{"id":"c310cee7-8db3-4c29-8488-785da17d827b","arxiv_id":"2507.17750","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For periodic TASEP, the current fluctuation function grows linearly with system size for positive tilt and saturates at -1 for negative tilt, while the relaxation gap decays polynomially or exponentially, respectively.","lead":"This paper studies how the amount of traffic flow in a one-dimensional particle system fluctuates over time when the system is nudged toward unusually high or low currents. It finds a sharp change in behavior: nudging toward high current makes the system relax fast, while nudging toward low current traps it in a long-lived jammed state.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central scaling results depend on the unproven Bethe-root selections of Assumptions 3.9 and 3.10; a direct numerical comparison with exact diagonalization is needed to validate the phase-transition claim.","rationale":"The paper is transparent: it labels the root selections as Assumptions, acknowledges Proposition 3.8's counterexample, and notes diagonalizability is open (Remark 2.2). It also correctly credits Derrida–Appert for the SCGF and the paper's γ>0 largest-eigenvalue formula reduces to known results. The genuine new content is the spectral gap scaling, and that is exactly where the root-selection conjecture is most fragile: a small change in which subset yields the second eigenvalue could change the gap from N^{-1} to O(1) or alter the exponential rate. The proposed numerical test is directly targeted: exact diagonalization for N=16–24 is feasible because the state-space dimension (≤184756) is manageable, and enumerating all Bethe subsets is also feasible at these sizes. Performing both and comparing would settle whether the assumptions hold or whether eigenvalue crossings invalidate them. The abstract's unqualified statement of a 'dynamical phase transition' should be read as conditional until then.","tokens_in":24771,"tokens_out":10335,"duration_ms":101151,"concrete_test":"Exact-diagonalize M_γ for N=16,p=8 (ρ=1/2) and N=18,p=6 (ρ=1/3) at γ=-1,-0.5,0.1,0.5,1,2, and compute the full spectrum. Separately, enumerate all C(N,p) subsets A, solve the Bethe consistency equation (3.14) for each, and rank the resulting eigenvalues (using the completeness result of Iwao–Motegi to ensure all solutions are found). Check whether the subsets from Assumptions 3.9 and 3.10 reproduce the true λ1 and λ2 from exact diagonalization. If they do, repeat at N=20,24 to confirm the predicted scaling; if any mismatch appears, the scaling laws in Results 2.3/2.4 are not justified beyond the assumptions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's main asymptotic claims (Results 2.3 and 2.4) are conditional on identifying the largest and second-largest eigenvalues of M_γ with specific subsets of Bethe roots. Assumption 3.9 (γ>0: A={1,...,p} for λ1 and minimal modifications (3.21) for λ2) and Assumption 3.10 (γ<0: A={1,...,p-1,N} for λ1 and (3.25) for λ2) are not proved. Proposition 3.8 shows that the γ>0 selection has no solution for γ<log(1-ρ), demonstrating that root selections can change with γ; the paper itself notes possible eigenvalue crossings immediately before stating the assumptions. The entire Euler-Maclaurin analysis in Section 4—Theorem 4.5 and Propositions 4.11/4.13—computes eigenvalues for these assumed subsets, but never establishes that these are the true λ1 and λ2. In particular, for γ<0 the second-largest eigenvalue is asserted to be one of four modified subsets (3.25), and the exponentially small gap estimate (4.50) would be wrong if a different subset had a larger real part. Since the new content beyond the known SCGF is precisely the spectral gap scaling, the phase-transition picture (polynomial vs exponential gap) inherits this uncertainty. The numerical Figures 1 and 2 show eigenvalue clouds but do not overlay the predicted eigenvalues or test the root selection; no independent check of Assumptions 3.9/3.10 is provided. Without such a check, Results 2.3/2.4 are conditional, matching the paper's own framing but not the unconditional tone of the abstract.