{"id":"108775ea-8c4f-4b11-954d-e1057a533789","arxiv_id":"1908.00694","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The perpendicular diffusion coefficient in collisionless astrophysical plasmas follows from three heuristic rules, yielding a new collisionless Rechester-Rosenbluth limit and identifying the parameter a^2 as the squared ratio of the ultra-scale to the bendover scale.","lead":"This paper proposes a simple set of rules for how charged particles diffuse across magnetic field lines in astrophysical plasmas. It derives new formulas for the diffusion coefficient and explains an adjustable parameter that previous theories had to insert by hand.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section III C contains a factor-2 inconsistency in the derivation of Eq. (9), so the prefactor (and hence the a^2 explanation) is not actually fixed by the heuristic.","rationale":"The reader's weakest assumption points to Section III C and the role of L_K, which is in the right neighborhood. My review sharpens that concern: the two derivations in Section III C are mutually inconsistent by a factor of 2, and the second derivation relies on an unproven identification of the running diffusion coefficient at the threshold with the asymptotic diffusion coefficient. This matters because the paper's headline result — explaining a^2 — is linearly sensitive to the prefactor in Eq. (9). However, the paper explicitly frames itself as heuristic, acknowledges its limitations in Section III I and the concluding remarks, and the simulation comparisons in Figs. 1 and 2 are visually consistent with Eq. (9), though not quantitative enough to fix the prefactor independently. The reader's CONDITIONAL verdict therefore remains appropriate; my concern would strengthen the conditions attached to acceptance rather than change the categorical verdict. A numerical check against Eq. (2) would settle whether the threshold ansatz yields the claimed prefactor.","tokens_in":7314,"tokens_out":21796,"duration_ms":207527,"concrete_test":"Use the time-dependent UNLT equation (Eq. 2), the systematic theory that motivated the threshold condition, to compute the asymptotic perpendicular diffusion coefficient in the CLRR parameter regime (short parallel mean free path, two-component turbulence with dominant 2D modes). Solve Eq. (2) numerically for the same spectral parameters as in Section IV, then extract the late-time κ⊥ and fit the prefactor c in κ⊥ = c (κFL/ℓ⊥)^2 κ||. If c = 1, the heuristic's Eq. (9) is supported; if c = 2 or any other value, the central a^2 explanation is not derivable from the threshold ansatz, and the letter would need to specify the correct prefactor before claiming to explain a^2.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III C derives the central formula Eq. (9), κ⊥ ≈ (κFL/ℓ⊥)^2 κ||, in two ways, and the two derivations are not equivalent. The first uses κ⊥/κ|| = ⟨Δx^2⟩/⟨Δz^2⟩ = ℓ⊥^2/L_K^2 with κFL = ℓ⊥^2/L_K. But rule (3) states that transverse complexity becomes significant when ⟨Δx^2⟩ ≥ 2ℓ⊥^2. At the onset, ⟨Δx^2⟩ = 2ℓ⊥^2, so the MSD ratio is 2ℓ⊥^2/L_K^2, and consistent algebra gives κ⊥ = 2(κFL/ℓ⊥)^2 κ||, a factor of 2 above Eq. (9). The second derivation instead sets the running subdiffusion coefficient d⊥(t_d) = κFL√(κ||/2t_d) equal to the final κ⊥ and reproduces Eq. (9), but this identifies the instantaneous running coefficient at the transition with the asymptotic diffusion coefficient — an assumption that is not derived; a subdiffusive precursor can leave an offset in ⟨Δx^2⟩, so the relation between d⊥(t_d) and the late-time κ⊥ is not fixed by the stated rules. The heuristic therefore does not actually pin down the prefactor in the CLRR limit. Because Eq. (15) and the claimed explanation a^2 = (s-1)/(q-1) inherit this prefactor linearly, an unresolved factor of 2 changes the predicted a^2 from 1/3 to 2/3 for the standard spectrum (s = 5/3, q = 3). The paper's own statement that these are heuristic arguments and lack general accuracy does not remove the need for the prefactor to be determined before a^2 can be said to be explained.