{"id":"8dcde1c1-04ca-42a4-a574-d42fba9c730a","arxiv_id":"2608.04395","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A zero-displacement ratio built from wave-function zeros probes Laughlin order and supports a composite-fermion-fluid description of the ν=1/5 Coulomb ground state.","lead":"This paper introduces a statistical measure of how the zeros of a fractional quantum Hall wave function are arranged around electrons, and uses it to detect phase transitions and to build a better variational description of the ν=1/5 state. The new 'zero displacement ratio' reveals that the Coulomb-interacting ν=1/5 state binds only two vortices per electron, forming composite fermions at an effective filling ν*=1/3.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'almost perfect' CFF overlap at ν=1/5 is computed with a per-size fitted λ_opt and only for N=3–6; without an out-of-sample larger-N check, the thermodynamic CF-fluid claim is not established.","rationale":"The reader's verdict was CONDITIONAL, and my independent read agrees that conditional acceptance is the right disposition. The reader's weakest_assumption focused on the heuristic zero-to-electron assignment. That is a real weakness, and the paper itself documents the ambiguity at λ=1 (outer zeros meander and become comparable to the 5th-nearest zero). But the CFF overlap in Table I, which is the strongest quantitative support for the CF-fluid claim, does not depend on the zero-assignment heuristic. The more load-bearing weakness is that the 'almost perfect' agreement is obtained by fitting λ_opt separately at each N on the same system, and the evidence stops at N=6. The fixed-λ=1 overlaps are much less impressive and already trend downward with N. Therefore, without a larger-N out-of-sample check, the paper's thermodynamic conclusion is overreaching. This does not invalidate the variational construction, nor does it require changing the conditional verdict; it sharpens the specific test that would move the verdict: compute overlaps at N≥7 with a fixed λ. The zero-assignment concern remains relevant for the ζ order-parameter part of the paper and should be addressed with a cluster-robust assignment, but it is secondary to the predictive-status concern for the headline claim.","tokens_in":14604,"tokens_out":10365,"duration_ms":127277,"concrete_test":"Compute the exact disk-geometry ν=1/5 Coulomb ground state at N=7 (and N=8 if numerically accessible) in the same angular-momentum sector used in Table I, and compute the CFF overlap at both λ=1 and the extrapolated λ_opt≈1.09 using variational Monte Carlo for the flux-attached wave function. If O(λ≈1.09) at N=7 is not substantially larger than O(λ=1), or if it drops well below the N=6 value of 0.986, then the 'almost perfect' agreement is a small-system fitting artifact rather than evidence for a robust CF-fluid thermodynamic description.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative support for the CF-fluid conclusion is Table I. At each N, λ_opt is chosen to maximize the overlap on that same finite system, so the reported O_VCFF values (0.999988, 0.999131, 0.997742, 0.985935 for N=3–6) are in-sample variational maxima, not predictive agreements. The un-fitted CCFF overlaps decrease steadily (0.9957 → 0.8935), meaning the 'agrees almost perfectly' headline rests on the fitted parameter. The near-size-independence of λ_opt is encouraging, but a statement over four tiny systems does not establish the paper's concluding claim that the construction 'reveals the true thermodynamic nature at tiny sizes.' The overlap with the exact state is already decreasing with N, so the relevant question is whether the fitted improvement survives larger systems. A secondary weakness, explicitly visible in the authors' own Fig. 4(d) and Fig. S3(d), is that the zero-clustering input becomes ambiguous at λ=1: the two outer zeros 'meander around farther away' and become comparable in distance to the 5th-nearest zero, so the ζ comparison in Fig. 5 may depend on a fragile nearest-neighbor zero assignment. However, the overlap table is independent of that assignment; the more load-bearing issue is that the headline quantitative claim is an in-sample fit at N≤6 with no predictive larger-N test.