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies current fluctuations in periodic TASEP by analyzing the tilted generator M_γ through the coordinate Bethe ansatz. Its main claims, stated as Results 2.3 and 2.4, are that in the thermodynamic limit at fixed density the largest eigenvalue behaves as λ_1(γ)=NΛ(γ,ρ)+O(1) for γ>0 and as λ_1(γ)=-1+exp(Nγρ)+exp(Nγ(1-ρ))+o(...) for γ<0, while the spectral gap closes polynomially, N^{-1}g(γ,ρ), for γ>0 and exponentially for γ<0. The technical core is a Cassini-oval parametrization of Bethe roots, leading to asymptotic equations for the consistency parameter C_{N,γ}, and Euler-Maclaurin estimates for sums over roots. The derivations are explicitly conditional on Assumptions 3.9 and 3.10, which identify λ_1 and λ_2 with specific sign-dependent choices of Bethe-root subsets.","tokens_in":25262,"tokens_out":7203,"duration_ms":81705,"significance":"If the central claims are correct, the paper provides a non-perturbative description of a dynamical phase transition in a paradigmatic KPZ-class model, complementing the known Derrida-Appert SCGF with subleading spectral data and giving a concrete mechanism for metastability at negative tilt. The paper has real strengths: a transparent geometric parametrization of the roots (Lemma 4.2), controlled Euler-Maclaurin error estimates, a priori bounds in Appendix A, and consistency checks against the known asymptotics of [9,10,13] in Remark 2.5. However, the decisive eigenvalue identifications are not proved, and the numerical evidence presented does not test them. The significance of the paper therefore remains conditional; establishing or numerically strongly supporting the root-selection assumptions would make the contribution substantial.","major_comments":[{"comment":"The central asymptotic statements depend on identifying λ_1 and λ_2 with the Bethe-root subsets in (3.20)-(3.21) for γ>0 and in (3.22)-(3.25) for γ<0, and these identifications are assumed rather than proved. Proposition 3.8 shows that the positive-tilt selection (3.20) fails for γ<log(1-ρ), and the text immediately before the assumptions explicitly acknowledges that eigenvalue crossings can change the selection. Theorems 4.5 and Propositions 4.11/4.13 compute eigenvalues for the assumed subsets but never rule out that another subset has a larger real part. Since the genuinely new content is the spectral-gap scaling, the phase-transition picture inherits this uncertainty. I recommend adding a direct numerical validation: for moderate N, compare exact diagonalization of M_γ with the predicted λ_1 and Re(λ_1-λ_2) under Assumptions 3.9 and 3.10, and report which Bethe subset realizes the second-largest eigenvalue. Figures 1 and 2 currently show eigenvalue clouds but do not overlay these predictions.","section":"Section 3.5, Assumptions 3.9 and 3.10; Results 2.3 and 2.4"},{"comment":"The spectral decomposition in Eq. (2.13) and the exponential convergence statement in Eq. (2.14) assume that M_γ is diagonalizable, while Remark 2.2 states that diagonalizability remains open. If M_γ is not diagonalizable, the correction term in (2.14) can contain polynomial factors in t that are not captured by the simple O(e^{-t gap} t^{-1}) bound. The eigenvalue asymptotics in Results 2.3 and 2.4 do not by themselves require diagonalizability, but the interpretation of the spectral gap as the relaxation rate in the moment-generating function does. The paper should either prove diagonalizability for the relevant γ or state the SCGF and gap results without relying on Eq. (2.13).","section":"Section 2.3, Eq. (2.13)-(2.14), and Remark 2.2"},{"comment":"The proof of Proposition 3.12 is not fully justified. The claim that C_{N,γ}>r_{cr}^p makes the p roots with largest real parts 'not uniquely determined' is asserted rather than proved; in the listed parity cases one still needs to show that a real-part tie actually occurs among the candidate roots. If no tie occurs, a unique p-element selection can exist even on a single Cassini oval, so the contradiction with simplicity of λ_1 does not follow from the given argument. Since this proposition is used to restrict the admissible range of C_{N,γ} in the γ>0 analysis, the argument should be completed or replaced by a direct numerical check.","section":"Section 3.5, Proposition 3.12"}],"minor_comments":[{"comment":"The paper should state explicitly that the spectral gap is Re(λ_1-λ_2); the leading term in Eq. (4.50) is purely imaginary, so the exponentially