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a heuristic theory of perpendicular diffusion for energetic particles moving collisionlessly in turbulent magnetic fields. Three rules are stated: perpendicular transport is governed by parallel transport, field-line random walk, and transverse complexity; the relevant turbulence scales are finite; and normal diffusion is restored when the transverse displacement satisfies <(Δx)^2> >= 2 ℓ_perp^2 (Eq. (3)). From these rules the author derives several asymptotic limits, the most important being the collisionless Rechester-Rosenbluth (CLRR) limit, Eq. (9), κ_perp ≈ (κ_FL/ℓ_perp)^2 κ_par. A composite formula Eq. (20) interpolates between the CLRR and field-line-random-walk limits. The paper then identifies the previously empirical factor a^2 in UNLT theory as a^2 = (L_U/ℓ_perp)^2, which for the Shalchi-Weinhorst spectrum gives a^2 = (s-1)/(q-1) and hence a^2 = 1/3 for s=5/3, q=3. Comparisons with test-particle simulations for two turbulence models are shown in Figs. 1 and 2. The text explicitly states that the heuristic cannot substitute for systematic theories.","tokens_in":7803,"tokens_out":8088,"duration_ms":78830,"significance":"If the central formula survives scrutiny, the paper would supply a simple physical interpretation of the parameter a^2 and establish a collisionless analogue of Rechester-Rosenbluth diffusion, a result of genuine interest for cosmic-ray transport in the heliosphere and beyond. The paper's strengths are its explicit derivation from stated rules, the use of no fitted parameters in the a^2 explanation, the transparent comparison with two sets of simulations, and its clear acknowledgment of the heuristic character of the arguments. However, the central quantitative prediction and the a^2 explanation depend on a prefactor that is not fixed by the rules and on an auxiliary relation that is not independently justified. The result is therefore potentially important but, in its current form, not fully established.","major_comments":[{"comment":"The two derivations of the CLRR limit are not equivalent. The first derivation uses κ⊥/κ∥ = ⟨Δx²⟩/⟨Δz²⟩ = ℓ⊥²/L_K² with κ_FL = ℓ⊥²/L_K. However, Rule 3 fixes the onset by ⟨Δx²⟩ = 2ℓ⊥², so the same algebra gives κ⊥ = 2(κ_FL/ℓ⊥)²κ∥. The second derivation instead sets the running subdiffusion coefficient d⊥(t_d) = κ_FL√(κ∥/2t_d) equal to the final κ⊥, which reproduces Eq. (9) but assumes without proof that the instantaneous running coefficient at the transition equals the asymptotic diffusion coefficient. Since a subdiffusive precursor can leave a residual offset, the prefactor of Eq. (9) is not determined by the stated rules. Because Eq. (15) and the identification a² = (s-1)/(q-1) inherit this prefactor linearly, the claimed explanation a² = 1/3 could become a² = 2/3 if the factor 2 is included. The heuristic must be modified to determine the prefactor from a stated rule.","section":"§III C, Eq. (9)"},{"comment":"The relation κ_FL = ℓ⊥²/L_K is used to eliminate L_K, but it is not a consequence of Rule 3. The rule fixes only the parallel distance at which the MSD satisfies ⟨Δx²⟩ = 2ℓ⊥²; it says nothing about whether the field-line random walk has already attained its asymptotic diffusive regime at that distance. Using the asymptotic κ_FL in κ_FL = ⟨Δx²⟩/(2|z|) at the onset therefore presupposes that the field lines are diffusive at the Kolmogorov scale, which is precisely the kind of statement the heuristic needs to establish. If this relation is instead intended as a separate postulate, it should be stated as such and its consequences for the numerical prefactor should be worked out. Without this step, the transition from the qualitative threshold to the quantitative Eq. (9) is incomplete.","section":"§III C"},{"comment":"The simulation comparisons do not currently provide a test of the prefactor in Eq. (9). In both figures the CLRR limit is shown as an asymptotic dashed line without uncertainty bands, and in Fig. 2 the two UNLT curves (a²=1/3 and a²=1) differ by a factor of three, so a factor of two in the CLRR prefactor could easily be hidden in the scatter. Please compare the CLRR and composite predictions against