{"id":"ac8f4a3e-8057-4ff9-a258-8336efc6d4c4","arxiv_id":"2507.08391","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Simulations show that torus knots in active ring polymers remain stretched to longer chain lengths than twist knots, and this difference grows with knot complexity.","lead":"Simulations of tangentially active ring polymers show that knot type changes the polymer size at which activity-driven collapse happens. Torus knots resist collapse longer as they get more complex, while twist knots collapse earlier, hinting that activity may favor torus knots.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The twist-knot branch of the central claim rests on a decreasing fit that omits 9_2 and on an extrapolation beyond the simulated range; if higher-complexity twist knots do not continue to shrink, the claimed torus-versus-twist dichotomy and topological selection conclusion weaken.","rationale":"The reader's identification of the twist-knot extrapolation as the weak point is correct and is the most load-bearing element of the paper. The empirical core—active rings collapse and the collapse point depends on topology—is credible: the simulation protocol follows ref. 63, torus knots show a consistent trend across many MC values, and the mechanistic rho_3D argument is plausible. However, the abstract's strongest quantitative prediction ('twist knots shrinks, eventually canceling the actively stretched regime altogether') goes beyond the data. The twist family has few points, the most complex measured point 9_2 is excluded from the fit, and no knot with p>40 or MCN≥10 is simulated. Because that prediction also supports the concluding claim that activity biases the knot spectrum toward torus knots, it is load-bearing. A conditional verdict is appropriate; the paper should either supply the missing high-p twist data or soften the extrapolated claims. I do not see an internal inconsistency in the torus branch, and I would not reject or accept outright without the additional check.","tokens_in":14999,"tokens_out":10421,"duration_ms":134550,"concrete_test":"Recompute Fig. 3b including 9_2 and perform a leave-one-out jackknife of the twist-family slope; then simulate at least one additional twist knot with p≳40 (MCN≥10, e.g., 10_1) under the same protocol at Pe=10, N up to 1024, and determine N_C with the same cumulative-R_g sigmoid criterion. If the slope is not robust to the excluded point or the new p>40 point does not lie below the extrapolated line, the 'eventually canceling the actively stretched regime' claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing part of the central claim is the decreasing twist-knot branch: 'the collapse point of ... twist knots shrinks, eventually canceling the actively stretched regime altogether.' This conclusion is drawn from Fig. 3b, where the twist-family dashed line is a linear fit of N_C−p versus p that explicitly excludes the most complex measured twist knot, 9_2, 'because of the difficulty of measuring its N_C' (Results, The collapse transition). No twist knot with p≳40 or MCN≥10 is simulated; the predicted disappearance at p≳40 is an extrapolation. If 9_2's true N_C lies above the fit, or if additional higher-complexity twist knots show N_C−p flattening or increasing, the claimed torus/twist dichotomy is not the monotonic trend asserted, and the concluding speculation that activity biases the knot spectrum toward torus knots loses its basis. The torus-knot branch and the qualitative early-collapse of twist knots are less vulnerable; the specific 'shrinks and cancels' prediction is the weak load-bearing element.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports molecular dynamics simulations of tangentially active ring polymers with various knot topologies (unknot, double-helix torus knots, and twist knots), for polymerization degrees N from 20 to 1024 at Péclet number Pe=10. The authors extract a collapse transition point N_C from the probability that the gyration radius falls below 0.9 times the passive value, and they find that torus knots collapse at larger N than twist knots, that N_C increases approximately linearly with the ideal length/diameter ratio p for torus knots while decreasing for twist knots, and that the stretched regime for twist knots is predicted to disappear for p≳40. The proposed mechanism is that stretched torus knots adopt ordered double-helical conformations with aligned non-neighboring bonds that suppress bead collisions, whereas twist knots contain noose-like constraints that promote collisions and collapse.","tokens_in":15360,"tokens_out":7820,"duration_ms":83028,"significance":"If the main claims hold, the paper offers a clear and potentially useful demonstration that knot topology can control the activity-driven swelling-collapse transition of ring polymers, and it proposes a mechanistic picture based on bond alignment and intra-molecular collision density. The systematic coverage of many topologies, the wide range of polymerization degrees, and the explicit measurements of bond correlations and collision density are strengths. The paper is likely to interest researchers