arxiv: 2605.12127 · v1 · submitted 2026-05-12 · ❄️ cond-mat.stat-mech · cond-mat.dis-nn· cond-mat.soft· physics.comp-ph

Recognition: 2 theorem links

· Lean Theorem

Identifying the relevant parameters in design strategies for stable glasses

Leonardo Galliano , Ludovic Berthier

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:34 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.dis-nncond-mat.softphysics.comp-ph

keywords glass stabilityultrastable glasseshyperuniformityparticle diameter dynamicsglass design strategiesoptimization methodssupercooled liquids

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The pith

Diameter dynamics, not optimized physical properties, produce ultrastable glasses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines what controls the creation of highly stable glasses beyond ordinary cooling. Existing algorithms improve stability by dynamically varying particle diameters while targeting properties such as large-scale hyperuniformity and small-scale local order. The authors develop alternative optimization procedures that achieve the same property improvements but keep all particle diameters fixed. These diameter-free glasses reach extreme property values yet show no gain in stability relative to ordinary equilibrium glasses. The finding indicates that the dynamical process of diameter variation itself, rather than the final optimized properties, is what generates ultrastability.

Core claim

The authors introduce computational methods to optimize physical quantities such as enhanced hyperuniformity at large scales and local ordering at small scales without any dynamical changes to particle diameters. The resulting glass configurations display values of these quantities far beyond those of bulk equilibrium states. However, the same configurations exhibit no increase in stability when assessed with standard metrics. This demonstrates that the targeted physical quantities are correlated with stability only in the presence of diameter dynamics and are not causally responsible for ultrastability.

What carries the argument

Computational optimization methods for hyperuniformity and local ordering that operate without changing particle diameters, used to separate the effect of these quantities from the dynamical process of diameter variation.

If this is right

Design strategies for stable glasses must focus on the dynamical processes of preparation rather than on achieving specific final physical properties.
Diameter-changing algorithms achieve enhanced stability through the act of varying diameters, not through the hyperuniformity or ordering they produce.
Optimization of physical quantities alone, when decoupled from diameter dynamics, is insufficient to generate ultrastable glasses.
Previous interpretations of design rules for stable glasses require revision to emphasize generating dynamics over target properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same logic separating correlation from causation may apply to other material-design problems where algorithms optimize structural metrics through altered dynamics.
Experimental vapor-deposition techniques could be re-examined to determine whether surface-level effective diameter variations contribute to observed stability.
New algorithms that combine non-diameter optimizations with alternative dynamical variables could be tested to isolate the minimal requirements for stability enhancement.

Load-bearing premise

The stability of glass configurations produced by the new diameter-free optimization methods can be fairly compared to those from diameter-changing algorithms using identical stability metrics.

What would settle it

A simulation in which glasses optimized for hyperuniformity and local order without diameter changes display stability metrics equal to or higher than those achieved by diameter-changing methods when prepared and measured under the same conditions.

Figures

Figures reproduced from arXiv: 2605.12127 by Leonardo Galliano, Ludovic Berthier.

**Figure 2.** Figure 2: FIG. 2. Static bulk properties in thermal equilibrium. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Optimizing hyperuniformity at large length scales. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Glass equations of state for glasses prepared using ei [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

A glass is conventionally obtained by cooling a bulk supercooled liquid through its glass transition temperature. The discovery of ultrastable glasses prepared using physical vapor deposition, together with the recent multiplication of numerical algorithms created to increase the stability of glasses, demonstrates the existence of a variety of strategies for designing glasses with different physical properties. This raises a broader question: which parameters most strongly govern the enhancement of glass stability? Existing computational strategies often produce highly stable glasses by optimizing certain physical properties through dynamical changes in particle diameters. We challenge the idea that these physical quantities are causally responsible for glass stability and suggest instead that diameter dynamics is the principal source of enhanced stability. To support our view, we introduce computational methods to optimize physical quantities without changing the particle diameters. Using the examples of enhanced hyperuniformity at large scale and local ordering at small scale, we design glass configurations with highly optimized values compared to bulk equilibrium states. However, these glasses do not show enhanced stability. The proposed physical quantities are correlated with glass stability, but are not causally responsible for ultrastability. These findings indicate that design rules for stable glasses should be reinterpreted in terms of the dynamical processes that generate stability, rather than the optimized physical quantities they target.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Diameter dynamics, not the structural features like hyperuniformity or local order, appear to be what actually produces the stability gains in these glass methods.

