| paper | d4-conf-aaai-2005-0083 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper states runtimes for Wrapper-Greedy and other algorithms, but none appears as a numbered theorem, lemma, corollary, or proposition asserting a computational result. The opponent’s shared-slate question is a plausible extension of the paper’s open challenge, but it cannot supply the required result anchor.
fails bit a — no named computational result to mirror
No numbered computational result is anchored; the paper’s greedy-algorithm runtime claims and empirical comparisons remain outside the required anchor.
This paper has no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result, so it provides no eligible anchor for the requested continuous mirror. It does give unnumbered complexity bounds for its greedy algorithms and reports experimental performance, but neither meets the anchor requirement. Without a named result to restate, I can’t make the required anchored case.
The proponent raises no mirror to defeat; their point is that the paper has no numbered complexity theorem. But the paper does give explicit computational claims for named algorithms: its complexity analysis assigns Wrapper-Greedy runtime \(O(mk^2n^2)\), for example, and compares it with exhaustive search. Those claims supply a concrete anchor even without theorem numbering.
A continuous population version follows the paper’s own open question about combining users’ preferences when they must agree on one subset. Suppose a large community must choose one shared slate of \(k\) images or documents from a discrete catalogue \(U\). Let each user type \(t\) have a complete DD-PREF statement \(P_t\), with rational population mass \(\mu_t\). The computational question is to maximize
\[
\sum_{t=1}^{\tau}\mu_t F_{\rm dd}(S,P_t,\alpha_t)
\quad\text{over } S\subseteq U,\ |S|=k,
\]
and determine the exact, approximation, or parameterized complexity in \(n,k,m,\tau,L\). The preference-type support can be small even when the audience is large: users choosing the same DD-PREF template are indistinguishable for this decision, so grouping them into mass preserves the model’s relevant information.
This keeps the catalogue and selected slate discrete; the population of people whose preferences determine the common choice is what becomes continuous. It is therefore a population mirror, not outcome-space continuity. It also has a strong author-recognition test: the paper itself identifies agreement among multiple users over a single subset as a remaining challenge. The absence of a numbered theorem makes the anchor less formal, but it does not erase the paper’s named algorithms, stated runtimes, or this direct route to a continuous computational question.
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.