{"id":"77d57940-18bb-4dd3-8f50-9c35d15ee612","arxiv_id":"2607.23907","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"In a visco-elasto-plastic rod, an intermediate remodeling rate preserves an encoded shape best, and uniform growth rescues shape memory by suppressing both elastic coarsening and noise-driven disorder.","lead":"This paper studies a minimal mathematical model of a growing, bendable rod whose rest shape slowly forgets its original form. It shows that while remodeling can either protect or erase an encoded shape, making the rod grow removes that trade-off and lets complex shapes stay reproducible under noise.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"High-plasticity diffusion boundary rests on dropping noise in the constraint derivative (Supp. II.B, Eq. S33); exact stochastic projection may shift t_D and g∞, so the quantitative phase boundaries need verification.","rationale":"The paper's central claim is that growth suppresses both elastic coarsening and noise-driven geometric disorder, enabling complex reproducible shapes. The low-plasticity coarsening argument is clean and well-verified. The high-plasticity 'lost' regime is the second pillar: without it there is no trade-off to be broken, and without g∞ there is no quantitative statement that growth rescues memory in the high-Pl quadrant. That pillar rests entirely on the large-η reduction where F is set to zero after dropping noise in the differentiated constraint (Supp. II.B, S33). This is the standard danger point in constrained stochastic systems: a Lagrange multiplier enforcing a holonomic constraint must generally be solved jointly with the noise, and the resulting Stratonovich/Ito drift is order σ, the same order as the diffusion. The paper's t_D = (d_eff−1)D0 and g∞ formula follow from a diffusive ansatz, not from a rigorous stochastic projection. The two numerical solvers—including the fully-nonlinear one—reproduce the predicted boundaries in the tested parameter window, which is real, independent support. But that verification is at a finite set of Pl, d, and σbar; it does not settle whether the analytic expression for the boundary is correct beyond the tested window, and the central claim's quantitative predictions (e.g., the location of the 'lost' region and the growth threshold) depend on it. I therefore view the appropriate verdict as conditional: the qualitative mechanism is solid and the numerics are reassuring, but the high-plasticity boundary should be re-derived without the F=0 ansatz or verified by a direct stochastic-projection simulation. If the exact projection preserves t_D and g∞ to within the numerical error bars, the paper can be accepted without change.","tokens_in":18533,"tokens_out":12352,"duration_ms":127402,"concrete_test":"Derive the exact large-η SDE by solving for F(t) from the full constraint d/dt Σθ_n^2=C using Itô calculus (do not set ζ=0), and compare the resulting mode-correlation decay time t_D and g∞ with Eqs. (S51)–(S52). A direct numerical check: in the existing small-angle solver, replace the explicit tension update in Eq. (S15) with a Lagrange multiplier obtained by projecting the noisy step back onto the sphere at each time step, so noise is not dropped in the constraint. Run Pl=10^2, 10^3, 10^4 with d=64, σbar=0.005 (and d=12, σbar=0.001–0.01). If the measured C_t0 decay time or the Fig. 2c boundary shifts by more than ~20% from the F=0 theory, the high-plasticity boundary must be revised.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"In the large-η limit, the paper derives γ_n θdot_n = F θ_n + sqrt(2σ/L) ζ_n, then in Supp. II.B differentiates the constraint Σθ_n^2=C while 'ignoring the noise' to set F=0 (Eq. S33). This is the pivotal step behind the 'lost via diffusion' boundary, t_D, and g∞. But dropping ζ in a stochastic constraint derivative is not a controlled approximation: white noise is unbounded, and the Lagrange multiplier enforcing d/dt Σθ_n^2=0 is a stochastic process of order sqrt(σ). The correct projected dynamics contain a noise-induced drift of order σ, the same order as the diffusion term. D_d and Φ(T_g)≤1 are therefore an ansatz, not a derived limit, in the Pl≳30 regime where the boundary is drawn. If that drift changes the decorrelation rate by an O(1) factor, the 'preserved'/'lost' boundary and g∞ shift quantitatively. The qualitative claim that growth suppresses disorder via the 1/L decay of D0 is not threatened.