small real gap comes from the 4π^2/N^2 term. Please clarify this in the statement of Result 2.4.","section":"Result 2.4 and Eq. (4.50)"},{"comment":"There is a typo: 'The the exact formulas' should read 'The exact formulas'.","section":"Remark 2.5"},{"comment":"The set 'A={1,3. . . , p, N}' contains a stray period; it should be 'A={1,3,...,p,N}'.","section":"Assumption 3.10"},{"comment":"The arXiv identifier printed in the reference, 1708.04907, does not match the URL, which points to 1511.03762; please correct the inconsistency.","section":"Reference [35]"},{"comment":"The sentence explaining that the sum over j is estimated by an integral and an error term 'both of order O(e^{Nγ(1-ρ)}) and cancelling each other' is confusing; please expand the cancellation explicitly.","section":"Section 4.2.1, Eq. (4.40)"},{"comment":"The last sentence, 'for finite γ close to 0 it provides a uniform bound in terms of γ', is imprecise; for a fixed nonzero γ the bound should be stated uniformly in N with the dependence on γ made explicit.","section":"Proposition A.1, item (ii)"}],"recommendation":"major_revision","confidential_remarks":"The authors are transparent about the conjectural status of the root-selection assumptions, which is commendable, but the abstract and Results 2.3/2.4 present the conclusions unconditionally. A major revision that adds a serious numerical test of Assumptions 3.9/3.10, or a proof of at least a nontrivial part of them, would substantially raise the value of the paper for the journal's readership. The topic fits the scope of cond-mat.stat-mech."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: the genuinely new content is the spectral-gap scaling at finite tilt gamma — polynomial N^{-1} gap for gamma>0 and exponentially small gap for gamma<0 — plus the implied dynamical phase transition. The SCGF part reproduces Derrida-Appert's 1999 result, and the paper says so in Remark 2.5. The gap result is new, and it extends the Gwa-Spohn/Golinelli-Mallick analysis from half-filling and zero tilt to arbitrary density and finite gamma using Cassini-oval machinery.\n\nWhat the paper does well: the asymptotic machinery is used carefully. Euler-Maclaurin with integral remainder, contour integrals, explicit dilogarithm expressions, and consistency checks against known limits (gamma->0+ and gamma->+infinity) give real internal coherence. The authors are transparent that Assumptions 3.9 and 3.10 are assumptions, and the introduction explicitly says the results hold under conjectures on the Bethe-root structure. That honesty earns credit.\n\nThe soft spots are real, and they are load-bearing. The identification of the largest and second-largest eigenvalues with specific Bethe-root subsets is not proven. Proposition 3.8 shows the positive-gamma selection cannot work for gamma < log(1-rho), which is why the negative-gamma assumption differs. But then the negative-gamma gap result depends on the second-largest eigenvalue being one of the modified sets in (3.25); if some other subset had a larger real part, the exponentially small gap could be wrong. The paper offers no proof and no direct numerical test. Figures 1 and 2 show eigenvalue clouds but do not overlay the predicted lambda1 and lambda2, nor do they check the assumed root choices against exact diagonalization. That is a missed opportunity, and it matters precisely because the gap scaling is the paper's main new contribution.\n\nThere is also a framing mismatch: the abstract states Results 2.3 and 2.4 unconditionally, while the introduction correctly labels them as conditional. For a paper whose novelty is the gap scaling, the abstract should carry the same caveat as the introduction.\n\nThe diagonalizability of M_gamma is open (Remark 2.2) — not fatal for the eigenvalue asymptotics, but worth noting.