the statistical uncertainty of the simulation data, or state the uncertainty in the simulation points. Such a comparison is necessary to support the claim that the heuristic actually explains the numerical value a²=1/3 rather than merely being consistent with a range of values.","section":"§IV, Figs. 1-2"}],"minor_comments":[{"comment":"The phrase 'In principle this could be a different scale such as the integral scale L⊥' acknowledges ambiguity, but the choice ℓ⊥ is then used for all subsequent formulas; please state what evidence from UNLT or simulations fixes this choice.","section":"§II, Rule 3"},{"comment":"The composite formula is presented as 'chosen so that' it has the two limits, but the interpolation coefficients (9/16 and 8/3 inside the square root) are not derived from the heuristic. Please label Eq. (20) as an interpolation formula and note that it does not contain the fluid limit.","section":"§III H, Eq. (20)"},{"comment":"Cases 7 and 8 are marked 'Only for small Kubo numbers' in the UNLT column, but Section III G states that similar reasoning applies for large Kubo numbers. Please clarify the intended domain of validity of the CLRR row.","section":"Table I"},{"comment":"The label 'a2 = 1/3, 1' should identify which of the two solid lines corresponds to which value.","section":"Fig. 2 caption"},{"comment":"The text contains many ligature/OCR artifacts (e.g., 'diffusion', 'v2'); please ensure the production version is clean.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is a compact single-author letter. The prefactor inconsistency in Section III C is the main technical concern; if the author can fix the factor of 2 or justify the second derivation, the paper may become acceptable. The editor may want a specialist in stochastic transport to check the validity of equating the running and asymptotic diffusion coefficients at the transition. The novelty of the CLRR result relative to Rechester-Rosenbluth and prior UNLT literature should also be checked carefully."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: the paper is a useful, honest heuristic, and the collisionless Rechester-Rosenbluth limit plus the a^2 = (L_U/ell_perp)^2 identification are genuinely new. But the central prefactor does not actually come out of the argument. There is a factor-2 inconsistency between the two derivations of Eq. (9), so the claim to have explained a^2 = 1/3 is not yet supported.\n\nWhat is good: the three-rule framework is clean and organizes the eight cases in Table I effectively. The CLRR limit and its Kubo-number sub-limits are new in the collisionless context, and the composite formula (20) is a sensible interpolating tool. The paper is candid: it states the rules are heuristics, notes the slab and 2D exceptions, and says it cannot substitute systematic theory. Those limitations are real but they are not hidden.\n\nThe soft spot is real and load-bearing. In Section III C the author first writes kappa_perp/kappa_parallel = ell_perp^2/L_K^2. But Rule (3) says the transition happens when <(Delta x)^2> = 2 ell_perp^2, so the ratio at onset should be 2 ell_perp^2/L_K^2. The second derivation, which equates the running subdiffusion coefficient to kappa_perp at t_d, does give Eq. (9) without the factor 2, but that identification is assumed, not derived; a subdiffusive precursor can leave a different offset. The two derivations cannot both be right, and nothing in the heuristic fixes the prefactor. Because Eq. (15) and the a^2 comparison inherit that prefactor linearly, the standard-spectrum prediction is ambiguous between 1/3 and 2/3. The author's caveat that heuristics lack general accuracy does not close that gap.\n\nThe simulation comparisons are visual, so they do not arbitrate the prefactor either. On the citation pattern: the paper builds on the author's own UNLT line, but that is the natural literature to use here, and the relevant external references (Rechester-Rosenbluth, Krommes, Matthaeus) are present.\n\nWho it is for: anyone doing transport modeling in heliospheric or astrophysical plasmas will find the asymptotic limits and the composite formula convenient. Whether the a^2 explanation is right is now an open question rather than a settled point.