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper asks when an initially patterned shape is remembered during growth and remodeling in a slender rod. The authors study a minimal visco-elasto-plastic 'plastica' model in the small-slope limit: tangent-angle modes evolve under overdamped elasticity and a rest-curvature field that relaxes to the current shape at rate η. Two failure modes are identified. At low plasticity the deterministic dynamics are replicator-like and coarse-grain to the fundamental mode; above a plasticity threshold, initial high-mode patterns are protected. At high plasticity the rod becomes fluid-like and noise drives anisotropic diffusion on the constraint sphere, erasing the pattern over a memory time t_D. Growth, modeled as uniform elongation, reduces both the elastic coarsening rate and the effective noise amplitude, and the authors derive criteria for a growth rate above which complex patterns are retained despite noise. The central claim is that growth breaks the plasticity trade-off between complexity and reproducibility. The paper includes analytical derivations in the Supplement, small-angle spectral simulations, fully-nonlinear checks, and a code repository.","tokens_in":18684,"tokens_out":6856,"duration_ms":78828,"significance":"If the quantitative phase boundaries are correct, this is a valuable conceptual result: it identifies two dimensionless knobs, plasticity and growth rate, that control whether an encoded mechanical pattern is remembered, degraded, or transformed. The model is deliberately minimal, and the deterministic coarsening derivation (Supplement II.A) is clean. The thresholds have no fitted parameters: ε comes from the initial perturbation and ε_σ from the noise strength, so the agreement with simulations is a genuine internal consistency check. The paper goes beyond linear stability by checking against fully-nonlinear finite-difference simulations and by considering an external-viscosity variant with similar phenomenology. These strengths make the manuscript a good candidate for a broadly read soft-matter journal, provided the high-plasticity stochastic projection is made rigorous or numerically verified.","major_comments":[{"comment":"The high-plasticity boundary, t_D, the criterion Φ(T_g)≤1, and g∞ all rely on the statement that the constraint force vanishes after differentiating Σ_n θ_n^2=C while 'ignoring the noise'. But from γ_n θdot_n = F θ_n + √(2σ/L) ζ_n, exact constraint enforcement gives F = −√(2σ/L) (Σ_n θ_n ζ_n/γ_n)/(Σ_n θ_n^2/γ_n), not F=0. Dropping the noise in this step is not controlled: white noise is unbounded, and after the θ_nF term is expanded the noise-induced drift is of order σ, the same order as the diffusion term. The authors' own remark in Supplement II.C that the tension does not vanish exactly at lower Pl with noise is direct evidence that the correction is not identically zero. Request either a proper stochastic projection (which may introduce an O(σ) drift that renormalizes d_eff and t_D) or direct numerical measurement of t_D and g∞ at the Pl values where the boundary is drawn, to confir","section":"Supplement II.B, Eq. (S33)"},{"comment":"The coarsening-protection threshold in the presence of noise is obtained by replacing the deterministic initial perturbation amplitude ε in Eq. (5) with ε_σ = σ/(μBq_1^2 C). This replacement is plausible but is not derived from the stochastic dynamics; it treats noise as if it were a static initial condition. Since the lower boundary of the 'preserved' region is one of the paper's main quantitative predictions, this step needs support, either by a stochastic multiscale derivation or by showing that the boundary coincides with a measured escape/fixation time from the basin of the initial mode. As written, the lower boundary is an ansatz rather than a consequence of the equations.","section":"Main text, Eq. (5) and Fig. 2c"},{"comment":"The growth-modified diffusion integral replaces d_eff(t) by d_eff(0). Since L(t) increases, q_n(t)=πn/L(t) decreases and d_eff(t) increases with time, so this approximation is not conservative at finite Pl: it underestimates the total angular drift Φ(T_g) and can therefore overestimate the critical growth rate g∞. At Pl→∞ the error vanishes because d_eff→d, and the authors state that the large-η limit is the regime of interest, but the text should state the approximation explicitly and give a bound or numerical check for finite Pl. This is a local fix, not a challenge to the central claim.","section":"Supplement III.B.2, Eq. (S50)"}],"minor_comments":[{"comment":"The elastic timescale is defined as τ_E=μL_0^2/B, but some passages write the elastic rate as B/(μL^2) with L appearing to be the current length. Please use a consistent symbol (L_0, L(t), or L_1) in the definitions of Pl and in the thresholds.","section":"Notation, Eq. (1) and Fig. 1"},{"comment":"The colorbar is cropped at m=12 with a '>12' label, while the text says the highest mode can go up to d=64. This makes the m-dependence of the preserved window difficult to read; consider plotting the full range or stating the crop explicitly in the caption.","section":"Fig. 2d"},{"comment":"The replacement d_eff(t)≈d_eff(0) is introduced with an unqualified '≈'. Since this approximation enters a published design rule, a sentence should state the size of the correction and why it is negligible in the regime shown in Fig. 3.","section":"Supplement III.B.2, Eq. (S50)"},{"comment":"Reference [42] is listed as 'To be submitted'. If it is not yet available, it should be marked as unpublished work or removed from the numbered reference list; if it is a preprint, a stable identifier is needed.