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript develops a geometrical diagnostic for fractional quantum Hall states based on the complex ratio ζ = (z1 - z_e)/(z2 - z_e) between the two nearest non-Pauli zeros around a fixed electron. The authors show that in the ν=1/3 Laughlin phase the distribution of ζ peaks near -1, that this peak flattens at a V1-V3 transition at η_c≈0.4 in agreement with the closing of the ground-state gap, and that at ν=1/5 the Coulomb ground state exhibits a hierarchy in which only two vortices are tightly bound per electron. They then construct a composite-fermion fluid trial state Ψ_CFF = ∏(z_i-z_j)^2 Ψ_{1/3,fluid}(λ) and report overlaps with the exact ν=1/5 Coulomb ground state that exceed the Laughlin overlap and are near unity when λ is tuned per system size.","tokens_in":14931,"tokens_out":5784,"duration_ms":66949,"significance":"If the central claim survives scrutiny, the zero displacement ratio would be a useful, computationally simple diagnostic for Laughlin-type order, and the CFF wave function at ν=1/5 would provide a physically motivated alternative to the CF crystal construction that has been the standard variational description at short distances. The manuscript's strongest evidence is partly parameter-free: the un-fitted CCFF overlaps in Table I exceed the Laughlin overlaps for all N=3-6, and the ζ distribution is raw wave-function data rather than a fit. The algebraic flux-attachment procedure allows exact overlaps for N≤6, and the near size-independence of λ_opt (1.088, 1.085, 1.083, 1.099) is encouraging. However, the load-bearing 'almost perfect' overlap claim is not parameter-free, and the zero-assignment ambiguity in the ν=1/5 regime weakens the interpretive part of the paper.","major_comments":[{"comment":"The 'almost perfect' agreement is an in-sample variational result. For each N, λ_opt is obtained by maximizing the overlap with the exact Coulomb ground state on that same system, so the O_VCFF column records optimized maxima rather than predictive agreements. The un-fitted CCFF overlaps (0.995733, 0.983465, 0.954991, 0.893517 for N=3-6) decrease steadily, which shows that the parameter-free part of the claim weakens with N. Please provide a predictive test: use a single fixed λ (for example the average λ_opt ≈ 1.09, or λ = 1) and report overlaps for all available N up to 7 or 8, or otherwise demonstrate that the fitted improvement is not merely an artifact of per-size optimization. Without this, the concluding statement that the CFF construction 'reveals the true thermodynamic nature at tiny sizes' is not supported.","section":"Composite-fermion fluids at ν=1/5, Table I"},{"comment":"The zero-to-electron assignment that underlies the 2CF claim is fragile at λ=1. Fig. S3(d) shows that the 3rd and 4th nearest zeros are no longer unambiguously closer than the 5th nearest zero, and the main text acknowledges that the outer zeros 'meander around farther away.' Because the ζ statistics for the 2CFs in Fig. 5 are computed from these assigned zeros, the conclusion that exactly two vortices are tightly bound may depend on the nearest-neighbor criterion. Please quantify the stability of the assignment, for example by testing alternative assignment rules, by tracking the fraction of configurations in which the nearest-neighbor ordering is ambiguous, or by showing that the ζ density maps are insensitive to the choice of the two 'next NN' zeros. If the assignment is not robust, the qualitative motivation for Eq. (3) should be softened.","section":"Supplement Sec. II and Fig. S3(d); main Fig. 4(d)"},{"comment":"The order-parameter claim is based on a single system size, N=6, on the torus. The kurtosis K drops at η_c≈0.4 and the gap closes at the same η_c, which is suggestive, but there is no finite-size scaling and no estimate of the uncertainty in the location of the kurtosis drop. Please show data for at least one or two other system sizes (for example N=4, 5, 7, or 8) or a finite-size extrapolation of the transition point. If this is not available, the text should be revised to call the kurtosis an indicative diagnostic rather than an order parameter.","section":"Evolution of zeros during the collapse of the ν=1/3 Laughlin phase, Fig. 3"},{"comment":"The comparison with the CF crystal construction of Ref. [34] is not quantitative. The text states that 'our CFF wave function at λ_opt shows consistently better overlaps for N=3-5,' but Table I