\n\nMy recommendation: send it to peer review. The heuristic deserves referee time, and the prefactor issue is exactly what referees should catch. I would not cite it in my own work until the prefactor is resolved, but I would bring it to reading group.","headline":"Plausible new heuristic for perpendicular diffusion, but a factor-2 inconsistency in the derivation of the central CLRR formula leaves the a^2 explanation unfixed.","tokens_in":8237,"tokens_out":5306,"would_cite":false,"duration_ms":47083,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["47.27.tb","96.50.Ci","96.50.Bh"],"model":"deepseek-v4-flash","headline":"The paper proposes that perpendicular transport of energetic particles in a turbulent magnetized plasma is controlled by just three effects: motion along the mean field, random walk of magnetic field lines, and transverse complexity.","keywords":["perpendicular diffusion","energetic particles","turbulent magnetic fields","collisionless Rechester-Rosenbluth limit","field line random walk","transverse complexity","Kolmogorov length","ultra-scale"],"falsifier":"Run test-particle simulations in two-component turbulence with a known bendover scale $\\ell_\\perp$, measure the field-line diffusion coefficient $\\kappa_{FL}$ and the parallel diffusion coefficient $\\kappa_\\parallel$, and check whether the perpendicular diffusion coefficient in the short-mean-free-path regime satisfies $\\kappa_\\perp/\\kappa_\\parallel = (\\kappa_{FL}/\\ell_\\perp)^2$; if the measured ratio instead follows the fluid limit $(\\delta B_x/B_0)^2$ with a different prefactor, the central claim is falsified.","tokens_in":7136,"feed_emoji":"🧲","tokens_out":7848,"duration_ms":69965,"temperature":0.7,"pith_summary":"The paper proposes that perpendicular transport of energetic particles in a turbulent magnetized plasma is controlled by just three effects: motion along the mean field, random walk of magnetic field lines, and transverse complexity. It claims that normal perpendicular diffusion appears only once a particle has wandered far enough sideways to leave its original field line, and that the diffusion coefficient at that moment is set by whichever transport regime the parallel and field-line motions have reached. From this heuristic it derives a collisionless version of the Rechester-Rosenbluth limit, $\\kappa_\\perp \\approx (\\kappa_{FL}/\\ell_\\perp)^2 \\kappa_\\parallel$. It also identifies the fitted parameter $a^2$ used in previous non-linear theories with $(L_U/\\ell_\\perp)^2 = (s-1)/(q-1)$, explaining why $a^2 = 1/3$ is needed for standard spectral indices. If correct, the result turns an adjustable parameter into a spectral prediction and changes the predicted perpendicular mean free path in certain regimes.","feed_headline":"Cosmic-ray sideways spread traced to field-line wandering","feed_subtitle":"The fit factor a²=1/3 is explained by turbulence spectral indices, replacing a fudge factor with a prediction.","key_machinery":"The central object is the threshold condition $\\langle (\\Delta x)^2 \\rangle \\ge 2\\ell_\\perp^2$, marking the onset of transverse complexity, i.e. the scale at which a particle can no longer be treated as tied to a single magnetic field line. Around this threshold the paper constructs a case table of eight combinations of ballistic or diffusive parallel motion with ballistic or diffusive field-line random walk; the normal-diffusion endpoints are the field-line random walk limit $\\kappa_\\perp = (v/2)\\kappa_{FL}$ and the collisionless Rechester-Rosenbluth limit $\\kappa_\\perp = (\\kappa_{FL}/\\ell_\\perp)^2 \\kappa_\\parallel$. The heuristic rule that carries the argument is that the final diffusion coefficient is determined by whichever transport regime is active when the threshold is crossed, and the quantitative link to spectral parameters comes from the ultra-scale identity $L_U = \\sqrt{(s-1)/(q-1)}\\,\\ell_\\perp$ for two-component 2D-dominated turbulence.","core_discovery":"The central claim is that the perpendicular diffusion coefficient is fixed by the