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The qualitative message—growth simultaneously suppresses elastic coarsening and noise-driven diffusion, thereby allowing complexity and reproducibility to coexist—is likely correct and is well supported by the deterministic and fully-nonlinear simulations. The main barrier is the uncontrolled F=0 step in Supplement II.B, which underpins the quantitative high-plasticity boundary and g∞. If the authors provide a proper stochastic projection or numerical verification of t_D and g∞ at the relevant parameter values, I would support acceptance. The coarsening-noise replacement in Eq. (5) should also be justified or reframed as heuristic. This is fixable within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth reading. The real contribution is the two-knob picture: plasticity protects complex shapes at moderate rates, then corrupts them by converting noise into geometric disorder, and growth suppresses both failure modes. The derivations are careful and the numerics are honest—deterministic coarsening via replicator dynamics, the noise-diffusion memory time, and the growth thresholds are all checked against both small-angle spectral and fully nonlinear solvers, with code available. That is real evidence and it earns the reader's confidence.\n\nThe main soft spot is exactly where the stress-test note points. In Supplement II.B, the high-plasticity effective dynamics are obtained by setting F=0 after differentiating the constraint and ignoring the noise. White noise is not small in this operation: the exact Itô projection of the constraint produces a noise-induced drift of order σ, the same order as the diffusion term that sets t_D and the Φ≤1 criterion. So the 'lost via diffusion' boundary, t_D, and g∞ are an ansatz in the Pl≳30 regime, not fully derived limits. If that drift changes the decorrelation rate by an O(1) factor, the quantitative boundaries shift. I don't think this kills the paper: the qualitative claim that growth suppresses noise-driven disorder via the 1/L decay of D0 does not rest on the exact F, and the low-plasticity coarsening threshold is on firmer ground. But the paper should either work out the stochastic projection properly or explicitly label those high-plasticity boundaries as approximate.\n\nThe circularity caveat is fair but not damaging: theory and simulations share the same model, so the agreement is internal consistency rather than external confirmation. The paper is honest about that, and the lack of fitted parameters in the criteria helps. The Drosophila midgut discussion is speculative and leans on an unpublished reference, but it is clearly framed as a prediction, not validation. Also minor: the 'optimal' window depends on finite mode count d and on order-one criteria, so the design rule is qualitative, not a precise prescription.\n\nWho gets value: anyone working on morphoelastic rods, buckling mode selection, noise in development, or soft actuators. It is a solid model paper, it deserves referee time, and I would send it out with a request to fix or soften the high-plasticity derivation.","headline":"A clean model-level phase diagram for shape memory in growing visco-elasto-plastic rods, with one genuine stochastic-projection gap in the high-plasticity branch that likely shifts boundaries but not the qualitative story.","tokens_in":19285,"tokens_out":2706,"would_cite":true,"duration_ms":29682,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Growth breaks the trade-off between shape complexity and reproducibility in remodeling rods.","keywords":["shape memory","morphogenesis","elastica","plasticity","growth","buckling modes","noise","viscoelastic rods"],"falsifier":"Simulate the full plastica at large plasticity without dropping the noise term in the tension equation; if the pattern is lost at a different time or growth rate than predicted by the F=0 formula, the trade-off-breaking claim fails. Alternatively, a physical experiment on a growing, remodeling gel rod that shows coarsening at high growth rather than preservation would refute it.","tokens_in":18325,"feed_emoji":"🌀","tokens_out":5766,"duration_ms":58246,"temperature":0.7,"pith_summary":"Elastic slender rods buckle into the simplest possible shape, so a complex initial pattern tends to coarsen away. This paper shows that internal remodeling (plasticity) can freeze that coarsening, but at high rates plasticity makes the rod's rest shape follow the current shape so closely that noise drives the pattern to diffuse away. The trade-off between these two failure modes leaves only a window of intermediate plasticity for shape memory. Uniform growth changes both: it slows elastic coarsening and dilutes noise, so with fast growth and high plasticity, complex initial patterns remain reproducible. The results frame remodeling rate and growth rate as two control knobs for whether an encoded shape is remembered, degraded, or transformed.","feed_headline":"Fast growth lets rods keep complex shapes","feed_subtitle":"Model shows that elongating a rod suppresses coarsening and noise-driven disorder, so intricate patterns stay reproducible.","key_machinery":"The central object is the plastica model: a one-dimensional elastica with