{"id":"f3eddb97-e48e-4c48-92ac-775009bbd43c","arxiv_id":"2608.10536","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The XNOR spin current has Gaussian, half-normal, and M-Wright limits on t^(1/4) or t^(1/8) scales with explicitly derived amplitudes, supported by parameter-free simulations.","lead":"This paper predicts exact long-time fluctuation laws for spin current in a constrained one-dimensional hopping model, giving explicit amplitudes for three initial states. The predictions are tested without any fitted parameters in large simulations, but the full proof is deferred to an unverified AI-generated companion manuscript.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (32) uniform counting bound is the load-bearing step; the domain-wall seam is the least secure part, and its proof is deferred to the unverified AI companion [22].","rationale":"The paper's exact coordinate maps, the algebraic derivation of σ_m^2, and the parameter-free numerical comparisons give substantial support for the conjectures. The weak point is not the algebra or the amplitudes; it is the probabilistic estimate that converts the tracer displacement into the fixed-cut current. Equation (33) is the single step that all three conjectures need, and the relevant uniform bound on E_t is explicitly deferred to the AI-generated companion [22], which the author states has not been independently verified line-by-line and will not be peer-reviewed. The homogeneous cases are less risky because the spin measure remains product Bernoulli at all times, making ζ_y(t) i.i.d. at fixed t and the sup over intervals of order t^{1/4} a standard Donsker-type estimate. The domain-wall seam is the genuinely delicate part: the active-zero density is the same on both sides, but the field near the interface is not product, and the paper only asserts, rather than proves, that the seam contribution is o_P(t^{1/4}). The numerics do not settle this because the accessible residual decreases only slowly and the smaller-bias moment corrections remain at the 10-60% level. These considerations do not move the reader's verdict: CONDITIONAL remains appropriate, and the stress-test confirms rather than overturns the weakest-assumption analysis.","tokens_in":22427,"tokens_out":37334,"duration_ms":385083,"concrete_test":"Test the domain-wall reduction directly at t=2^18 (m=0.7, L=2048): compute E_t = N_t + δ Q_t - δ B from the measured tagged-zero quantities, following Eq. (31), for several thousand trajectories. Check whether the 95th percentile of |E_t|/t^{1/4} continues to decay (at t=1024 and t=65536 the paper's total reduction residual decreases from 0.128 to 0.073) rather than plateaus, and separately measure the sup over intervals of length up to C t^{1/4} of the centered active-zero field near the interface. If |E_t|/t^{1/4} plateaus, Eq. (33) and Conjecture 3.2 fail.","verdict_should_be":"UNCHANGED","load_bearing_attack":"All three conjectures rest on the same bridge: N_t = -δ Q_t + o_P(t^{1/4}) in Eq. (33). The error E_t in Eq. (32) is a density fluctuation over an interval whose endpoint A0(t) is the tracer position, of order t^{1/4}, and in the domain-wall case the interval can cross the expanding interface. The paper explicitly defers the uniform endpoint estimate to the AI-generated companion [22] (Sec. 1.2: no line-by-line verification; not peer-reviewed). This is not an internal contradiction, but it is the point where the derivation could fail. For homogeneous initial data the spin measure is reversible product Bernoulli, so ζ_y(t) is i.i.d. at fixed t and a sup bound gives E_t = O_P(t^{1/8}); the genuinely delicate case is the domain-wall seam, where the field is not product and the assertion is only that the seam contribution is o_P(t^{1/4}). Similarly, the zero-magnetization independence between S and Q̄_t relies on the coupling estimate Q_t - Q̄_t = O_P(1), also deferred. If any of these bounds fails, the corresponding conjecture loses its derivation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the fixed-cut spin current of the continuous-time stochastic XNOR process, in which a block abca with b≠c exchanges its middle spins at rate one, and formulates three conjectures with explicit amplitudes. For homogeneous Bernoulli initial data with 0<m<1, Conjecture 3.1 asserts t^{-1/4}J_hom(t) converges weakly to a centred Gaussian with variance σ²_m = 2m²(1-m²)/((3+m²)√π), together with convergence of all fixed moments; for a Bernoulli domain wall, Conjecture 3.2 asserts the half-normal limit H_m with the same scale; and for homogeneous data at m=0, Conjecture 3.3 asserts that t^{-1/8}J_hom(t) converges to the