| paper | d4-journals-mss-2020-0038 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The cited numbered results give learning-efficiency guarantees, a reduction, and a welfare improvement, but none states a computational result under the required test; the paper’s hardness remark is unnumbered. The opponent is right that the proposed hybrid graph-limit optimization would be new modeling, not a continuous computational question anchored by these results.
fails bit a — no named computational result to mirror
No result is covered by a qualifying mirror: Theorems 3.2, 3.3, and 3.5 establish efficiency guarantees; Lemma 4.4 gives a reduction; and Theorem 6.2 proves a welfare improvement. The paper does not number its claim that optimal network design is hard.
I can’t make an anchor-based positive case under your criteria: the paper has no numbered result asserting a computational complexity or algorithmic result.
Theorems 3.2, 3.3, and 3.5 establish asymptotic \(\epsilon\)-efficiency of celebrity graphs under different arrival-order regimes. Lemma 4.4 reduces the multi-issue efficiency analysis to a single-issue one. Theorem 6.2 shows that, for sufficiently large populations, some multi-layer guinea-pig graph yields greater expected welfare than the best guinea-pig graph. These are analytical or structural claims, not complexity results about computing a network or an equilibrium.
The paper does say in §1.1 that finding an optimal observability graph is hard even for one issue with a known order. But that claim is unnumbered and has no named theorem to quote and restate as an anchor. Treating it as one would break your anchor requirement. So there is no eligible anchor here, and I can’t honestly supply the required per-anchor continuous problem.
The proponent offers no continuous question to defeat. Their references to Theorems 3.2, 3.3, 3.5, Lemma 4.4, and Theorem 6.2 identify analytical results, not complexity or algorithmic results. The first three prove efficiency guarantees for celebrity networks under different arrival regimes; Lemma 4.4 proves a reduction between multi-issue and single-issue analyses; Theorem 6.2 proves that some multi-layer network improves on the best single-layer guinea-pig network. None classifies the complexity of computing a solution. The paper’s remark that finding an optimal graph is hard is not developed here as a named computational result.
The strongest possible repair would be to ask how to compute an optimal or \(\epsilon\)-efficient network for a high-multiplicity society, perhaps represented by a continuum graph kernel. That regime is plausible: many agents could share the same signal and issue characteristics. But it does not mirror the cited results. For fixed \(\epsilon\), their construction uses \(M(\epsilon)\) celebrities, so \(M/N\) tends to zero as the population grows. A population measure loses those zero-mass agents, even though their actions influence almost everyone. Preserving that channel requires a hybrid model with finitely many distinguished agents attached to a continuum, or a more elaborate multi-scale limit. Either may be a worthwhile new model, but neither is the population-distribution mirror of the stated theorems. Arbitrary arrival distributions also refer to named agents and permutations; moving them to types requires a new order model.
The same issue applies to Theorem 6.2. One could optimize layer masses in a continuum model, but that would pose a new optimization problem. The theorem itself only establishes a welfare improvement; it gives no computational result to continuize.
So the negative case is strong under the programme’s anchor requirement: none of the proponent’s named results supplies an eligible computational claim, and the obvious continuations require substantial new modeling. It is weaker as a universal claim that no scenario could yield a worthwhile continuous problem. A carefully designed hybrid network-design problem might be interesting; the paper simply does not establish that case.
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.