| paper | d4-conf-atal-2014-0087 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Neither named result asserts an algorithm, a complexity bound, or hardness: one characterizes network structure and the other describes contagion dynamics. The clique and biclique hardness claims are cited background, while the paper’s simulations do not provide a numbered computational guarantee. The proposed role-mass direction is an extension, but it cannot supply the missing eligible result.
fails bit a — no named computational result to mirror
No named computational result is covered; the proposed direction concerns Theorem 2’s common-knowledge characterization and Proposition 1’s contagion result, while the simulations remain unmirrored.
I cannot make a qualifying positive case under your anchor rule: the paper has no numbered result asserting that a problem is in P, NP-hard, FPT, or another complexity class.
The closest result is Theorem 2, proved here. It connects common knowledge among a set of agents to the presence of a complete bipartite subgraph among them. Proposition 1, also proved here, says that in any connected network, if every agent’s threshold is \(d_{\max}+1\), contagion reaches every agent within at most the graph’s diameter. These are substantive structural and dynamic results, but neither classifies the complexity of a computational problem. The NP-hardness statements in Section 4.1 concern maximal clique and biclique enumeration; they appear as background claims citing other work, not as numbered results of this paper.
There is a plausible direction for a mirror: a large platform population with a small number of communication roles, each role sharing a threshold and wall-access pattern. Give each role rational mass \(\mu_t\), and ask whether a positive mass of agents can share common knowledge and begin collective action. But preserving the paper’s exact knowledge structure may require encoding individual neighborhoods, making the number of types grow with the population; collapsing to a few roles may change the model. That is a real weakness, and the paper’s numbered results do not supply a computational anchor to overcome it.
So I would not offer a per-anchor continuous problem here: there are no eligible anchors. The paper may support a future continuous-dynamics question, but presenting it as a mirror of a named computational-complexity result would overstate the case.
The strongest case against a mirror is that the paper has no named computational result to mirror. Theorem 2 characterizes common knowledge through graph structure, and Proposition 1 bounds how quickly contagion spreads under a particular threshold condition. Neither classifies the complexity of a computational problem. The maximal-clique and biclique hardness claims in Section 4.1 are cited background, not results proved by this paper. Its main contributions are epistemic and dynamic, with simulations.
The best version of a mirror of Theorem 2 would give rational masses to finitely many network roles, specify links between roles, normalize thresholds, and ask for the largest mass of agents who can share common knowledge and coordinate. That is more credible than assigning mass to people while discarding their links. But preserving the paper’s exact knowledge structure either requires types that encode increasingly detailed neighborhoods, so the support can grow with the population, or assumes a finite block network with highly regular links. The latter could support a worthwhile new weighted graph problem, but it is a special continuous network model, not a computational result established by this paper.
Proposition 1 has a similar problem. The networks in the paper are sparse: their maximum degrees stay small relative to population size. If thresholds are normalized as fractions of the population, \((d_{\max}+1)/n\) tends to zero. If thresholds remain absolute counts, a distribution of population mass does not preserve the local edges and finite paths that drive the result. A dense graphon model avoids that sparse-limit collapse, but exact common knowledge depends on specific links and higher-order beliefs; a graphon records links only up to sets of measure zero. A finite block model can retain the relevant structure, but again it is a restrictive added assumption.
So the proponent’s proposed positive-mass question is not a strong mirror of either result. Its most defensible form is a new computational study of continuum network games, built around a chosen block or graphon model. That might be valuable, and the authors could plausibly recognize it as a natural extension. This is where the negative case is weak: the paper does not rule out such an extension. What it does support strongly is the narrower conclusion that the paper itself offers no eligible computational-complexity anchor, and that a continuous version preserving its central results needs substantial network structure beyond a population distribution over types.
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.