M-Wright law with scale a₀ = 1/(√6π^{1/4}), represented as B_{-G(0)/2} with G(0) independent of B. Section 4 derives the amplitudes through an exact chain of coordinate maps (spin → bond variables → zero-range gap variables → squeezed SSEP). The fixed-cut current is expressed through the displacement of a tagged SSEP hole via the reduction N_t = -δQ_t + o_P(t^{1/4}) (Eq. (33)), and the coefficients follow from the equilibrium geometric gap distribution (ρ = (1-m²)/(3+m²)) and the classical tagged-particle variance (2ρ/√π). Section 5 reports parameter-free simulations: Wasserstein distances decrease monotonically with time in all three settings, and the intermediate reductions (J_hom + mQ_t and N_t + Q_t/2 residuals) are checked directly. The proofs of the key uniform density-fluctuation estimate for E_t (Eq.","tokens_in":22654,"tokens_out":30065,"duration_ms":257560,"significance":"If the conjectures hold, the paper provides the first complete, model-specific full counting statistics for the continuous-time XNOR process: previous work [18,19,20] anticipated the t^{1/4}/t^{1/8} scales and the half-normal and M-Wright shapes, but not the amplitudes. The amplitudes are genuinely derived rather than fitted — σ²_m combines the equilibrium geometric gap parameter ρ with the classical SSEP tagged-particle variance, and a₀ follows from the same input at ρ=1/3, δ=1/2 — and all internal constants (variance, standardized kurtosis 3π/2, E|X₀|, E[X₀⁴]) are mutually consistent. The numerical strategy is a strength: it tests the conjectured laws parameter-free, checks the intermediate tracer reductions directly (Eqs. (44)–(45) and (51)), reports finite-volume controls, and clearly discloses the companion's unverified status. The main reservations are that the single reduction (33) on which all three conjectures rest depends on a uniform counting estimate deferred to an unverified document, and that the m=0.5 numerics converge markedly more slowly than at the other parameter values.","major_comments":[{"comment":"All three conjectures pass through the single reduction N_t = -δQ_t + o_P(t^{1/4}) in Eq. (33). The error term E_t in Eq. (32) is a density fluctuation over a contiguous interval whose endpoint A_0(t) is the random tracer position of order t^{1/4}; the text asserts |E_t| = O_P(t^{1/8}) in the homogeneous cases and an o_P(t^{1/4}) estimate for the domain-wall seam, and defers the proofs to companion [22]. Section 1.2 states that [22] is an AI-generated draft, not peer-reviewed, for which the author has not completed an independent line-by-line verification. Within the present manuscript, Eq. (33) is therefore an assumption rather than a derived statement, and the abstract's claim that the amplitudes are obtained 'starting from the microscopic XNOR dynamics' overstates the status of the derivation. The homogeneous-case bound appears provable with standard random-walk sup-fluctuation estimates (the active-zero field ζ_y(t) is i.i.d. at fixed t under the stationary product measure, and the tracer displacement is tight at scale t^{1/4} by the classical tagged-particle theorem), and I ask that it be supplied in an appendix. The domain-wall seam bound must then either be proved or explicitly labelled as a conjecture-level input, with the abstract and Section 4 reworded accordingly.","section":"§4.4, Eqs. (32)–(33)"},{"comment":"At the largest common time t=16384 the m=0.5 rows deviate from the parameter-free predictions far beyond Monte Carlo error: the homogeneous fourth moment is 0.02012 versus the predicted 0.01271 (roughly 18 standard errors from unity), the domain-wall second moment is 0.07606 versus 0.06510 (16.8% high), and 2.89% of the domain-wall currents retain negative sign. The trends in the reported time grid are decreasing, and the directly tested tracer reduction reproduces the predicted variance of Q_t/t^{1/4} very well (Eq. (45)), so slow finite-time convergence — the colour-sum fluctuation contributes relative corrections of order t^{-1/8} to t^{-1/4} — is the most plausible interpretation. Nevertheless, on the data shown the abstract's sentence that the simulations 'provide numerical support for all three conjectures' is stronger than the m=0.5 evidence warrants. I recommend extending the m=0.5 runs to longer times (the paper itself identifies this as the most useful further test) or, alternatively, adding a quantitative comparison of the observed overshoot with the expected finite-time corrections.","section":"§5.1, Table 1; §5.2, Table 3"},{"comment":"The fixed-moment convergence statements are part of the conjectures, and the paper tests them numerically, but the required