\n\nWho this is for: specialists in exact large deviations and Bethe ansatz for driven lattice gases. The paper deserves a serious referee. The methods are nontrivial, the conditional results are worth pinning down, and the conjectures could be tested numerically. I would send it to review, but I would insist the authors either prove or numerically substantiate the root selections and align the abstract with the conditional framing.","headline":"New spectral-gap scaling for finite tilt in periodic TASEP, derived under explicit but unproved root-selection assumptions; the abstract overstates the certainty.","tokens_in":25666,"tokens_out":2850,"would_cite":true,"duration_ms":33971,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C22","60K35"],"pacs":[],"model":"deepseek-v4-flash","headline":"For periodic TASEP, a positive tilt in the jump-counting parameter makes current fluctuations ballistic with $O(N)$ relaxation, while a negative tilt pins the largest eigenvalue near $-1$ and makes relaxation exponentially slow.","keywords":["totally asymmetric simple exclusion process","current fluctuations","large deviations","tilted generator","spectral gap","Bethe ansatz","Cassini oval","dynamical phase transition"],"falsifier":"Take a periodic TASEP ring of moderate size, such as $N=18$, $p=6$, compute the full spectrum of the tilted generator by exact diagonalization for a grid of $\\gamma$ values around zero, and compare $\\lambda_1$ and $\\lambda_2$ with the paper's formulas: a gap that is not $O(N^{-1})$ for some $\\gamma>0$, or a $\\lambda_1$ for $\\gamma<0$ that deviates from $-1+e^{N\\gamma\\rho}+e^{N\\gamma(1-\\rho)}$ beyond the stated exponentially small error, would falsify the central claim. More directly, extract the Bethe roots from the exact top eigenvectors and check whether they match the sets $A$ in Assumptions 3.9 and 3.10.","tokens_in":24600,"feed_emoji":"➡️","tokens_out":15427,"duration_ms":145954,"temperature":0.7,"pith_summary":"This paper investigates the statistics of the time-integrated particle current in the totally asymmetric simple exclusion process (TASEP) on a ring, controlled by a tilt parameter $\\gamma$ that exponentially weights jumps. Using the coordinate Bethe ansatz together with the Cassini-oval geometry of its roots, the authors derive the large-$N$ behaviour of the scaled cumulant generating function (the largest eigenvalue $\\lambda_1$) and of the spectral gap. The message is that the sign of $\\gamma$ is a dynamical phase-transition parameter: for $\\gamma>0$ the current is enhanced, $\\lambda_1$ grows linearly in $N$, and the gap closes as $N^{-1}$; for $\\gamma<0$ the current is suppressed, $\\lambda_1$ approaches $-1$ exponentially, and the gap is exponentially small. If the claims are correct, they provide a complete leading-order picture of how conditioning a driven lattice gas on atypical current changes both its large-deviation rate function and its relaxation timescale.","feed_headline":"TASEP current flips between fast and metastable at zero tilt","feed_subtitle":"Positive tilt: current grows linearly with N, relaxation time N. Negative tilt: exponential metastability.","key_machinery":"The engine of the argument is the coordinate Bethe ansatz in the variable $Z_j=2e^\\gamma z_j^{-1}-1$, which converts the tilted-generator eigenvalue problem into the choice of $p$ roots among the $N$ solutions of $(1-u)^p(1+u)^{N-p}=C$ for a single unknown consistency parameter $C$. The roots are labelled along Cassini ovals, the level sets $|1-u|^{\\rho}|1+u|^{1-\\rho}=r^{\\rho}$ with foci at $\\pm1$, and the topological change of the oval at the critical radius $r_{\\rm cr}$ organizes the calculation. The largest and second-largest eigenvalues are identified with specific root sets: $A=\\{1,\\dots,p\\}$ and its minimal modification for $\\gamma>0$, and $A=\\{1,\\dots,p-1,N\\}$ and further modifications for $\\gamma<0$. Thermodynamic limits are then taken using the Euler-Maclaurin formula and contour integrals, so that sums over $p$ roots become integrals along the Cassini contour, with the dilogarithm entering through $\\log(1+u)$.","core_discovery":"Under Assumptions 3.9 and 3.10 on the selection of Bethe roots, this paper derives the thermodynamic-limit spectrum of the tilted TASEP generator from the coordinate Bethe ansatz. As $N \\to \\infty$ at fixed density $\\rho=p/N$, the largest eigenvalue behaves as $\\lambda_1(\\gamma)=N\\Lambda(\\gamma,\\rho)+O(1)$ for $\\gamma>0$, while for $\\gamma<0$ it behaves as $\\lambda_1(\\gamma)=-1+e^{N\\gamma\\rho}+e^{N\\gamma(1-\\rho)}+o(e^{N\\gamma\\rho}+e^{N\\gamma(1-\\rho)})$. The spectral gap obeys $\\lambda_1-\\lambda_2=N^{-1}(g(\\gamma,\\rho)+o(1))$ for $\\gamma>0$ and is exponentially small for $\\gamma<0$. The constants $\\Lambda$ and $g$ are explicit: $\\Lambda=\\Lambda_\\infty(u_*(r_*(\\gamma)))$ and $g=g_\\infty(u_*(r_*(\\gamma)))$, where $r_*$ solves $\\gamma=G_\\infty(u_*(r_*))$, and $u_*$ is the point where the Cassini oval meets the boundary of the rightmost root domain. The paper presents this as a dynamical phase transition between an active phase with ballistic current and fast relaxation and an inactive, metastable phase with suppressed current.","pith_inferences":["Beyond the paper: the same root-selection method suggests that the full top-of-spectrum structure for $\\gamma>0$ is an effective single-particle tower, with each eigenvalue labelled by a finite modification of $A=\\{1,\\dots,p\\}$ and the first corrections to $\\lambda_1$ appearing in units of $N^{-1}$; exact diagonalization of moderate rings could test this tower directly.","Beyond the paper: the exponentially small gap for $\\gamma<0$ invites a nucleation picture in which the system is stuck in a jammed configuration and must cross an exponentially rare bottleneck to reach the biased steady state, and the Cassini-oval critical radius $r_{\\rm cr}$, where the two ovals merge, is a natural candidate for setting that barrier.","Beyond the paper: because the argument uses only the level-set geometry of the Bethe equation and a selection rule for the top eigenvalues, the same $\\gamma\\gtrless0$ dichotomy may appear in other Bethe-ansatz-solvable driven lattice gases, and checking one such model would show whether this phase transition is generic or specific to TASEP.","Beyond the paper: a direct finite-size crossover test is to set $\\gamma=c/N$ and vary $c$; the paper's two regimes predict a collapse onto the functions $\\Lambda$ and $g$ at $c$ of order one, with a crossover location computed from the limiting equation $\\gamma=G_\\infty(u_*(r_*))$."],"forward_implications":["For any fixed $\\gamma>0$, the biased system relaxes on a timescale of order $N$, faster than the $N^{3/2}$ KPZ relaxation at $\\gamma=0$, with explicit limiting forms for the gap constant, including $\\mathrm{Re}\\,g \\sim 2e^\\gamma\\pi\\sin(\\pi\\rho)$ as $\\gamma\\to+\\infty$ and $\\mathrm{Re}\\,g \\sim (4\\pi^{4/3}/3^{2/3})\\gamma^{1/3}[\\rho(1-\\rho)]^{2/3}$ as $\\gamma\\to0^+$.","For $\\gamma<0$, the moment-generating function $E[e^{\\gamma Y(t)}]$ reaches its asymptotic exponential growth rate only after times exponential in $N$, because the second eigenvalue is exponentially close to the first; this is a concrete signature of metastability in the suppressed-current phase.","Because $\\lambda_1$ is linear in $N$ for $\\gamma>0$ and saturates near $-1$ for $\\gamma<0$, the Legendre-Fenchel transform yields a large-deviation rate function with a ballistic positive-current tail and a distinct negative-current tail, reproducing and refining the universal large-deviation forms found in earlier work.","The root-selection rules imply that, near the top of the spectrum, eigenvalues come in nearly degenerate clusters obtained by moving one Bethe root to a neighbouring index; for $\\gamma<0$ these clusters sit within exponentially small distance of $-1$, so the spectral density has a spiky structure.","The leading negative-$\\gamma$ asymptotics is independent of the details of the Bethe-root set, as stated in Corollary 4.12: any selection with $p-1$ roots from the right oval and one from the left oval gives the same exponential leading behaviour, making the inactive-phase prediction robust within the Bethe-ansatz framework."],"supporting_citations":[{"why":"Supplies the coordinate Bethe ansatz for the TASEP spectral gap at half-filling and the minimal-modification selection rule for the second eigenvalue.","marker":"[4]"},{"why":"Extends the gap Bethe-ansatz calculation to arbitrary density, providing the baseline the paper's finite-density asymptotics build on.","marker":"[5]"},{"why":"Gives the decoupling transformation and root-labelling strategy that Section 3.3 follows to reduce the Bethe equations to a single consistency parameter.","marker":"[7]"},{"why":"Derives the Bethe ansatz equations for the tilted TASEP current, from which the paper's spectral analysis starts.","marker":"[9]"},{"why":"Provides the earlier closed-form SCGF for all gamma; the paper's lambda_1 asymptotics are shown to agree with its equations (53), (57), and the expansion near Eq. (25).","marker":"[10]"},{"why":"Gives