in active matter, polymer physics, and knot theory. However, the most novel quantitative claim for twist knots rests on a limited dataset and an extrapolation beyond the simulated range, so the significance is conditional on strengthening that branch.","major_comments":[{"comment":"The decreasing trend of N_C−p with p for twist knots, which underlies the abstract's claim that the stretched regime is 'eventually canceling' and the discussion's speculation about activity biasing the knot spectrum, is not adequately supported. The text states that the linear fit for twist knots excludes the most complex simulated twist knot, 9_2, 'because of the difficulty of measuring its N_C,' and no twist knot with p≳40 or MCN≥10 is simulated; the predicted disappearance at p≳40 is an extrapolation. If the true N_C of 9_2 lies above the fitted line, or if additional higher-complexity twist knots flatten or reverse the trend, the claimed torus-versus-twist dichotomy in the collapse-point scaling would be substantially weakened. Please report the fit including 9_2 with its uncertainty, simulate at least one or two additional twist knots beyond 9_2, or explicitly demote the 'eventually canceling' statement to a conjecture.","section":"Results: The collapse transition (Fig. 3)"},{"comment":"The collapse point N_C is extracted from P(N) = P(R_g < 0.9 <R_g^0(N)>), where the factor 0.9 is arbitrary and is introduced to keep P close to zero at small N. Since every quantitative result in the paper is a statement about N_C and its dependence on p, the authors should demonstrate that the family ordering and the linear increase/decrease of N_C are insensitive to the chosen threshold, for example by repeating the analysis with thresholds in a range such as 0.85–0.95. Without this sensitivity check, the linear fits in Fig. 3b could reflect the threshold choice rather than a physical trend.","section":"SI: Determination of the collapsing point"}],"minor_comments":[{"comment":"The WCA cutoff is written as r_c = 6√2 σ, which does not match the standard cutoff 2^(1/6) σ for the WCA potential; please verify the intended formula and correct the typography.","section":"Methods, Eq. (1)"},{"comment":"The damping time is written as 'τ γ = .3τ', which is unclear; presumably this means τ_γ = 3τ, but the notation should be clarified.","section":"Methods, Langevin dynamics"},{"comment":"The quantity N_T is used to delimit the collapse threshold range (135≲N_T≲145) but is never formally defined; please define it and state how it is determined.","section":"Results and Fig. 2 caption"},{"comment":"The abstract states that the collapse point 'grows linearly with the minimum crossing number,' while the analysis in Fig. 3 plots N_C against the ideal length/diameter ratio p; please state explicitly how p maps to the minimum crossing number for the simulated knots.","section":"Abstract and Fig. 3"},{"comment":"The volume V_P = N π/4 σ^3 is described as the volume of a tube of radius 2σ and length Nσ, but such a tube has volume 4π N σ^3; this inconsistency affects the reported absolute values of ρ_3D (e.g., the asymptotic value ~0.3σ^{-3}), even though relative comparisons across topologies may be unaffected.","section":"Results: Bead collisions and loop formation"},{"comment":"The linear fits in Fig. 3b are described in the caption but no fit parameters, uncertainties, or goodness-of-fit measures are reported; please include them in the caption or in the SI.","section":"Results: The collapse transition (Fig. 3b)"}],"recommendation":"major_revision","confidential_remarks":"This paper is well within the scope of cond-mat.soft and addresses a question of current interest. My main concern is that the most novel quantitative claim—the shrinking and eventual disappearance of the twist-knot stretched regime—is based on a fit that omits the largest-p data point and on an extrapolation beyond the simulated range. This is fixable either by additional simulations of higher-complexity twist knots or by appropriately softening the claim. The torus-knot branch and the qualitative early collapse of twist knots appear well supported, so I do not see grounds for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper reports a genuinely new result—the first systematic comparison of torus and twist knots in tangentially active ring polymers—and the torus branch is well supported. The twist branch is the soft spot: the decreasing N_C trend excludes the most complex twist knot (9_2) because it is hard to measure, and the 'stretched regime disappears for p≳40' is an extrapolation beyond the simulated range. That does not sink the paper, but it is the part to scrutinize.\n\nWhat is new: Ref 63 characterized collapse for unknotted active rings; Refs 60-62 studied knot formation in active linear polymers. Here they pre-tie two knot families and find opposite scaling of the collapse point with knot complexity. The torus result is clean: N_C grows linearly with p over many topologies, with a plausible mechanism—ordered double-helix conformations reduce oppositely oriented near-neighbor bonds and collision density. The ρ_3D and bond-correlation measurements support this.