does not include the corresponding CF crystal overlaps reported by Chang et al. Since this comparison is the basis for the claim that the fluid construction overcomes the short-distance competition between liquid and crystal orders, the CF crystal overlap values from Ref. [34] should be listed explicitly, or the claim should be rephrased as a qualitative statement.","section":"Composite-fermion fluids at ν=1/5"}],"minor_comments":[{"comment":"The abstract says the CFF state agrees almost perfectly for 3-5 electrons, while Table I reports N=3-6; please harmonize the wording (for example, '3-6 electrons').","section":"Abstract and Table I"},{"comment":"The phrase 'electron desity' should read 'electron density.'","section":"Supplement, Fig. S5 caption"},{"comment":"The text reports λ_opt = 1.091 ± 0.008 but Table I lists four values without uncertainties; please state explicitly how the mean and standard error are computed from the per-size values.","section":"Composite-fermion fluids at ν=1/5"},{"comment":"The kurtosis K is a functional of the distribution rather than a physical order parameter; consider using the term 'diagnostic' or 'indicator' in the caption and text to avoid confusion with Landau-type order parameters.","section":"Fig. 3(d)"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely publishable if the authors add a predictive overlap test with fixed or larger-N data and address the zero-assignment robustness concern. The current Table I overstates the case for 'almost perfect' agreement, but the underlying diagnostic is promising and the parameter-free CCFF overlap is a genuine result that should be preserved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this: the paper proposes a new statistical probe of zero clustering in FQH ground states, the zero displacement ratio ζ, and uses it to argue that the ν=1/5 Coulomb state is a 2CF fluid rather than a Laughlin state or CF crystal. The probe is good; the thermodynamic claim is not yet proven.\n\nThe genuinely new piece is Eq. (2): ζ = (z1 - ze)/(z2 - ze). The distribution of ζ in the Laughlin phase peaks at -1, and its kurtosis tracks the V1-V3 transition at η_c≈0.4, matching the closing of the gap. That is clean and internally consistent. The CFF construction Ψ_CFF = ∏(zi-zj)^2 Ψ_{1/3 fluid}(λ) is a reasonable variational idea, and the parameter-free version at λ=1 beats the Laughlin state for N=4-6, which is real progress.\n\nThe soft spot is the 'almost perfect' headline. Table I's O_VCFF values use λ_opt chosen to maximize overlap with the same exact ground state at each N. The un-fitted CCFF overlaps drop from 0.9957 at N=3 to 0.8935 at N=6. Four tiny systems with a fitted parameter do not establish that the CFF 'reveals the true thermodynamic nature at tiny sizes'—that's the authors' language, and it goes further than the data. The zero-assignment heuristic also looks fragile in the Coulomb case: the authors' own Fig. 4(d) and Fig. S3(d) show the outer zeros meandering so far that the 3rd/4th nearest zero distances become comparable to the 5th, so the ζ statistics for those zeros are not robust. That is a secondary concern, because the overlap table doesn't depend on that assignment. The paper also doesn't ship code or data, which would help others check the ED and zero-finding steps.\n\nWho it's for: anyone working on FQH variational wave functions or zero-structure diagnostics. The ζ diagnostic could be widely useful. The CFF construction is a thoughtful alternative to the CF crystal. It deserves a serious referee, with the expectation that the authors either go to larger N (spherical geometry or Monte Carlo) and separate fitted from predictive quantities, or tone down the thermodynamic conclusion.","headline":"New zero-displacement ratio is a solid diagnostic; the CFF wave function is promising but the 'almost perfect' overlap claim rests on a fitted parameter at N≤6.","tokens_in":15481,"tokens_out":3081,"would_cite":true,"duration_ms":33512,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["73.43.Cd","73.43.