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Comment on "Observation of Kardar--Parisi--Zhang universal scaling in two dimensions"

T0 review · 3 major / 5 minor · reviewed 2026-07-31 · grok-4.5

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Pith's one-line read Reanalysis finds polariton coherence decays exponentially in time and Gaussian in space, not with KPZ stretched exponentials.

desk verdict Solid public reanalysis: Widmann’s KPZ collapse is mostly a normalization artifact; the data prefer exponential–Gaussian over the windows they actually used. read the letter →

arxiv 2607.24152 v1 pith:NFFJXEUY submitted 2026-07-27 cond-mat.quant-gas

J. Bloch , M. Escalera , Q. Fontaine , F. Helluin , A. Minguzzi , L. Canet , S. Ravets This is my paper · ORCID
classification cond-mat.quant-gas
keywords Kardar-Parisi-Zhangpolaritoncondensatefirst-ordercoherenceSchawlow-Townesdatacollapsenormalizationdriven-dissipativetwo-dimensionalscaling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This comment re-examines interferometry data on a two-dimensional polariton condensate that were claimed to show Kardar–Parisi–Zhang (KPZ) universal scaling in the decay of first-order coherence. Over the same space-time windows used in the original analysis, and for both square and triangular lattices at every reported pump power, the measured coherence instead follows a simple exponential decay in time (Schawlow–Townes) and a Gaussian decay in space. With the corresponding exponents β = 0.5 and χ = 1, and after proper normalization that removes a short-time non-universal offset, the full space-time maps collapse cleanly onto one non-KPZ curve. The apparent collapse onto the KPZ scaling function is shown to be an artifact of incorrect normalization: when the same data are plotted without that artifact, or with the correct normalization under KPZ exponents, the collapse fails. The central claim of KPZ universal scaling in those windows is therefore not supported by the data.

What carries the argument

Proper normalization of g^(1) by the factor κ that forces the extrapolated fit through unity at the origin, together with weighted least-squares comparison of pure stretched-exponential (KPZ) versus pure exponential/Gaussian forms and the resulting quality of collapse under the two sets of exponents.

What would settle it

A re-fit of the same public data sets inside the identical gray-shaded windows that recovers lower residuals for KPZ stretched exponentials than for exponential/Gaussian forms, or a properly normalized collapse onto the KPZ scaling function that remains tight for all pump powers.

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Extended reading notes

Core claim

Over the space-time windows analyzed in the original work, |g^(1)(δr, δt)| exhibits exponential temporal and Gaussian spatial decay for all pump powers and both lattice geometries; the reported data collapse onto the KPZ scaling function is an artifact of incorrect normalization, so KPZ universal scaling is not the appropriate description of those measurements.

Load-bearing premise

That the fixed windows taken from the original paper, plus a direct comparison of pure KPZ stretched exponentials against pure exponential/Gaussian forms under correct normalization, are enough to rule out KPZ scaling inside those same windows.

Editorial extensions

If this is right

  • Claims of two-dimensional KPZ scaling in polariton coherence must be re-checked with the correct short-time normalization before being accepted.
  • Exponential (Schawlow–Townes) temporal decay is the operative description over the reported experimental windows.
  • Gaussian spatial decay with χ = 1, not the KPZ roughness exponent, organizes the spatial data.
  • Future collapse analyses of condensate coherence will need to treat the non-universal offset κ explicitly or risk spurious scaling.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same normalization artifact could affect other reported KPZ collapses in driven-dissipative condensates that skip the short-time offset.
  • If finite-size Schawlow–Townes physics already dominates inside the chosen windows, larger samples or shorter-time probes would be required to expose any intermediate KPZ regime.
  • A mixed model that interpolates from non-universal short-range coherence through a possible KPZ window into long-time exponential decay could still be tested once the pure forms are properly normalized.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This Comment reanalyzes the experimental g^(1)(δr,δt) maps of Widmann et al. (Science 392, 221 (2026)), which reported KPZ universal scaling in a 2D polariton condensate lattice. The authors argue that within the space-time windows used in the original analysis, the temporal decay is exponential (Schawlow–Townes) and the spatial decay Gaussian, for all pump powers and both square and triangular lattices, supported by semi-log curvature tests (Figs. 1–3) and weighted least-squares residuals (Table I). They further show that the KPZ collapse reported in Ref. [1] is an artifact of omitting the normalization factor κ: with proper normalization the KPZ representation fails to collapse, while a β=1/2, χ=1 representation collapses cleanly (Figs. 8–11). Analytic toy datasets (Figs. 6–7) demonstrate that an incorrect κ can both destroy a genuine KPZ collapse and manufacture a spurious KPZ-like collapse from exponential-Gaussian data.