internal viscosity µ, rest-curvature remodeling rate η, and an end-shortening constraint that makes the tension a Lagrange multiplier. In mode space the dynamics reduce to a replicator-like competition among bending modes (with decaying selection strength e^{−ηt}) at low plasticity, and to anisotropic Brownian motion on the constraint sphere at high plasticity, with mode-dependent mobility γ_n = µ + Bq_n²/η. Two dimensionless numbers carry the argument: the plasticity number Pl = ητ_E and the normalized growth rate gτ_E. The work also supplies explicit formulas for the coarsening threshold, the diffusion memory time t_","core_discovery":"The paper establishes that in a minimal visco-elasto-plastic rod—the 'plastica'—the fate of an initially encoded multi-mode shape depends on two dimensionless numbers: the plasticity number Pl = ητ_E and the normalized growth rate gτ_E. At low plasticity, bending modes compete like replicators with fitness proportional to −q_n², so the lowest mode excludes all others and erases complexity. Moderately fast remodeling arrests that coarsening because the rest curvature tracks the current shape before selection completes, protecting the pattern. At high plasticity, the rod behaves as a nearly fluid thread: the rest shape adiabatically follows the current shape, the constraint force vanishes at l","pith_inferences":["The replicator-dynamics mapping suggests the same trade-off may appear in any adaptive system where competing components have frequency-dependent fitness and a decaying selection strength—for example, regulatory networks with plasticity—so the 'growth suppresses both failure modes' result might generalize beyond rods.","The paper treats internal viscosity only; the supplement's external-viscosity version shows intermediate coarsening transients, hinting that the phase diagram depends on where dissipation acts—an extension worth exploring for tissues immersed in fluid.","A direct experimental test could use a swelling or growing gel rod with tunable remodeling rate and measure the Pearson correlation of mode spectra over time; the predicted non-monotonic memory with plasticity, and the rescuing effect of growth, are observable.","The assumption of constant bending rigidity B during growth is conservative; if the rod thins as it elongates, coarsening would be suppressed even faster, so the qualitative result is robust but the quantitative thresholds would shift."],"forward_implications":["Below a minimum plasticity, any multi-mode pattern deterministically coarsens to the fundamental buckling mode, so complexity cannot be encoded without remodeling.","Above a second, higher plasticity, noise converts into geometric disorder and the pattern is lost after a plasticity-dependent memory time; the window of successful memory shrinks for more complex initial shapes.","Growth shifts both boundaries: even at zero plasticity, sufficiently fast growth suppresses coarsening, and sufficiently fast growth makes noise diffusion unable to erase the pattern.","In the high-growth, high-plasticity quadrant, arbitrary initial conditions (including random ones) produce reproducible, complex shapes, providing a design rule for morphogenesis and for fluctuation-tolerant soft structures.","The theory makes quantitative predictions for biological systems: an early constriction in a developing gut should be amplified into a stereotyped loop only within a finite window of remodeling rates, a window that growth widens."],"fun_headline_variants":["Growth beats the shape memory trade-off","Fast growth lets rods preserve complex shapes","Elongating rods locks in encoded patterns","Optimal plasticity preserves rod shape memory"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The predictions for how noise destroys a pattern at high plasticity rest on assuming the rod's tension is effectively zero once the rest shape tracks the current shape; if that tension is not negligible, the boundary between remembered and lost patterns changes.","fun_headline_variants_meta":{"raw":{"variants":["Growth beats the shape memory trade-off","Fast growth lets rods preserve complex shapes","Elongating rods locks in encoded patterns","Optimal plasticity preserves rod shape memory"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000276,"raw_usage":{"total_tokens":1448,"prompt_tokens":676,"completion_tokens":772,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":420,"completion_tokens_details":{"reasoning_tokens":729}},"tokens_in":420,"tokens_out":772,"duration_ms":7745,"temperature":1.0,"reasoning_tokens":729,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T23:33:49.757986+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the full plastica at large plasticity without dropping the noise term in the tension equation; if the pattern is lost at a different time or growth rate than predicted by the F=0 formula, the trade-off-breaking claim fails. Alternatively, a physical experiment on a growing, remodeling gel rod that shows coarsening at high growth rather than preservation would refute it.","supporting_citations":[],"review_version":1}