\n\nThe twist part: all twist knots do collapse earlier than torus knots; that is robust. But the claim that N_C − p shrinks linearly and the stretched regime vanishes is built on a fit that drops 9_2, and the disappearance at p≳40 is an extrapolation. If 9_2 or higher-complexity twist knots flatten or reverse the trend, the dichotomy would weaken, though the qualitative 'twist knots collapse earlier' would survive. The 0.9 threshold in the collapse criterion is a bit arbitrary, but it is applied consistently, so it likely does not create the trend.\n\nThe mechanism is correlational—they do not directly manipulate collision probability—but it is physically plausible and the data support it. The paper is honest about the 9_2 exclusion and the extrapolation. No code/data, but that is common for this type of simulation study.\n\nIf you work on active polymers or knot physics, this is worth reading. The torus result is likely to be cited; the twist prediction is a testable target for future simulations.\n\nI would send this to peer review. The twist-branch fit should be checked, but the core finding is solid enough to warrant referee time.","headline":"New torus-vs-twist collapse result with a solid torus branch; the twist 'vanishing stretched regime' rests on an excluded point and extrapolation.","tokens_in":15787,"tokens_out":4584,"would_cite":true,"duration_ms":47441,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["61.25.H-","82.35.Lr"],"model":"deepseek-v4-flash","headline":"Knot topology shifts the collapse point of tangentially active ring polymers: twist knots collapse earlier, and complex twist knots lose the actively stretched regime entirely, while torus knots become more resistant as their crossing…","keywords":["active polymers","ring polymers","knot topology","collapse transition","tangential activity","torus knots","twist knots","Kremer-Grest model"],"falsifier":"Simulate tangentially active twist knots with ideal length/thickness ratio $p \\gtrsim 40$ (minimal crossing number $\\gtrsim 10$) with sufficient statistics and extract $N_C$; if $N_C$ does not keep decreasing below the unknot threshold and instead flattens or rises, the claimed disappearance of the stretched regime for complex twist knots is refuted.","tokens_in":1638,"feed_emoji":"🪢","tokens_out":2335,"duration_ms":78349,"temperature":0.7,"pith_summary":"The paper asks whether the knot tied in a ring polymer changes how the polymer behaves when its monomers actively push themselves along the chain. Simulating tangentially active rings with different knots, it finds that knot family and knot complexity shift the polymer size at which the active stretched state collapses: torus knots collapse later as their minimal crossing number grows, while twist knots collapse earlier, and sufficiently complex twist knots lose the stretched regime altogether. The proposed mechanism is geometric: stretched torus knots relax into ordered double-helix conformations whose strands move in the same direction, suppressing collisions, whereas twist knots carry noose-like constraints that seed collisions and deadlock-driven collapse. If correct, topology becomes a tunable handle on active polymer size and phase behavior.","feed_headline":"Twist knots end the stretched phase of active polymer rings","feed_subtitle":"Simulations show knot family shifts the collapse point, so knotting can tune active materials.","key_machinery":"The load-bearing objects are the collapse point $N_C$ and two structural observables: the bond correlation function $\\beta(\\delta) = \\langle \\sum_{i,j} \\mathbf{t}_i \\cdot \\mathbf{t}_j / N \\rangle$, whose argmin gives the typical loop size, and the density $\\rho_{3D}$ of close oppositely oriented non-neighboring bonds, which measures collision-prone strand contacts. The mechanism is that stretched torus knots arrange as intertwined double helices with aligned bonds ($\\beta$ minimum near $\\delta/N = 1/4$), keeping $\\rho_{3D}$ near zero, while twist knots lack such order and accumulate noose-like constraints that raise $\\rho_{3D}$ and seed deadlocks. Knot complexity enters through the ideal knot length/diameter ratio $p$, which for torus knots grows linearly with $\\mathrm{MCN}$.","core_discovery":"The central discovery is a family-dependent collapse transition in tangentially active ring polymers. For unknotted rings there is a known activity-induced transition from a stretched to a collapsed state at a polymerization degree $N_C$. Extending this to knotted rings, the paper shows $N_C$ scales linearly with the ideal knot length/diameter ratio $p$ (equivalently minimal crossing number $\\mathrm{MCN}$) for double-helix torus knots, whereas for twist knots $N_C$ decreases with $p$; extrapolation suggests twist knots with $\\mathrm{MCN} \\gtrsim 10$ no longer support an extended active phase. The cause is the shape of the stretched state: torus knots form regular double helices in which non-neighboring bonds are aligned, keeping the density $\\rho_{3D}$ of oppositely oriented close bonds near zero, while twist knots display noose-like regions that create