| paper | d4-journals-mss-2025-0031 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper’s numbered results establish behavioral equivalences and characterizations, but make no computational claim, so bit (a) fails. The proposed market-frequency decomposition is a new aggregate stochastic inference problem; this paper neither formulates nor computes it.
fails bit a — no named computational result to mirror
No result is covered by a computational mirror: Theorems 1–4 give behavioral equivalences or representations, and Theorem 5 is an attributed axiomatic characterization; the proposed decomposition lies outside them.
The paper contains no named computational result of the required kind. Theorem 1 (proved here) equates shortlisting with optimal limited attention; Theorems 2–4 (proved here) give further behavioral equivalences; Theorem 5 is a characterization attributed to Sen (1986). None asserts that a computational problem is in P, hard, fixed parameter tractable, or otherwise classifies its complexity. The paper studies representations of one decision maker’s choice function, not algorithms for a computational problem. So there is no eligible anchor, lead, or per-anchor continuous problem to offer.
The most plausible population extension would be a market with many consumers who repeatedly face the same menus and fall into a small number of complete behavioral types. Let type \(t\) specify a consumer’s full menu-choice rule \(c_t\), including their preference and attention behavior, and let \(\mu_t\) be that type’s population share. One could ask whether observed market frequencies \(q_A(x)\) admit a decomposition \(q_A(x)=\sum_t \mu_t \mathbf{1}[c_t(A)=x]\), where each \(c_t\) is list-rational, equivalently has competitive limited attention by Theorem 4. This is a plausible high-multiplicity research extension, but it turns the paper’s deterministic individual choice into aggregate stochastic choice. The paper itself describes stochastic extensions as future work, and Theorem 4 makes no computational claim about this decomposition problem. It cannot honestly serve as the required anchor.
So the positive case is limited to a plausible adjacent direction, not a continuous mirror anchored in a named computational result of this paper.
The paper has no named computational result to continue. Theorem 1 equates shortlisting with optimal limited attention; Theorems 2–4 give behavioral equivalences for salient attention, rationalizability, and list rationality. They characterize individual choice functions. None studies an algorithm, complexity, or computational problem. Theorem 5 is an axiomatic characterization attributed to Sen. This leaves no eligible result to anchor a continuous mirror.
The proponent’s market example is the strongest candidate, and it still changes the object. A continuum of consumers with complete behavioral types \(c_t\) is a plausible high-multiplicity setting. But the proposed frequencies \(q_A(x)=\sum_t\mu_t\mathbf{1}[c_t(A)=x]\) are stochastic aggregate choices. Theorem 4 concerns one deterministic choice function; it says nothing about whether those frequencies admit a decomposition into list-rational types, or how to compute one. Testing that decomposition could be a worthwhile new inverse problem. If each consumer’s full choice function is observed instead, the paper’s results apply type by type, and population mass adds no computational question.
The other theorems have the same limitation: applying their equivalences to many people either repeats the individual characterization for each type or requires an aggregation and inference problem the paper never formulates. Adding a collective decision rule would require another model layer. So the negative case is strong for the proposed task: no continuous mirror of a computational result in this paper has been identified. Its honest weak point is the universal claim that no adjacent project could be worthwhile; the mixture problem may merit study on its own, but it is a new computational theory of aggregate behavioral data.
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.