uniform integrability estimates are also deferred to [22]. The numerical tables show that fourth-moment convergence is markedly slower than second-moment convergence in all three settings: Table 1 (m=0.5) gives a fourth-moment ratio of 1.58 at t=16384, and Table 6 shows the m=0 fourth moment at t=65536 still 8–15% below prediction for L=512 and L=1024. I recommend either providing the moment estimates (for the Gaussian cases at least, standard concentration arguments should suffice) or restating the conjectures as weak convergence plus the specific moments for which the numerics actually provide support.","section":"§3.1–3.3, Eqs. (12), (14), (18)"}],"minor_comments":[{"comment":"The captions of Figures 3 and 5 end with 'm = 0.284248'; the value 0.284248 is σ_{0.7} = sqrt(σ²_{0.7}), so the symbol should be σ, not m.","section":"§5.1, Fig. 3; §5.2, Fig. 5"},{"comment":"In the Conclusions, 'estabilishing' should be 'establishing'.","section":"§6"},{"comment":"The sentences describing the ensembles ('10,000, 20,000, and 10,000 trajectories, respectively') should state explicitly that these sample sizes correspond to m = 0.5, 0.7, 0.8 in that order; the current phrasing is ambiguous on first reading.","section":"§5.1 and §5.2, first paragraphs"},{"comment":"At the largest m=0 time the lattice spacing t^{-1/8} = 1/4 is the same order as the reported W1 distance (0.0627); a sentence explaining how the lattice discretisation is excluded from the W1 comparison would help the reader interpret the remaining distance.","section":"§5.3"},{"comment":"Given that the pivotal estimates of Section 4 are delegated to [22], the manuscript would benefit from identifying which numbered statements in [22] correspond to the uniform bound on E_t and to the bound Q_t - Q̄_t = O_P(1) used in Section 4.6, so that the dependency structure is checkable.","section":"§4.4, Ref. [22]"},{"comment":"The SSEP domain-wall fluctuation variance Σ²_{SSEP,dw}(m) is quoted without a pointer to the exact expression in Ref. [26]; a one-line indication would help the reader verify the formula.","section":"§3.4, Eq. (23)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest and the physics is very likely correct; I do not recommend rejection. My 'major revision' recommendation rests on two fixable points: the load-bearing uniform counting estimate behind Eq. (33) is not part of the peer-reviewed record, and the m=0.5 numerical support is weaker than the abstract claims. The editor may also wish to consider a policy point: the pivotal technical content of this submission is delegated to a companion explicitly excluded from peer review, which is unusual even for a conjectures paper; requiring the homogeneous-case estimate in an appendix would remove the main structural objection. The current disclosure of AI usage is exemplary and should be kept."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a genuinely useful paper, and the main reason to hesitate is exactly what the author flags himself. The new content is small but concrete: the explicit variance sigma_m^2 for homogeneous biased data, the zero-magnetization amplitude a0, and the extension of the charged single-file picture to homogeneous biased Bernoulli initial states. The coordinate maps from XNOR to zero-range process to tagged SSEP are exact and clearly presented; the order-statistic identity (30) is exact; and the parameter-free numerical tests are honest and show real convergence trends. Wasserstein distances decrease monotonically in all three settings, and the long m=0.7 run lands close to the predictions. That is genuine evidence, not curve fitting. Soft spots, in order of importance. First, the load-bearing uniform counting estimate in Eqs. (32)-(33) is asserted and deferred to companion [22], which is AI-generated, not verified line-by-line by the author, and will not be peer-reviewed. The paper states this plainly, and I do not read it as concealment. But it means the three conjectures are not yet derived. They are well-motivated conjectures with strong numerical support. If that uniform endpoint bound fails, the reduction N_t = -delta Q_t + o_P(t^{1/4}) breaks and all three conjectures lose their derivation. Second, the numerics at m=0.5 still show a second moment about 16.6% above prediction and fourth moment about 58% above at t=16384; the trends are decreasing but cannot exclude persistent corrections. Third, no code or data are shipped, only available on request. For a paper whose main evidence is simulation, that is an unnecessary obstacle. Fourth, the zero-magnetization test still has lattice spacing t^{-1/8} = 1/4 at the largest time, and fourth-moment