# Precedence review: Critical mixing in the Sherrington–Kirkpatrick model

**Preprint:** [Critical mixing in the Sherrington–Kirkpatrick model](paper.pdf) (OpenAI, September 25, 2026)

**Write-up:** [precedence-findings.pdf](precedence-findings.pdf) (October 8, 2026)

The write-up reports three kinds of finding:
- **(A)** techniques and theory from earlier papers that the preprint reuses without attribution;
- **(B)** earlier, uncited partial progress on the same problem;
- **(C)** a published result that would replace a large part of the argument.

There are 12 findings: 5 Strong and 4 Partial in (A), 2 Partial in (B), and 1 Major in (C). Of the 25 earlier works involved, 19 are absent from the preprint's bibliography.

| ID | Grade | Technique or result | Earlier work |
|---|---|---|---|
| S1 | Strong | Planted stochastic-localization framework for SK: Gaussian observation, TAP at the observation field, planted law and likelihood transfer | El Alaoui–Montanari–Sellke 2022 |
| S2 | Strong | Spherical saddle-point representation with a field, in one- and two-replica form | Kosterlitz–Thouless–Jones 1976; Baik–Lee 2015; Baik et al. 2020; Landon 2020; Nguyen–Sosoe 2018; Du–Huang 2026 |
| S3 | Strong | Brézin–Hikami duality for GOE characteristic polynomials with an external source | Brézin–Hikami 2001 |
| S4 | Strong | One-step Polchinski renormalization, composed across scales | Bauerschmidt–Bodineau 2019; Bauerschmidt–Bodineau–Dagallier 2023; Bauerschmidt–Dagallier 2022; Anari–Koehler–Vuong 2024 |
| S5 | Strong | Capacity–measure criterion for the log-Sobolev inequality, with dyadic slicing | Barthe–Roberto 2003; Barthe–Cattiaux–Roberto 2004; Bakry–Coulhon–Ledoux–Saloff-Coste 1995 |
| P1 | Partial | Signed two-spin curvature estimate, credited only through a companion lemma | Wang 2026 |
| P2 | Partial | Density bounds for weighted chi-square sums | Bobkov–Naumov–Ulyanov 2020; Götze–Naumov–Spokoiny–Ulyanov 2017 |
| P3 | Partial | Fixed-spectrum Haar second-moment comparison | Bhattacharya–Sen 2015; Du–Huang 2026 |
| P4 | Partial (B) | Critical-temperature bounds on the partition function and covariance | Du–Huang 2026; El Alaoui–Gaitonde 2022 |
| P5 | Partial (B) | Local convexity of the TAP free energy at positive observation strength | Celentano 2022 |
| P6 | Partial | Large-field reduction to sparse principal submatrices | Bandeira–El Alaoui–Rödder 2026 |
| C1 | Major (C) | The spectral-cap route (§§15–19, about 70 pages) is not needed for the log-Sobolev exponent: the support profile of Theorem 14.2 already gives it | Hermon–Peres 2016; Diaconis–Saloff-Coste 1996 |

**Grades:**
- **Strong:** the earlier technique is reused essentially intact without credit.
- **Partial:** only a fragment is reused, or the credit is only indirect.
- **Major:** a component of the main theorem becomes a citation.

**Other files:**
- LaTeX source: [precedence-findings.tex](precedence-findings.tex)
- Machine-readable findings: [precedence-findings.json](precedence-findings.json)
- Statistics: [precedence-stats.json](precedence-stats.json)