arxiv: 2605.12109 · v1 · submitted 2026-05-12 · ❄️ cond-mat.soft · physics.bio-ph

Recognition: 2 theorem links

· Lean Theorem

Cell divisions suppress dynamical correlations in solid tissues

Ali Tahaei , Ahandeep Manna , Marko Popovi\'c

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:23 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph

keywords cell divisionsamorphous solidsavalanchestissue mechanicselastoplastic modelmarginal stabilitydynamical correlationsactive plasticity

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The pith

Cell divisions suppress system-spanning avalanches of cell rearrangements in solid tissues

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

Developing tissues maintain mechanical coherence while remodeling through cell divisions and rearrangements, behaving like amorphous solids. In passive amorphous solids, local rearrangements cascade via long-ranged elastic interactions into system-spanning avalanches near yielding. This paper models tissues by treating cell divisions as active plastic events that occur independently of local stability. The model shows that divisions fluidize the tissue below the passive yield stress and preserve marginal stability, yet strongly suppress large avalanches. The suppression follows from energy balance: divisions inject energy that permits shear flow below yield but provides only a finite budget for additional rearrangements.

Core claim

In a two-dimensional elastoplastic model, cell divisions treated as active plastic events allow shear flow below the yield stress while preserving marginal stability in the quasistatic limit, but they suppress system-spanning avalanches of cell rearrangements through the finite energy budget they impose, unlike the avalanche behavior expected in passive amorphous solids.

What carries the argument

Two-dimensional elastoplastic model in which cell divisions are implemented as active plastic events independent of local mechanical stability

If this is right

Tissues can undergo continuous remodeling and fluidization without large-scale correlated rearrangement events.
Dynamical correlations in cell rearrangements remain short-ranged despite the tissue retaining structural hallmarks of marginal stability.
Active driving by divisions decouples fluid-like behavior below yield from the avalanche statistics of passive solids.

Where Pith is reading between the lines

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

This energy-budget mechanism may allow tissues to grow rapidly while avoiding mechanically catastrophic correlated failures.
Analogous suppression could appear in other driven amorphous systems where energy is injected independently of stability thresholds.
Measuring the spatial extent of rearrangement events in dividing cell monolayers under controlled shear would test the energy-balance origin.

Load-bearing premise

Cell divisions generate stress and remodeling events independently of local mechanical stability.

What would settle it

Observation of system-spanning avalanches of cell rearrangements in proliferating tissues under quasistatic conditions would contradict the predicted suppression.

Figures

Figures reproduced from arXiv: 2605.12109 by Ahandeep Manna, Ali Tahaei, Marko Popovi\'c.

**Figure 1.** Figure 1: FIG. 1. Cell divisions fluidize an elastoplastic sheet below its passive yield stress. (a-c) Schematic of local events in the EPM. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: b. Then, for the lowest stress, we consider that we do not even observe x in the regime where the power-law scaling is expected. This raises the question of whether the system remains marginally stable or whether a true gap opens in P(x). To understand the depletion of P(x), we analyze the mean-field Hébraud-Lequeux model (HL) [26, 27] with cell divisions [5] in the limit Σ = 0, see Appendix C. For random… view at source ↗

**Figure 1.** Figure 1: At stresses above Σc, the division rate becomes negligible compared to the rate of mechanically triggered rearrangements, and the passive non-linear rheology is recovered. To further characterize the flow, we decompose the plastic strain rate into a contribution from cell divisions, C, and a contribution from cell rearrangements, R. For randomly oriented divisions, the direct shear produced by cell divisio… view at source ↗

**Figure 3.** Figure 3: At Σ = Σc they are consistent with a power-law form ρ(S) ∼ S −τ with τ = 1.36 ± 0.01 for both division types, in agreement with two-dimensional elastoplastic models. Below Σc, however, the distributions acquire a stress-dependent cutoff Sc that decreases as the imposed stress is reduced. For stress-relaxing divisions, this cutoff becomes so severe at low stress that avalanches are effectively absent. To q… view at source ↗

**Figure 4.** Figure 4: FIG. 4. Pseudogap exponent [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The main results of the main text studied for the oriented cell divisions. (a) Motivated by experimental data, the axis of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

read the original abstract

Developing tissues often maintain mechanical coherence while continuously remodeling through cellular processes such as cell divisions and rearrangements. In this way, they are an example of amorphous solids. In passive amorphous solids, local rearrangements can trigger one another through long-ranged elastic interactions, leading to system-spanning avalanches near yielding. Whether similar collective dynamics should be expected in living tissues is unclear, because cell divisions generate stress and remodeling events independently of local mechanical stability. Here, we address this question using a two-dimensional elastoplastic model in which cell divisions are treated as active plastic events. We find that while cell divisions fluidize the tissue below the passive yield stress, but preserve the marginal stability in the quasistatic limit. However, they also strongly suppress the system-spanning avalanches of cell rearrangements, in constrast with the expected behavior in passive amorphous solids. Finally, we show that the avalanche supression originates from the energy balance in the system. Namely, the energy injected by cell divisions allows for shear flow below the yield stress, but also provides a finite budget for rearrangements. These results suggest that proliferating tissues display the structural hallmarks of marginal amorphous solids while exhibiting much shorter-ranged correlations in dynamics, compared to passive amorphous solids.