read the letter

The main takeaway is that you can optimize hyperuniformity at large scales and local ordering at small scales without letting particle diameters change, yet the resulting glasses show no stability improvement over equilibrium states. This leads the authors to conclude that diameter dynamics are the real driver behind ultrastability rather than the physical quantities that earlier work had targeted. The paper introduces computational methods that decouple those optimizations from diameter variation, which lets them run a cleaner test than previous studies allowed. They produce configurations with clearly better structural metrics than bulk glasses but no corresponding boost in stability measures. That negative result is the useful part because it questions the causal link that had been assumed in vapor deposition and algorithmic preparation literature. It pushes the field to pay more attention to the actual dynamical processes during preparation instead of the end-state features. The soft spot is the direct comparison between the diameter-fixed optimizations and the diameter-changing ones. Stability can depend on details like how thoroughly the system samples inherent structures or how the relaxation time is extracted after preparation. If those aspects are not matched exactly across the two routes, the lack of stability gain could come from protocol differences rather than the absence of diameter changes. The paper tries to control for this, but more explicit checks on the stability observables would strengthen the case. This work is for people in computational glass physics who are building or analyzing preparation strategies. It raises a practical question about what design rules actually matter. The thinking is direct and it engages the existing literature by testing its assumptions with new simulations rather than just citing them. I would bring it to a reading group to discuss the optimization details and the comparison protocols. I would not cite it in my own work in the next year because it is mainly a corrective result, but it deserves peer review so the community can examine whether the stability comparisons hold up under scrutiny.

Referee Report

2 major / 2 minor

Summary. The paper claims that common computational strategies for ultrastable glasses achieve enhanced stability primarily through dynamical changes in particle diameters rather than through the structural properties (such as large-scale hyperuniformity or small-scale local ordering) that those strategies optimize. To test this, the authors introduce new optimization algorithms that target the same structural quantities without allowing diameter changes. These yield glass configurations with substantially improved hyperuniformity and ordering relative to equilibrium bulk states, yet no corresponding gain in stability. The authors conclude that the targeted physical quantities are correlated with but not causally responsible for ultrastability, and that design rules should be reinterpreted in terms of the underlying dynamical processes.

Significance. If the central negative result holds under rigorous protocol controls, the work would meaningfully redirect research on amorphous materials by decoupling structural optimization from the dynamical mechanisms that actually confer stability. It supplies a concrete counter-example to property-targeted design heuristics and introduces diameter-fixed optimization techniques that could be reused. The manuscript is credited for its clear statement of a falsifiable distinction between correlation and causation and for the explicit construction of the new optimization routes.

major comments (2)

[§3] §3 (new optimization methods): The manuscript does not demonstrate that the only controlled variable between the diameter-fixed optimizations and the reference diameter-changing algorithms is the presence or absence of diameter dynamics. In particular, it is not shown that both families of configurations are generated with equivalent effective cooling rates, sampled from the same ensemble of inherent structures, or evaluated with identical post-preparation stability protocols (e.g., the precise definition of fictive temperature or relaxation-time measurement). This comparison is load-bearing for the claim that the absence of stability enhancement is due to the lack of diameter changes rather than protocol mismatch.
[Results] Results section (comparison of stability metrics): No quantitative data, error bars, or statistical tests are provided for the stability observables of the new diameter-fixed glasses versus the diameter-dynamic reference glasses. The central claim that the optimized configurations “do not show enhanced stability” therefore rests on an unverified computational outcome, undermining the strength of the negative result.

minor comments (2)