Significance. If correct, the Comment overturns the central claim of a high-profile Science paper and, equally important, identifies a general mechanism — a normalization offset 2 ln κ / t^{2β} — by which scaling collapses of coherence maps can be spuriously produced or destroyed. This is a falsifiable, methodologically portable point relevant to all KPZ experiments on driven-dissipative systems. The strengths are concrete: the reanalysis covers both lattice geometries and all available pump powers, uses model-insensitive curvature diagnostics, provides analytic control datasets (Figs. 6–7) that demonstrate both the destruction of a true KPZ collapse and the fabrication of a fake one under wrong κ, and supplies full-map collapses in both representations with and without normalization (Figs. 4–5, 10–11). The toy-model construction reproducing the qualitative features of Ref. [1]'s Fig. 3B from non-KPZ data is a genuinely sharp argument.

major comments (3)
  1. [§II, Table I] Sec. II and Table I: the temporal fits compare a pure stretched exponential (the |δr|=0 asymptote of Eq. (3)) against a pure exponential, but the analyzed temporal cuts (Figs. 1–3) are taken at |δr|=a/√2, not zero. At fixed nonzero separation the KPZ prediction is the crossover form of Eq. (8), t^{2β}F(C1 r0/t^{1/z}), which over a finite window is not a stretched exponential and can curve on a t^{2β} semilog plot. The full-map collapses (Figs. 4, 10, 11) do address the full scaling form and substantially mitigate this, but Table I as presented only excludes the asymptotic model. The authors should either fit the full form (8) to the temporal cut or state explicitly why the asymptotic comparison is adequate within the gray windows.
  2. [Table I] Table I: no degrees of freedom, fit-parameter counts, or weight definitions are given for the WLS values, so the phrase 'systematically and significantly larger' cannot be assessed as a statistical statement. The triangular-lattice temporal row (204.6 vs 125.5) has both residuals very large relative to the square-lattice values (12.97 vs 4.07), suggesting neither model fits that cut well; reduced chi-square values (or residuals plots) for each fit are needed to support the exclusion claim, particularly since this is the load-bearing quantitative evidence in Sec. II.
  3. [§IV B, Figs. 8–9] Sec. IV B and Figs. 8–9: the procedure determining κ needs to be stated precisely and reproducibly. The caption of Fig. 8 indicates κ is set by the δt→0 extrapolation of the temporal fit within the KPZ window, while Sec. I B defines it via g_fit(0,0)=1/κ. It should be made explicit (i) which fit (stretched exponential or exponential) is used to set κ in each representation, (ii) that the same κ is used when comparing representations (i) and (ii), and (iii) how sensitive the collapse quality in panels b of Figs. 10–11 is to the κ value. Fairness of the (i)-vs-(ii) comparison hinges on this.
minor comments (5)
  1. [Figs. 8–9 captions] Captions of Figs. 8 and 9: the panel lettering in the caption text ('obtained b using the KPZ exponents and without normalization, c ... with normalization, d using β=0.5, χ=1') appears offset by one relative to the panels described in Sec. IV B (a: no normalization, b: normalized, c: exponential-Gaussian). Please reconcile.
  2. [§V] Typo in Conclusion: 'Scahwlow-Townes' should be 'Schawlow–Townes' (also 'Shawlow-Townes' in the Fig. 8/9 captions).
  3. [§IV A] Sec. IV A: the phrase 'hide the true features of a dataset and mislead for alien ones' is unclear; please rephrase (e.g. 'and mimic features of a different universality class').
  4. [§IV B] Sec. IV B: the authors note that Ref. [1] discarded certain data points within the gray windows while the Comment uses all points. It would help the reader to mark (e.g. by symbol or color) which points were excluded in Ref. [1] in Figs. 8–11, so the effect of that selection can be judged directly.
  5. [Eq. (7)] Eq. (7) contains a stray extra parenthesis in 'F(C1|δr|/δt^{1/z}))'; also the rendering of g^{(1)} is inconsistent between the abstract and main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: external data reanalysis with standard model comparison; self-citations supply published methodology only.

full rationale

This comment re-analyzes publicly released interferometry maps from Widmann et al. against two externally defined families of forms (KPZ stretched exponentials with literature exponents β≈0.24, χ≈0.39 versus Schawlow–Townes exponential / Gaussian with β=0.5, χ=1). Weighted least-squares residuals, 1D cut curvature, and full space-time collapses are computed on the same fixed windows; κ is fixed by extrapolating the fitted g^{(1)} to the origin, a standard normalization step. The self-citation to Fontaine et al. Nature 2022 supplies that normalization procedure already validated on independent data; it does not define the Widmann observables, force the exponent choice, or replace the model comparison. Analytic toy maps (Eqs. 8–9) illustrate how wrong κ can fake a KPZ-looking collapse; that demonstration is pedagogical, not a fitted-input-as-prediction loop. No uniqueness theorem, ansatz smuggling, or definitional identity equates the claimed exponential-Gaussian description to its inputs. The derivation is therefore self-contained against external benchmarks.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The comment rests on standard driven-dissipative KPZ theory for polariton phase, the known finite-size Schawlow–Townes crossover, and a normalization convention from prior coherence work. Free parameters are ordinary fit amplitudes and the scalar κ fixed by extrapolating short-scale fits; no new physical entities are introduced. Load-bearing domain choices are the adoption of Widmann’s windows and the pure two-model comparison.