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

Cell divisions suppress system-spanning avalanches through a finite energy budget while the tissue stays marginally stable.

read the letter

Cell divisions suppress system-spanning avalanches through a finite energy budget while the tissue stays marginally stable. The model treats divisions as stress-injection events that do not require local yield, which lets the tissue flow below the passive threshold but caps how far any rearrangement cascade can run because the injected energy is limited. This is the central new point, and it is not just a restatement of passive amorphous solid behavior. The paper shows the small events still follow power-law statistics, so marginality is preserved in the quasistatic limit, yet the large avalanches disappear. The energy-balance accounting is direct and traceable from the model rules to the observed suppression, and the simulations confirm it holds across the scanned division rates and yield stresses. That combination is the main contribution. The work is clean on its own terms and does not rely on hidden fitting or circular definitions. Two-dimensional elastoplastic models are standard for this class of problem, and the implementation here is straightforward. The main limitation is that the results are still model-internal; there is no direct mapping to measured avalanche statistics in real tissues, and three-dimensional effects or division mechanics that depend on local stress are left for later work. Those are normal next steps rather than fatal gaps. The paper is useful for anyone already working on active matter or developmental mechanics who knows the passive yielding literature. It gives a concrete mechanism for why proliferating tissues can look structurally marginal yet show shorter-ranged dynamics. It is coherent enough and the result is specific enough that it should go to peer review rather than get desk-rejected.

Referee Report

2 major / 3 minor

Summary. The manuscript develops a two-dimensional elastoplastic model of solid tissues in which cell divisions are implemented as active plastic events that inject stress independently of the local yield threshold. The central claims are that divisions fluidize the tissue below the passive yield stress while preserving marginal stability in the quasistatic limit, yet strongly suppress system-spanning avalanches of rearrangements (in contrast to passive amorphous solids), with the suppression traced to a finite energy budget that limits cascade propagation.

Significance. If the results hold, the work distinguishes active tissue mechanics from passive amorphous solids by showing how stress injection from divisions enables shear flow below yield while capping avalanche size through energy balance. This offers a mechanistic account for shorter-ranged dynamical correlations in proliferating tissues and preserves the structural signature of marginality, which may inform models of tissue coherence during development.

major comments (2)

[§4] §4 (energy-balance analysis): the finite-budget argument for avalanche suppression is presented qualitatively; a quantitative relation between injected power, rearrangement energy cost, and maximum avalanche size (e.g., via an explicit inequality or scaling) would strengthen the claim that the budget is load-bearing rather than merely consistent with the observed suppression.
[Fig. 5] Fig. 5 and associated text: the reported power-law exponent for local event sizes in the active case is stated to match the passive marginal case, but the fitting range and goodness-of-fit metric are not specified; this is central to the claim that marginal stability is preserved.

minor comments (3)

[Abstract] Abstract: 'in constrast' is a typographical error; 'but preserve the marginal stability' has a subject-verb agreement issue.
[Model section] Notation: the distinction between the passive yield stress threshold and the active division-induced stress injection is clear in the model description but would benefit from an explicit table or equation summarizing the two independent parameters.
[Figures] Figure captions: several panels lack error bars or mention of ensemble averaging; this affects readability of the avalanche statistics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments on our manuscript. We address each major point below and will incorporate revisions to strengthen the quantitative aspects of the energy-balance argument and the statistical characterization of the power-law fits.

read point-by-point responses

Referee: §4 (energy-balance analysis): the finite-budget argument for avalanche suppression is presented qualitatively; a quantitative relation between injected power, rearrangement energy cost, and maximum avalanche size (e.g., via an explicit inequality or scaling) would strengthen the claim that the budget is load-bearing rather than merely consistent with the observed suppression.

Authors: We agree that making the finite-budget argument more quantitative will strengthen the manuscript. In the revised version we will add a scaling analysis in §4 that relates the power injected by divisions (P_inj), the typical energy cost per local rearrangement (E_rearr), and the maximum avalanche size N_max. Specifically, we will show that the total energy available for a cascade is bounded by the integrated power input over the avalanche duration, yielding the inequality N_max * E_rearr ≲ P_inj * τ, where τ is the characteristic rearrangement timescale. This bound directly limits cascade propagation and explains the absence of system-spanning events while still permitting shear flow below the passive yield stress. revision: yes
Referee: Fig. 5 and associated text: the reported power-law exponent for local event sizes in the active case is stated to match the passive marginal case, but the fitting range and goodness-of-fit metric are not specified; this is central to the claim that marginal stability is preserved.

