Resolved Equilibration-Time Lead-In for Open-Boundary ASEP

Definitions and mathematical statement

The supplied record does not determine a well-posed open mathematical problem. Its recoverable question is: how long does the stochastic system under discussion take to reach equilibrium? The title identifies the context as the asymmetric simple exclusion process (ASEP) with open boundaries, but the supplied statement specifies neither the process nor its state space, transition rates, initial conditions, boundary parameters, stationary distribution, convergence criterion, or asymptotic size parameter. Consequently, no precise equilibration-time or mixing-time assertion can be extracted without additional source material.

The accompanying text labels a result as "Theorem 1 ([1, Theorem 1.1])" and gives the hypothesis \[ \beta<\alpha. \] The meanings and admissible domains of $\alpha$, $\beta$, and $\rho$, and the definition of the random height $h(t,0)$, are absent. As $t\to\infty$, the damaged display appears to describe three distributional limits involving centering by $\mu t$ or $\mu_\rho t$, scaling by $\sigma t^{1/3}$ or $\sigma_\rho t^{1/2}$, and limiting distribution functions $F_{\mathrm{GSE}}$, $F_{\mathrm{GOE}}$, and $\Phi$, respectively. Here the source identifies the first two as Tracy--Widom GSE and GOE distribution functions, and $\Phi$ as the standard normal distribution function, \[ \Phi(s)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{s}e^{-u^2/2}\,{\,\mathrm{d}} u, \qquad s\in{\mathbb{R}}. \] The source calls $\mu,\sigma,\mu_\rho,\sigma_\rho$ explicit constants, but supplies no formulas or parameter dependence. The probability expressions and their signs are corrupted. The regime thresholds are rendered as "12" and "21"; interpreting these as $1/2$ would require confirmation. The intended quantification over $s$ and the Tracy--Widom normalization conventions are also unspecified. Thus these fragments are retained as provenance, not asserted as a reconstructed theorem.

The supplied verification field classifies the statement as unrecoverable and reports that the equilibration-time question is a lead-in immediately followed by a claim that the reported joint work obtains the sharp cutoff profile. It therefore does not identify a separate open problem. This conflicts with the supplied open-status label and broad KPZ mixing-time assessment. No new conjecture, cutoff formula, or general KPZ universality claim is asserted here.

Short English statement

The record asks how long an open-boundary ASEP system takes to equilibrate, but omits the model and the meaning of equilibration. Its adjoining limit theorem is corrupted and cannot be stated reliably. Supplied verification says the question introduces work obtaining a sharp cutoff profile, whereas other supplied fields label it open. Human source review is required before a precise mathematical target can be selected.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30006087$, exact source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection. Title: "Resolved Equilibration-Time Lead-In for Open-Boundary ASEP." No individual proposer is supplied; the proposed year is 2024.
• Supplied report citation: Mini-Workshop: Mixing Times in the Kardar--Parisi--Zhang Universality Class (2025), Oberwolfach Reports, pp. 3001--3020, DOI 10.4171/owr/2024/51. https://doi.org/10.4171/owr/2024/51. The supplied literature-source label is "Oberwolfach Report 51/2024." The 2025 designation and 2024 report identification are retained without reconciliation.
• Supplied literature source: "Busani et al., KPZ mixing-times workshop report." https://ems.press/journals/owr/articles/14298798. This attribution does not establish authorship of the extracted question or of the unidentified theorem reference.
• The extracted text cites "[1, Theorem 1.1]," but supplies no corresponding bibliographic entry. That reference cannot be identified from this record.
• Literature assessment checked at 2026-08-22: supplied dated curation, not independently verified. It labels the broad KPZ equilibration or mixing-time question open and reports model-specific asymptotics and cutoff results without a general answer. The background explicitly requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification field instead reports that the official report presents the question as a lead-in to joint work obtaining the sharp cutoff profile, rather than as an open problem. It marks the statement unrecoverable, promotes no clean statement, and retains the original record for provenance. The record's supplied update timestamp is 2026-09-16T12:06:53Z; this is not an independently verified source-check date.