state of parallel and field-line transport at the moment transverse complexity first becomes significant, meaning $\\langle (\\Delta x)^2 \\rangle \\ge 2\\ell_\\perp^2$. Combining that threshold with diffusive parallel motion and diffusive field-line random walk gives $\\kappa_\\perp \\approx (\\kappa_{FL}/\\ell_\\perp)^2 \\kappa_\\parallel$, the collisionless Rechester-Rosenbluth limit, with the Kolmogorov length satisfying $\\kappa_{FL} = \\ell_\\perp^2/L_K$. For two-component turbulence dominated by 2D modes, the paper uses the field-line diffusion coefficient in the large-Kubo-number limit together with the ultra-scale formula $L_U = \\sqrt{(s-1)/(q-1)}\\,\\ell_\\perp$ to obtain $a^2 = (L_U/\\ell_\\perp)^2 = (s-1)/(q-1)$; with $s = 5/3$ and $q = 3$, this is exactly $a^2 = 1/3$, the value earlier theories had to insert by hand to match simulations. The heuristic therefore claims to explain the previously empirical factor $a^2$ as a consequence of the turbulence spectrum.","pith_inferences":["If the identification $a^2 = (s-1)/(q-1)$ holds, measurements of perpendicular diffusion at different particle energies could be used to infer the inertial-range and energy-range spectral indices of the ambient turbulence, turning transport observations into a turbulence diagnostic.","The same threshold argument may transfer to other problems where particles decorrelate from magnetic field lines, such as cosmic-ray transport in the interstellar medium or energetic electron transport in fusion devices, provided the relevant field-line diffusion coefficient is replaced appropriately.","A direct test of the threshold picture would be to measure the running perpendicular diffusion coefficient at intermediate times: the heuristic predicts a subdiffusive $d_\\perp(t) \\sim t^{-1/2}$ plateau before normal diffusion is restored in the collisionless Rechester-Rosenbluth regime.","The paper leaves the large-Kubo-number discrepancy with systematic theory open; if the collisionless Rechester-Rosenbluth interpretation is correct, the missing ingredient is likely a first-principles derivation of the field-line diffusion coefficient at high Kubo numbers rather than another fitted factor."],"forward_implications":["In the short-parallel-mean-free-path, small-Kubo-number regime, perpendicular diffusion is predicted to scale as $(L_\\parallel/\\ell_\\perp)^2 (\\delta B_x/B_0)^4 \\kappa_\\parallel$ rather than the fluid limit $(\\delta B_x/B_0)^2 \\kappa_\\parallel$.","The parameter $a^2$ in non-linear transport theories is no longer free: for two-component 2D-dominated turbulence it equals $(s-1)/(q-1)$, so the common value $a^2 = 1/3$ follows from the spectral indices $s=5/3$, $q=3$.","The composite formula for the perpendicular mean free path interpolates between the collisionless Rechester-Rosenbluth limit at short parallel mean free paths and the field-line random walk limit at long parallel mean free paths.","For slab turbulence the threshold condition is never met, so the final state remains compound subdiffusion rather than normal perpendicular diffusion.","Comparisons with existing test-particle simulations for two-component and critical-balance turbulence are consistent with the predicted asymptotic limits and the composite interpolation."],"supporting_citations":[{"why":"Supplies the original resistive Rechester-Rosenbluth formula that the paper's collisionless version generalizes.","marker":"[12]"},{"why":"Provides the Kolmogorov-Lyapunov length concept and the equivalent form of the transport coefficient in Eq. (10).","marker":"[6]"},{"why":"Introduces the unified non-linear transport theory whose diffusive form contains the parameter $a^2$.","marker":"[16]"},{"why":"Derives the time-dependent UNLT equation whose exponential factor motivates the threshold condition $\\langle (\\Delta x)^2 \\rangle \\ge 2\\ell_\\perp^2$.","marker":"[19]"},{"why":"Documents the earlier need for $a^2 = 1/3$ to match simulations, the discrepancy this paper aims to explain.","marker":"[9]"},{"why":"Gives the ultra-scale formula $L_U = \\sqrt{(s-1)/(q-1)}\\,\\ell_\\perp$ used to derive $a^2$.","marker":"[15]"},{"why":"Uses