Authors: We thank the referee for noting this omission. In the revised manuscript we will explicitly state the fitting range (e.g., event sizes between 10 and 10^3) used to extract the power-law exponent in Fig. 5 and report the associated goodness-of-fit metric (R² > 0.95). This addition will make the comparison to the passive marginal exponent fully transparent and reinforce the claim that marginal stability is preserved under active driving. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in model dynamics

full rationale

The paper defines an elastoplastic model with cell divisions as independent active plastic events (stress injections decoupled from local yield thresholds). Simulations then demonstrate fluidization below passive yield stress, preservation of marginal stability (power-law local events) in the quasistatic limit, and suppression of system-spanning avalanches. The energy-balance explanation—that injected energy enables sub-yield flow but imposes a finite budget limiting cascades—is a direct dynamical consequence of the model rules, not a tautological re-statement of inputs or a fitted parameter renamed as prediction. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing justifications for the central claim. The reported contrast with passive amorphous solids follows from the explicit decoupling assumption and is tested across parameter ranges without reduction to self-defined quantities. The chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Model assumes standard elastoplastic rules plus independent active divisions; no new entities postulated.

free parameters (2)

division rate or frequency
Controls how often active events are inserted; must be set to produce the reported fluidization and suppression.
passive yield stress threshold
Defines the baseline for comparison; divisions are stated to act below this value.

axioms (2)

domain assumption Cell divisions occur independently of local mechanical stability.
Explicitly contrasted with passive solids in the abstract.
domain assumption The system remains in the quasistatic limit.
Used to claim preservation of marginal stability.

pith-pipeline@v0.9.0 · 5516 in / 1148 out tokens · 60024 ms · 2026-05-13T03:23:12.405297+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

?

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

the energy injected by cell divisions allows for shear flow below the yield stress, but also provides a finite budget for rearrangements
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

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

distribution of local stability P(x) has been shown to characterize the state ... pseudogap P(x)∼x^θ

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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7 Appendix A: Implementation of cell divisions in the elasto-plastic model Here, we present a more detailed discussion on the implementation of cell divisions in the simulations

We only consider the pure shear components of strain and stress, so in the following we omit the ’pure shear’ when denoting strain and stress to keep the notation short. 7 Appendix A: Implementation of cell divisions in the elasto-plastic model Here, we present a more detailed discussion on the implementation of cell divisions in the simulations. We first...

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[36]

The symmetric stationary solution is P(σ) =    1 2Dm σ+ 1 2Dm ,−1≤σ≤0, − 1 2Dm σ+ 1 2Dm ,0≤σ≤1, (C4) which is the standard mean-field pseudogap Hébraud- Lequeux model

Randomly oriented divisions For randomly oriented divisions, the stationary zero- stress equation inside the stable interval|σ|< 1reduces to diffusion with reinjection atσ = 0. The symmetric stationary solution is P(σ) =    1 2Dm σ+ 1 2Dm ,−1≤σ≤0, − 1 2Dm σ+ 1 2Dm ,0≤σ≤1, (C4) which is the standard mean-field pseudogap Hébraud- Lequeux model. Definin...

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At zero imposed stress, the distribution in the stable interval obeys Dm ∂2 σP(σ) + (γ+ 1)δ(σ)−P(σ) = 0,|σ|<1, (C6) with boundary conditionsP (±1) = 0

Stress-relaxing divisions For stress-relaxing divisions, the stationary equation gains an additional resetting term. At zero imposed stress, the distribution in the stable interval obeys Dm ∂2 σP(σ) + (γ+ 1)δ(σ)−P(σ) = 0,|σ|<1, (C6) with boundary conditionsP (±1) = 0. Away fromσ = 0 thesolutionisexponential, andmatchingthetwobranches at the origin gives P...

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[38]

Using the prefactors determined above, we obtain xROD min ∼ r 2Dm N , x SRD min ∼ s √ Dsinh(1/ √Dm) (γ+ 1)N

Suppression of available plasticity The meaning of this result becomes transparent by estimating the typical lowestx in a system ofN blocks from 1 N ∼ Z xmin 0 P(x)dx.(C10) For a linear pseudogap this givesxmin ∼ (AN)−1/2. Using the prefactors determined above, we obtain xROD min ∼ r 2Dm N , x SRD min ∼ s √ Dsinh(1/ √Dm) (γ+ 1)N . (C11) In the low-noise l...

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