-f"],"model":"deepseek-v4-flash","headline":"The zero displacement ratio ζ diagnoses the Laughlin phase, and its statistics identify the ν=1/5 Coulomb ground state as a composite-fermion fluid at effective filling 1/3.","keywords":["fractional quantum Hall effect","zero displacement ratio","non-Pauli zeros","Laughlin state","composite fermion fluid","ν = 1/5","exact diagonalization","topological phase transition"],"falsifier":"Compute the overlap $O$ between $\\Psi_{\\mathrm{CFF}}$ built from the $\\nu^*=1/3$ parent at $\\lambda=\\lambda_{\\mathrm{opt}}$ and the exact $\\nu=1/5$ Coulomb ground state for $N=7$-$10$ in disk or spherical geometry; if $O$ falls below the overlap of the Laughlin state or of the composite-fermion crystal state as $N$ grows, the claim that the $\\nu=1/5$ state is a composite-fermion fluid rather than a crystal-tinged Laughlin state fails. A second check is the $\\zeta$ density map: if at larger $N$ the two-vortex-composite-fermion map no longer matches the $\\nu=1/3$ electron map, the geometrical argument for two-vortex binding is not robust.","tokens_in":14384,"feed_emoji":"🌀","tokens_out":13547,"duration_ms":132424,"temperature":0.7,"pith_summary":"Fractional quantum Hall wave functions are characterized by where their zeros sit: a Laughlin state at filling $1/m$ places $m$ zeros on each frozen electron, only one of which statistics requires, and the extra non-Pauli zeros encode the correlation. This paper proposes a complex zero displacement ratio $\\zeta$, the ratio of the displacements from an electron to its two nearest non-Pauli zeros, and argues that its statistical distribution acts as an order parameter for the Laughlin topological phase. In a transition driven by the $V_3$ pseudopotential, the sharp peak of $\\zeta$ near $-1$ flattens at the same coupling where the energy gap closes, so the ratio detects the collapse of Laughlin order. Applied to the Coulomb ground state at $\\nu=1/5$, the same statistics show that only two zeros bind tightly to each electron, forming two-vortex composite fermions at effective filling $1/3$; the resulting composite-fermion fluid wave function overlaps the exact ground state almost perfectly for 3-5 electrons. The result matters because it offers a geometric, wave-function-based measure of how close a realistic state is to a model fractional quantum Hall state, and it resolves the long-standing competition between liquid and crystal correlations at short distances.","feed_headline":"Zeros reveal ν=1/5 as a composite-fermion fluid","feed_subtitle":"A zero-displacement ratio tracks the Laughlin phase and matches the 1/5 Coulomb state almost perfectly for 3-5 electrons.","key_machinery":"The central object is the zero displacement ratio $\\zeta = (z_1 - z_e)/(z_2 - z_e)$, a complex number comparing the displacements from an electron at $z_e$ to its two nearest non-Pauli zeros. The non-Pauli zeros are the $m-1$ extra zeros, beyond the one required by the Pauli principle, that a Laughlin wave function at filling $1/m$ places at each frozen electron; they are the carriers of correlation. The ratio is bounded by the unit circle, with $|\\zeta|=1$ meaning the two zeros are equidistant from the electron, $\\zeta=-1$ meaning they sit diametrically opposite (the Laughlin hallmark), and $\\zeta=1$ avoided because zeros repel each other. The machinery is statistical: the paper accumulates $\\zeta$ over thousands of randomly fixed electron configurations, plots its density, and tracks the argument distribution $P(\\phi)$ and its kurtosis as an order parameter. For $\\nu=1/5$, the ratio is generalized to $\\zeta_{ij}$ for the $i$-th and $j$-th nearest zeros, and the construction $\\Psi_{\\mathrm{CFF}} = \\prod_{i<j}(z_i-z_j)^2\\,\\Psi_{1/3\\,\\mathrm{fluid}}(\\lambda)$ is the wave-function ansatz whose parent state is tuned near the $\\nu^*=1/3$ transition so that short-range crystalline correlations complement the liquid.","core_discovery":"The paper's central discovery is that the geometry of non-Pauli zeros around individual electrons is a quantitative diagnostic of topological order in fractional quantum Hall states. Concretely, it defines $\\zeta = (z_1 - z_e)/(z_2 - z_e)$ for each electron, where $z_1$ and $z_2$ are the two nearest non-Pauli zeros; in a Laughlin-like state the two zeros sit nearly opposite one another, giving a sharp peak near $\\zeta = -1$, whereas repulsion between zeros and electrons keeps the ratio away from $0$ and $1$. On the torus, as the $V_3$ pseudopotential is switched on against $V_1$, the argument distribution $P(\\phi)$ changes from a sharp peak at $\\phi=\\pi$ to a flat plateau at $\\eta_c\\approx 