2 claims investigated in this paper
| 1 | Theorem 1Theorem · main result | No defect found | Deep auditfull source check |
| 2 | Theorem 2Theorem · main result | No defect found | Deep auditfull source check |
Theorem 1
No defect found
No counterexample or nontrivial proof gap survived the recorded audit of the hierarchy direction.
Theorem 1. If the region family is a hierarchy, there exists a mechanism that is stable and strategy-proof for doctors.
This record reports an unsuccessful attempt to find a defect within the stated scope. It is not a proof that the result is correct.
What was tested
The audit reconstructed the hierarchy mechanism and checked archived finite suites covering 4,284 hierarchical markets, 1,638,144 outcomes and 59,927,040 unilateral-deviation checks, with zero recorded failures. The proof logic and theorem quantifiers were also reviewed against the published version.
Limits
The finite search is selective and does not prove unrestricted sufficiency. The publication review reconciled the archived counts and source logic but did not rerun all 59,927,040 deviation checks.
Source
Full check, pp. 769–772. The stability definition, mechanism quantifiers and Theorem 1 were checked on rendered pages of the published version.
Evidence rerun
Partial. The archived package integrity and reported counts were reconciled; the full historical computation was not rerun during publication review.
Theorem 2
No defect found
No counterexample or nontrivial proof gap survived the recorded audit of the non-hierarchy impossibility direction.
Theorem 2. If the region family is not a hierarchy, no mechanism is stable and strategy-proof for doctors across the paper's admitted domain.
This record reports an unsuccessful attempt to find a defect within the stated scope. It is not a proof that the result is correct.
What was tested
The audit checked the paper's decisive three-profile non-hierarchy example: at the baseline there are two stable matchings, and whichever one a putative stable mechanism selects, one doctor can misreport so that the other becomes uniquely stable and is strictly better under that doctor's true ranking. An exact certificate, a separate finite stability checker and a full 576-report stable-selection model corroborate the case split.
Limits
The theorem is about a mechanism over the full admitted domain, not impossibility for every fixed non-hierarchical profile. The finite certificate supports the decisive construction but does not by itself prove every step of the general theorem.
Source
Full check, pp. 772–774, 787–788. Theorem 2, the three-profile example and the general non-hierarchy proof were checked on rendered pages of the published version.
Evidence rerun
Partial. The archived exact certificate and model outputs were reconciled and the logical case split was rechecked; the entire historical computation was not rerun during publication review.
Authors and corrections
- Authors
- The authors were not contacted; author notification is not a publication requirement.
- Correction
- None published.
History
- October 2026Deep audit completed: no defect found within the recorded scope
- 31 October 2026Full published-version source check completed
- 6 November 2026Record version 1.0 approved for release
Versions
- Version 1.06 November 2026First release.
Released versions are never edited; each keeps its own address.
Use of AI in this case
AI systems were used in the historical audit and in later review. The record distinguishes AI and computational evidence from human verification and does not treat AI agreement as human confirmation.