free parameters (3)
  • normalization factor κ = dataset-dependent (e.g. from stretched-exp or ST intercepts in gray windows)
    Scalar so that κ times the extrapolated g^{(1)}_fit(0,0) equals 1; fixed from temporal-fit intercepts (stars in Figs. 8–9) and applied to all collapse plots.
  • amplitudes A, B (or T, R in expo-Gauss toy model) = per power / toy example (e.g. T=10^{-3} ps, R=10^{-3} µm in Eq. 9)
    Non-universal decay amplitudes in temporal and spatial fits and in analytic toy maps (Eqs. 8–9); fitted or chosen to illustrate collapse behavior.
  • space-time analysis windows = as in Ref. [1] Fig. 3 and SM
    Gray-shaded δt and |δr| ranges taken from Widmann et al. for fair comparison; treated as fixed rather than re-optimized.
assumptions (5)
  • domain assumption In the phase-dominated regime, g^{(1)} ∝ exp(−½ C_θθ) with C_θθ obeying KPZ scaling when the phase maps to KPZ (Eqs. 1–3).
    Sec. I A, citing Altman et al. PRX 2015; standard in the subfield but not re-derived here.
  • domain assumption For finite systems, long-time coherence crosses over to simple exponential Schawlow–Townes decay g^{(1)}(0,δt)∼e^{−δt/τ}.
    Sec. I A, Eqs. 4; used to motivate β=0.5 as the competing temporal form.
  • domain assumption Short-scale non-universal transient implies g^{(1)}_fit(0,0)=1/κ ≠ 1, so experimental maps must be multiplied by κ before testing universal collapse (Eqs. 5–7).
    Sec. I B, citing Fontaine et al. Nature 2022; central to the artifact argument.
  • standard math 2D KPZ exponents are approximately β≈0.24, χ≈0.39, z≈1.62, with FRG scaling function F from Kloss et al.
    Sec. I A; numerical/FRG inputs used as the KPZ benchmark representation.
  • ad hoc to paper Weighted least-squares residuals and visual collapse quality in fixed windows are adequate to prefer exponential-Gaussian over KPZ stretched exponentials.
    Table I and Secs. II–IV; model-selection criterion chosen by the comment authors.

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Pith. "Pith review of Comment on "Observation of Kardar--Parisi--Zhang universal scaling in two dimensions"." pith.science (2026). https://pith.science/paper/NFFJXEUY

@misc{pith2026260724152,
  author       = {Pith},
  title        = {Pith review of: Comment on "Observation of Kardar--Parisi--Zhang universal scaling in two dimensions"},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NFFJXEUY}},
  note         = {Machine review of arXiv:2607.24152}
}
abstract

In their paper published in Science 392, 221 (2026), Widmann and collaborators reported interferometry experiments to explore the emission coherence decay of a two-dimensional polariton condensate generated in an array of coupled resonators. The authors claim evidence of Kardar--Parisi--Zhang (KPZ) universal scaling in the measured spatio-temporal coherence decay. We argue in the following that the data were not properly analyzed. We re-analyze the experimental data acquired both with the square and the triangular lattices for various values of the excitation power. Instead of stretched exponential decays, in the space (time) windows considered in the paper we find that the measured $|g^{(1)}(\delta {\bf r}, \delta t)|$ at $\delta t=0$ ($|\delta {\bf r}| $ close to $0$) rather show Gaussian (exponential) decay for all excitation powers. As a result, using as temporal and spatial exponents $\beta=0.5$ and $\chi=1$, the data for all pump powers are found to collapse onto a single curve, which is not the KPZ scaling function. In particular, we show that the data collapse onto the KPZ scaling function presented in the paper is an artifact stemming from incorrect data normalization. We thus conclude that the main claim of the paper is not justified as the spatio-temporal decays of the coherence over the space-time windows analyzed in the paper are not well described by the KPZ universal behavior.

Figures

Figures reproduced from arXiv: 2607.24152 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

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Reference graph

Works this paper leans on

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Reviewed July 31, 2026 · model on record in the stance chip above.