposition 1 characterizes which constraint systems are propositionally definable; Theorem 1 gives a recursive identity for enumerating feasible coalitions; and Lemmas 1 and 2 support the finite search procedures. None states a complexity bound or algorithmic guarantee. Algorithms 1 and 2 are contributions, but their speed claims are empirical. So this paper offers no named computational result whose complexity landscape a continuous mirror could chart.
The most promising reconstruction would take many interchangeable agents in a few types, describe each coalition by its type composition, and optimize over fractional quantities of coalition templates. That could be a sensible continuous coalition-formation problem. But it needs values to depend only on type composition and constraints to respect those types. The paper’s model instead permits arbitrary values and constraints on named subsets. Preserve all those distinctions in the types and the support may grow with the population; collapse them and the resulting problem is a new symmetric restriction.
The same issue blocks the closest theorem-level candidates. Theorem 1 branches on whether a particular agent belongs to a coalition. In a continuous population, mass of one type can be split across many coalitions, so the branch becomes a new mass-allocation model. Lemmas 1 and 2 likewise rely on each individual being assigned once and on finite lists of coalitions. A fractional packing LP over coalition templates might be worthwhile, but it would not be a continuous restatement of those results.
This is strong grounds against a *mirror of this paper’s results*, not proof that every continuous coalition-formation model is uninteresting. The negative case is weaker if “mirror” is broadened to include new, type-symmetric welfare models; under the stated anchor requirement, however, that broadening cannot supply the missing result.
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.