the high-gamma spectral-gap asymptotics for ASEP conditioned on enhanced flux that the paper matches in Eq. (2.18).","marker":"[13]"},{"why":"Introduces the Riemann-surface and Cassini-oval picture for periodic TASEP Bethe roots that the asymptotic analysis is built on.","marker":"[32]"},{"why":"Proves that the Bethe ansatz equations have exactly the right number of solutions, justifying the search for the top eigenvalues among these root sets.","marker":"[34]"}],"fun_headline_variants":["TASEP current: ballistic for positive tilt, metastable for negative","Positive tilt drives TASEP to fast flow, negative to metastability","Dynamical phase transition in TASEP current fluctuations","TASEP relaxation: polynomial vs exponential under tilt","Zero tilt marks TASEP transition between active and inactive"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole result rests on the unproven belief that the two leading eigenvalues correspond to specific sign-dependent selections of roots of the Bethe equations, and if at some tilt the true leading eigenvalues switch to different root selections, the predicted scaling laws would change; the authors themselves show that the positive-tilt selection already fails for $\\gamma<\\log(1-\\rho)$.","fun_headline_variants_meta":{"raw":{"variants":["TASEP current: ballistic for positive tilt, metastable for negative","Positive tilt drives TASEP to fast flow, negative to metastability","Dynamical phase transition in TASEP current fluctuations","TASEP relaxation: polynomial vs exponential under tilt","Zero tilt marks TASEP transition between active and inactive"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00024,"raw_usage":{"total_tokens":1594,"prompt_tokens":1094,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":710,"completion_tokens_details":{"reasoning_tokens":414}},"tokens_in":710,"tokens_out":500,"duration_ms":5169,"temperature":1.0,"reasoning_tokens":414,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:39:46.749447+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a periodic TASEP ring of moderate size, such as $N=18$, $p=6$, compute the full spectrum of the tilted generator by exact diagonalization for a grid of $\\gamma$ values around zero, and compare $\\lambda_1$ and $\\lambda_2$ with the paper's formulas: a gap that is not $O(N^{-1})$ for some $\\gamma>0$, or a $\\lambda_1$ for $\\gamma<0$ that deviates from $-1+e^{N\\gamma\\rho}+e^{N\\gamma(1-\\rho)}$ beyond the stated exponentially small error, would falsify the central claim. More directly, extract the Bethe roots from the exact top eigenvectors and check whether they match the sets $A$ in Assumptions 3.9 and 3.10.","supporting_citations":[{"cited_title":"Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model","cited_arxiv_id":null,"evidence_quote":"Extends the gap Bethe-ansatz calculation to arbitrary density, providing the baseline the paper's finite-density asymptotics build on."},{"cited_title":"Spectral gap of the totally asym- metric exclusion process at arbitrary filling","cited_arxiv_id":null,"evidence_quote":"Gives the decoupling transformation and root-labelling strategy that Section 3.3 follows to reduce the Bethe equations to a single consistency parameter."},{"cited_title":"Exact large deviation function in the asymmetric exclusion process","cited_arxiv_id":null,"evidence_quote":"Derives the Bethe ansatz equations for the tilted TASEP current, from which the paper's spectral analysis starts."},{"cited_title":"Universal large-deviation function of the Kardar–Parisi–Zhang equation in one dimension","cited_arxiv_id":null,"evidence_quote":"Provides the earlier closed-form SCGF for all gamma; the paper's lambda_1 asymptotics are shown to agree with its equations (53), (57), and the expansion near Eq. (25)."},{"cited_title":"Riemann surface for TASEP with periodic boundaries","cited_arxiv_id":null,"evidence_quote":"Introduces the Riemann-surface and Cassini-oval picture for periodic TASEP Bethe roots that the asymptotic analysis is built on."},{"cited_title":"Bethe roots for periodic TASEP and algebraic curve","cited_arxiv_id":"2504.19690","evidence_quote":"Proves that the Bethe ansatz equations have exactly the right number of solutions, justifying the search for the top eigenvalues among these root sets."}],"review_version":1}