collisions and deadlocks, triggering collapse.","pith_inferences":["If the twist-knot trend holds experimentally, knot type could act as a reporter of the active phase: measuring the knot spectrum of active DNA rings might reveal whether the population was in the stretched or collapsed regime.","Hydrodynamic interactions are neglected here; a testable extension is to repeat the simulations with explicit solvent and check whether the linear growth of $N_C$ for torus knots survives.","The mechanism suggests a route to knot-selective sorting: choosing activity levels such that twist knots collapse while torus knots remain extended could separate knots by family in a microfluidic device.","The collapsed state resembles metastable tight knots in semiflexible polymers; comparing collapse kinetics of active rings with passive tight knots could isolate the role of activity in stabilizing the collapsed phase."],"forward_implications":["Knot complexity becomes a design parameter: torus knots with many crossings yield active rings that stay extended at arbitrarily large lengths, while complex twist knots collapse as soon as they are long enough to tie.","The collapse point of a torus-knotted active ring can be predicted from the ideal knot's length/thickness ratio $p$, connecting a geometric knot invariant to a dynamical phase boundary.","Activity should bias the knot spectrum of a population of randomly knotted active rings toward torus knots, since complex twist knots cannot form or persist in the extended state.","The double-helix stretched conformation suppresses inter-strand collisions, so observables like $\\rho_{3D}$ in the stretched state could serve as an early indicator of collapse onset."],"supporting_citations":[{"why":"Establishes the activity-induced swelling-collapse transition in unknotted active rings that this work extends to knotted rings.","marker":"[63]"},{"why":"Supplies the Flory-type scaling $R_g \\propto N^{\\nu} p^{-\\nu+1/3}$ and the use of ideal knot length/thickness ratio $p$.","marker":"[64]"},{"why":"Provides the ideal knot $p$ values for different knot topologies used to parametrize knot complexity.","marker":"[65]"},{"why":"Establishes the geometry and physics of knots, the basis for interpreting $p$ as the minimum rope length needed to tie a knot.","marker":"[73]"},{"why":"Defines motility-induced phase separation, the collision/deadlock framework used to explain collapse.","marker":"[37]"},{"why":"Introduces deadlocks in active ring melts, the mechanism adapted here to single-ring strand-loop entanglements.","marker":"[59]"}],"fun_headline_variants":["Knot family sets collapse point for active ring polymers","Twist knots shrink stretched regime, torus knots expand it","Active polymer collapse depends on knot topology","Torus knots hold stretch, twist knots collapse earlier","Knot complexity tunes active ring collapse"],"cache_read_input_tokens":17920,"weakest_assumption_plain":"The twist-knot branch of the central claim rests on a decreasing fit of collapse point versus knot complexity from which the most complex twist knot studied, $9_2$, was excluded, and on an extrapolation to complexities beyond the simulated range; if including $9_2$ or higher-complexity data overturns this downward trend, the claimed torus-versus-twist dichotomy would be substantially weakened.","fun_headline_variants_meta":{"raw":{"variants":["Knot family sets collapse point for active ring polymers","Twist knots shrink stretched regime, torus knots expand it","Active polymer collapse depends on knot topology","Torus knots hold stretch, twist knots collapse earlier","Knot complexity tunes active ring collapse"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000783,"raw_usage":{"total_tokens":3451,"prompt_tokens":933,"completion_tokens":2518,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":549,"completion_tokens_details":{"reasoning_tokens":2446}},"tokens_in":549,"tokens_out":2518,"duration_ms":21389,"temperature":1.0,"reasoning_tokens":2446,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:21:57.054772+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate tangentially active twist knots with ideal length/thickness ratio $p \\gtrsim 40$ (minimal crossing number $\\gtrsim 10$) with sufficient statistics and extract $N_C$; if $N_C$ does not keep decreasing below the unknot threshold and instead flattens or rises, the claimed disappearance of the stretched regime for complex twist knots is refuted.","supporting_citations":[{"cited_title":"Y.; Feigel, A.; Rabin, Y","cited_arxiv_id":null,"evidence_quote":"Supplies the Flory-type scaling $R_g \\propto N^{\\nu} p^{-\\nu+1/3}$ and the use of ideal knot length/thickness ratio $p$."},{"cited_title":"Ideal Knots ; World Scientific, 1998","cited_arxiv_id":null,"evidence_quote":"Provides the ideal knot $p$ values for different knot topologies used to parametrize knot complexity."},{"cited_title":"G.; Dubochet, J.; Stasiak, A","cited_arxiv_id":null,"evidence_quote":"Establishes the geometry and physics of knots, the basis for interpreting $p$ as the minimum rope length needed to tie a knot."}],"review_version":1}