0.4$, and its kurtosis drops to about $2$, matching the closure of the ground-state energy gap; the paper reads this as the $\\zeta$ statistics functioning as an order parameter for the collapse of the $\\nu=1/3$ Laughlin phase. At $\\nu=1/5$, the pure Coulomb ground state does not bind four zeros per electron in the Laughlin square pattern; instead two zeros bind tightly while the outer two meander, indicating composite fermions carrying two vortices at effective filling $\\nu^*=1/3$. Defining $\\Psi_{\\mathrm{CFF}} = \\prod_{i<j}(z_i-z_j)^2\\,\\Psi_{1/3\\,\\mathrm{fluid}}(\\lambda)$, with the parent fluid taken at a mixing parameter $\\lambda_{\\mathrm{opt}}\\approx 1.09$, the overlap with the exact $\\nu=1/5$ Coulomb ground state reaches $0.999988$, $0.999131$, $0.997742$, and $0.985935$ for $N=3,4,5,6$, uniformly better than the model Laughlin wave function and better than the artificial crystallite-embedded composite-fermion crystal for $N=3$-$5$. The $\\zeta$ density map for these two-vortex composite fermions closely resembles that of electrons at $\\nu=1/3$, which the paper takes as direct evidence that the $\\nu=1/5$ Coulomb state is a composite-fermion fluid.","pith_inferences":["At larger $N$ or on different geometries the nearest-neighbor assignment used to define $\\zeta$ may become ambiguous because the two outer zeros in the $\\nu=1/5$ case can wander closer to a different electron; testing the order parameter there would show whether the assignment, not the physics, is what limits the method.","The fact that $\\lambda_{\\mathrm{opt}}\\approx 1.09$ sits just below the $\\nu^*=1/3$ parent transition suggests a general variational principle: realistic low-filling quantum Hall states inherit near-critical correlations from their parent state, and tuning the parent toward its own phase boundary is a tunable handle even when the final filling is deep in the liquid regime.","The same zero-clustering statistics could be applied to fractional Chern insulators, where there are no Landau levels and the meaning of zeros is less direct; if the $\\zeta$ signature survives there, it would supply a local wave-function diagnostic for topological order in lattice systems."],"forward_implications":["The $\\nu=1/5$ Coulomb ground state for $N=3$-$6$ electrons is better described as a fluid of two-vortex composite fermions at effective filling $1/3$ than as a Laughlin $1/5$ liquid or a crystallite-embedded composite-fermion crystal: the CFF overlap is $0.999988$, $0.999131$, $0.997742$, $0.985935$, versus $0.985392$, $0.947491$, $0.909861$, $0.842390$ for the Laughlin state.","The zero displacement ratio can serve as an order parameter: on the torus the kurtosis of $P(\\phi)$ drops from its Laughlin value to about $2$ at $\\eta_c\\approx 0.4$, the same coupling at which the ground-state energy gap closes, marking the collapse of Laughlin order into a charge-ordered phase.","A generalized ratio $\\zeta_{ij}$ shows that at $\\nu=1/5$ the four zeros per electron do not form the Laughlin square pattern under Coulomb interaction; only two zeros bind tightly, so the picture of four evenly bound zeros is not the right zeroth-order description.","The CFF construction with $\\lambda$ tuned near the $\\nu^*=1/3$ parent transition provides a variational family that captures the crystalline correlations present in the short-distance Coulomb ground state without explicitly embedding a lattice.","The near-perfect agreement at $N=3$-$5$ suggests the composite-fermion-fluid description, not the composite-fermion-crystal mixture, already reveals the thermodynamic nature of the $\\nu=1/5$ state at tiny sizes."],"supporting_citations":[{"why":"supplies the model many-body wave function at filling $1/m$ whose zero structure is the starting point.","marker":"[1]"},{"why":"provides the pseudopotential framework that defines the model Hamiltonians $H_0$ used throughout.","marker":"[2]"},{"why":"establishes that at filling $1/m$ a frozen electron sees $m$ zeros, one Pauli and the rest non-Pauli, the distinction the analysis relies on.","marker":"[3]"},{"why":"introduces composite fermions as electrons binding an even number of vortices, the picture behind the two-vortex binding at $\\nu=1/5$.","marker":"[4]"},{"why":"provides the geometrical description of quantum Hall states through a metric, the conceptual