| paper | d4-journals-geb-2025-0050 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1's proof explicitly constructs a finite path to \(\mu^T\), so it gives a constructible reachability result even without a stated runtime bound. But complete types include strict priority ranks, making every student's rank vector unique; the model has no repeated-type population to aggregate. Priority categories and mass coalitions would change the admission and deviation rules, so no author-recognizable population mirror survives.
fails bit b-none — no population with multiplicity to relax
The proposed direction focuses on Theorem 1's TTC reachability claim; it leaves Corollaries 1–2 and Theorems 2–4 uncovered.
A plausible positive direction would use large school districts with many applicants but few complete preference and priority profiles. A type would record a student’s ranking and priority category at each school; \(\mu_t\) would be that type’s share of applicants. The state would record how much mass of each type is assigned to each school, and a candidate question would ask whether a mass analogue of the TTC allocation can be reached from any initial assignment by farsighted mass transfers.
But that is a proposed extension, not a continuous mirror anchored in this paper’s computational results. The paper has no named computational result of the required kind. Theorem 1, proved here, says that the singleton containing the TTC matching is a farsighted stable set. Corollary 1 restricts the coalitions needed to reach it, and Corollary 2 says the same singleton is stable for horizon \(k\geq 3\). Theorems 2–4 establish analogous stability claims for FCT, CT, and ETTC. None asserts a complexity classification or presents a computational formulation that the paper analyzes. The proof of Theorem 1 constructs improving paths, but it does not state a running-time result.
The proposed mass model also replaces the paper’s strict rankings of named students with priority categories and individual coalitions with mass coalitions. That may be a reasonable research extension for repeated applicant profiles, but it changes the dynamics the paper studies. So I cannot honestly supply a qualifying anchor or a per-anchor prover question: the strongest positive case here is only a plausible new direction, not a paper-anchored ChoCo mirror.
The paper gives no computational result to continuize. Theorem 1 says the TTC matching is a farsighted stable set; Theorems 2–4 say the same for three variants. Corollaries 1 and 2 restrict the coalitions and lookahead needed to reach those matchings. These are results about existence and structure of improving paths, not about the complexity of finding a matching, deciding stability, or computing a path. The paper does not pose or analyze any such computational problem.
The proponent’s large-district model is the strongest possible starting point, but it exposes why this would be a new project rather than a mirror. In the paper’s model, a student’s complete type includes her strict priority rank at every school. Since each school’s priority order is strict, students have distinct complete types, so the exact model offers no repeated types to aggregate. Replacing exact ranks with priority categories can create multiplicity, but it also changes how schools choose whom to admit or evict. A model retaining strict priorities through continuous priority scores faces a related issue: there is no highest-priority individual of positive mass to form the finite TTC cycles used in the proofs. Defining mass cycles and mass coalitions may be sensible, but the resulting dynamics and their computational questions would have to be built from scratch.
One could ask whether such a redesigned mass model has a farsightedly stable assignment, or how to compute it. But the former is a new stability theorem, and the latter needs a new input representation and algorithmic task. The finite paper’s reachability result does not supply either. So none of its named results survives as a ChoCo computational mirror; the proposed scenario is plausible as a separate continuous-matching project.
The negative case is strongest against a *paper-anchored* mirror, not the universal claim that no continuous school-choice project could be worthwhile. The large-district setting could support useful research, but this paper gives little reason to prioritize it for a programme focused on computational complexity.
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.