non-linear theory with the factor $a^2$ that the collisionless limit is compared against.","marker":"[14]"},{"why":"Provides another non-linear-theory form with $a^2$ that the new prediction replaces.","marker":"[21]"},{"why":"Supplies test-particle simulation data compared with the CLRR and composite formulas.","marker":"[20]"},{"why":"Defines the NRMHD turbulence model used in the simulation comparison showing agreement.","marker":"[13]"}],"fun_headline_variants":["Turbulence spectrum explains cosmic-ray diffusion fudge factor","a²=1/3 from turbulence, not by fitting","Cosmic-ray sideways spread traced to field-line wandering","Diffusion factor a²=1/3 derived from turbulence spectrum"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that at the moment a particle first strays far enough sideways to feel the turbulence's transverse complexity, the distance it has travelled along the mean magnetic field is a fixed length, and that this length is related to the field-line diffusion coefficient by exactly $\\kappa_{FL} = \\ell_\\perp^2/L_K$; the paper offers no independent derivation of that relation, and if it fails, the new formula and the explanation of $a^2$ do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Turbulence spectrum explains cosmic-ray diffusion fudge factor","a²=1/3 from turbulence, not by fitting","Cosmic-ray sideways spread traced to field-line wandering","Diffusion factor a²=1/3 derived from turbulence spectrum"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000526,"raw_usage":{"total_tokens":2496,"prompt_tokens":862,"completion_tokens":1634,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":478,"completion_tokens_details":{"reasoning_tokens":1565}},"tokens_in":478,"tokens_out":1634,"duration_ms":12400,"temperature":1.0,"reasoning_tokens":1565,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:37:10.182891+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run test-particle simulations in two-component turbulence with a known bendover scale $\\ell_\\perp$, measure the field-line diffusion coefficient $\\kappa_{FL}$ and the parallel diffusion coefficient $\\kappa_\\parallel$, and check whether the perpendicular diffusion coefficient in the short-mean-free-path regime satisfies $\\kappa_\\perp/\\kappa_\\parallel = (\\kappa_{FL}/\\ell_\\perp)^2$; if the measured ratio instead follows the fluid limit $(\\delta B_x/B_0)^2$ with a different prefactor, the central claim is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the original resistive Rechester-Rosenbluth formula that the paper's collisionless version generalizes."},{"cited_title":"& Shalchi, 2018, Ap&SS, 363, 116","cited_arxiv_id":null,"evidence_quote":"Provides the Kolmogorov-Lyapunov length concept and the equivalent form of the transport coefficient in Eq. (10)."},{"cited_title":"H., & Bieber, J","cited_arxiv_id":null,"evidence_quote":"Introduces the unified non-linear transport theory whose diffusive form contains the parameter $a^2$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the time-dependent UNLT equation whose exponential factor motivates the threshold condition $\\langle (\\Delta x)^2 \\rangle \\ge 2\\ell_\\perp^2$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the earlier need for $a^2 = 1/3$ to match simulations, the discrepancy this paper aims to explain."},{"cited_title":"H., Bieber, J","cited_arxiv_id":null,"evidence_quote":"Gives the ultra-scale formula $L_U = \\sqrt{(s-1)/(q-1)}\\,\\ell_\\perp$ used to derive $a^2$."},{"cited_title":"H., Qin, G., Bieber, J","cited_arxiv_id":null,"evidence_quote":"Uses non-linear theory with the factor $a^2$ that the collisionless limit is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides another non-linear-theory form with $a^2$ that the new prediction replaces."},{"cited_title":"& Weinhorst, B., 2009, AdSpR, 43, 1429","cited_arxiv_id":null,"evidence_quote":"Supplies test-particle simulation data compared with the CLRR and composite formulas."},{"cited_title":"W., Gray, P","cited_arxiv_id":null,"evidence_quote":"Defines the NRMHD turbulence model used in the simulation comparison showing agreement."}],"review_version":1}