background for reading zero-cluster geometry as physics.","marker":"[13]"},{"why":"supplies model anisotropic wave functions whose zero structure evolves continuously, the precedent for using zero displacement ratios to locate transitions.","marker":"[14]"},{"why":"defines the $V_1$-$V_3$ pseudopotential competition and locates the transition of the $\\nu^*=1/3$ parent state used to select $\\lambda_{\\mathrm{opt}}$.","marker":"[20]"},{"why":"provides the level-spacing ratio in disordered interacting systems that inspired the definition of the complex zero displacement ratio.","marker":"[21]"},{"why":"contains the detailed evolution of ratio distributions and the construction details of the composite-fermion fluid wave function.","marker":"[23]"},{"why":"constructs the composite-fermion crystal with a crystallite parent, the comparison baseline whose overlap the CFF state surpasses for $N=3$-$5$.","marker":"[34]"}],"fun_headline_variants":["Zero-displacement ratio orders FQH phase collapse","Two-vortex composite fermions match ν=1/5 Coulomb state","Geometry of zeros reveals ν=1/5 as composite-fermion fluid","A single zero ratio tracks Laughlin phase to trivial"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the two nearest non-Pauli zeros around each electron can be unambiguously identified as belonging to that electron; in the $\\nu=1/5$ Coulomb case the two outer zeros can wander so far that they come closer to a different electron, so the $\\zeta$ statistics and the composite-fermion-fluid comparison depend on that nearest-neighbor assignment.","fun_headline_variants_meta":{"raw":{"variants":["Zero-displacement ratio orders FQH phase collapse","Two-vortex composite fermions match ν=1/5 Coulomb state","Geometry of zeros reveals ν=1/5 as composite-fermion fluid","A single zero ratio tracks Laughlin phase to trivial"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000711,"raw_usage":{"total_tokens":3311,"prompt_tokens":1166,"completion_tokens":2145,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":782,"completion_tokens_details":{"reasoning_tokens":2073}},"tokens_in":782,"tokens_out":2145,"duration_ms":23768,"temperature":1.0,"reasoning_tokens":2073,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:43:29.746346+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the overlap $O$ between $\\Psi_{\\mathrm{CFF}}$ built from the $\\nu^*=1/3$ parent at $\\lambda=\\lambda_{\\mathrm{opt}}$ and the exact $\\nu=1/5$ Coulomb ground state for $N=7$-$10$ in disk or spherical geometry; if $O$ falls below the overlap of the Laughlin state or of the composite-fermion crystal state as $N$ grows, the claim that the $\\nu=1/5$ state is a composite-fermion fluid rather than a crystal-tinged Laughlin state fails. A second check is the $\\zeta$ density map: if at larger $N$ the two-vortex-composite-fermion map no longer matches the $\\nu=1/3$ electron map, the geometrical argument for two-vortex binding is not robust.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"establishes that at filling $1/m$ a frozen electron sees $m$ zeros, one Pauli and the rest non-Pauli, the distinction the analysis relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"introduces composite fermions as electrons binding an even number of vortices, the picture behind the two-vortex binding at $\\nu=1/5$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the geometrical description of quantum Hall states through a metric, the conceptual background for reading zero-cluster geometry as physics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the $V_1$-$V_3$ pseudopotential competition and locates the transition of the $\\nu^*=1/3$ parent state used to select $\\lambda_{\\mathrm{opt}}$."},{"cited_title":"Oganesyan and D","cited_arxiv_id":null,"evidence_quote":"provides the level-spacing ratio in disordered interacting systems that inspired the definition of the complex zero displacement ratio."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"contains the detailed evolution of ratio distributions and the construction details of the composite-fermion fluid wave function."},{"cited_title":"Chang, C","cited_arxiv_id":null,"evidence_quote":"constructs the composite-fermion crystal with a crystallite parent, the comparison baseline whose overlap the CFF state surpasses for $N=3$-$5$."}],"review_version":1}