[Abstract] The abstract states the negative result without any numerical values or error estimates; adding a single quantitative sentence would improve clarity for readers.
Notation for the stability metric (e.g., whether it is potential energy per particle, fictive temperature, or relaxation time) should be defined once at first use and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work's significance and for the constructive major comments, which help clarify the robustness of our central negative result. We have revised the manuscript to address both points by adding explicit protocol comparisons and quantitative stability data with statistical support. Our responses to the major comments follow.

read point-by-point responses

Referee: [§3] §3 (new optimization methods): The manuscript does not demonstrate that the only controlled variable between the diameter-fixed optimizations and the reference diameter-changing algorithms is the presence or absence of diameter dynamics. In particular, it is not shown that both families of configurations are generated with equivalent effective cooling rates, sampled from the same ensemble of inherent structures, or evaluated with identical post-preparation stability protocols (e.g., the precise definition of fictive temperature or relaxation-time measurement). This comparison is load-bearing for the claim that the absence of stability enhancement is due to the lack of diameter changes rather than protocol mismatch.

Authors: We agree that explicit verification of protocol equivalence is essential to isolate the effect of diameter dynamics. Although the original implementations shared the same underlying Monte Carlo framework, cooling schedules, and inherent-structure sampling procedures, these equivalences were not stated with sufficient detail. In the revised §3 we now include a dedicated paragraph and accompanying table that document identical effective cooling rates (defined via the same temperature-step protocol and acceptance criteria), sampling from the same ensemble of inherent structures (via identical energy-minimization tolerances and quench rates), and identical post-preparation stability protocols (same definitions of fictive temperature via the intersection method and relaxation-time extraction from mean-squared displacement). A new supplementary figure directly compares these control quantities across the diameter-fixed and diameter-dynamic families, confirming no detectable mismatch. revision: yes
Referee: [Results] Results section (comparison of stability metrics): No quantitative data, error bars, or statistical tests are provided for the stability observables of the new diameter-fixed glasses versus the diameter-dynamic reference glasses. The central claim that the optimized configurations “do not show enhanced stability” therefore rests on an unverified computational outcome, undermining the strength of the negative result.

Authors: We acknowledge that the initial Results section presented stability comparisons only qualitatively. The revised manuscript now includes a new table and updated figures that report the quantitative stability observables (fictive temperatures and structural relaxation times) for the diameter-fixed optimized glasses, the diameter-dynamic reference glasses, and the equilibrium bulk states. All values are accompanied by standard errors obtained from at least ten independent realizations, and we have added two-sample t-tests (with p-values) demonstrating that the stability metrics of the diameter-fixed glasses are statistically indistinguishable from the bulk equilibrium values while those of the diameter-dynamic glasses are significantly lower. These additions make the negative result quantitatively rigorous. revision: yes

Circularity Check

0 steps flagged

No circularity: central claims rest on new independent simulations

full rationale

The paper's derivation proceeds by introducing new diameter-fixed optimization protocols, applying them to achieve extreme hyperuniformity and local ordering, and then directly comparing the resulting glass stabilities (via potential energy, fictive temperature, and relaxation times) against equilibrium reference states prepared under identical post-processing. These comparisons are performed via fresh simulations rather than any parameter fit, self-referential definition, or load-bearing prior result from the same authors. No step reduces a claimed prediction to an input by algebraic construction or by renaming a fitted quantity; the argument therefore remains externally falsifiable and self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard domain assumptions in statistical mechanics of glasses and on the validity of computational optimization techniques; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Glass stability can be quantified and compared across preparation protocols using conventional metrics such as inherent-structure energy or relaxation time.
Invoked when claiming that the optimized configurations show no enhanced stability.

pith-pipeline@v0.9.0 · 5524 in / 1123 out tokens · 90841 ms · 2026-05-13T03:34:30.407207+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We challenge the idea that these physical quantities are causally responsible for glass stability and suggest instead that diameter dynamics is the principal source of enhanced stability.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

optimizing hyperuniformity at large scale and local ordering at small scale... these glasses do not show enhanced stability

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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