precision is limited; the finite-volume checks look fine. The citation pattern is fair. Earlier work on shapes and exponents is credited, including Gopalakrishnan et al. for the half-normal and M-Wright anticipations. I do not see fitted parameters, circularity, or overclaiming. The main risk is the companion proof, and the author says so. Who this is for: people working on full counting statistics, single-file universality, and kinetically constrained models. It deserves a serious referee, not a desk reject. I would send it to review with the expectation that the referee checks the reduction carefully, asks for code and data, and treats the companion as unverified. I would also bring it to reading group; the physics is worth the time.","headline":"Honest, useful paper: the new amplitudes are concrete and the exact maps to SSEP are clean, but the load-bearing uniform counting estimate is deferred to an unverified AI companion, so the results are well-supported conjectures rather than a completed derivation.","tokens_in":716,"tokens_out":1142,"would_cite":true,"duration_ms":23429,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C22","60K35","60F05"],"pacs":["05.40.-a","05.60.-k"],"model":"deepseek-v4-flash","headline":"The paper conjectures exact long-time laws for spin-current fluctuations in the stochastic XNOR model: Gaussian on the $t^{1/4}$ scale, half-normal for domain walls, and an M-Wright law on the $t^{1/8}$ scale at zero magnetization.","keywords":["stochastic XNOR process","anomalous current fluctuations","full counting statistics","single-file diffusion","tagged particle in SSEP","M-Wright distribution","half-normal law","kinetically constrained hopping"],"falsifier":"Measure the residual $E_t$ from Eq. (32) in a simulation that also records the tagged zero-bond displacement: for homogeneous $0<m<1$ and for the domain wall, the ratio $|E_t|\\,t^{-1/4}$ should converge to zero in probability. If instead it stays bounded away from zero, the identity $N_t = -\\delta Q_t + o_P(t^{1/4})$ fails and all three conjectures lose their derivation. Independently, at $m=0.5$ the ratio $\\mathbb{E}[(t^{-1/4}J_{\\rm hom}(t))^2]/\\sigma_m^2$ should approach 1; the paper's own data show it about 16.6% above the target at $t=16384$, so longer runs with $L\\ge1024$ to $t\\gtrsim 10^5$ would settle whether the amplitude is correct.","tokens_in":22148,"feed_emoji":"📊","tokens_out":11093,"duration_ms":92162,"temperature":0.7,"pith_summary":"The paper aims to pin down the exact long-time distribution of the spin current through a fixed cut in the stochastic XNOR hopping model, a one-dimensional kinetically constrained dynamics where exchanges happen only when the two outer spins of a four-site block agree. It formulates three conjectures with explicit amplitudes: a Gaussian limit on the $t^{1/4}$ scale for a homogeneous magnetized state, a half-normal limit on the same scale for a domain-wall state, and an M-Wright limit on the $t^{1/8}$ scale for a homogeneous zero-magnetization state. The conjectures are derived from an exact sequence of coordinate transformations that converts XNOR dynamics into the motion of a tagged tracer in the symmetric simple exclusion process (SSEP), with the spin current emerging as a signed sum over the conserved equal-spin pairs swept past the cut. Parameter-free simulations support all three distributions. If correct, this gives the complete full counting statistics for a continuous-time constrained transport model and sharpens the contrast with ordinary SSEP, which stays Gaussian at zero magnetization.","feed_headline":"XNOR current fluctuations pinned to exact distribution laws","feed_subtitle":"Coordinate mapping to tracer motion in SSEP gives Gaussian, half-normal, and M-Wright limits with no fitted parameters.","key_machinery":"The load-bearing construction is an exact coordinate change. In bond variables $d_j = \\mathbf{1}\\{\\eta_j \\ne \\eta_{j+1}\\}$, the allowed XNOR move becomes $011 \\leftrightarrow 110$, so zero bonds (equal-spin pairs) are conserved, non-overtaking objects that move through runs of $11$ pairs. Counting complete $11$ pairs between zero bonds gives gap occupations $\\xi_i$ with a product geometric stationary law evolving as a constant-rate zero-range process; squeezing each $11$ rod to a point maps the system to SSEP, with each zero bond a labelled hole. The tagged-hole displacement $Q_t$ obeys the classical $t^{1/4}$ Gaussian limit. An order-statistic identity converts $Q_t$ into the active-zero current $N_t$ across the cut via $N_t = -\\delta Q_t + o_P(t^{1/4})$, and colour decoration then produces the three laws: multiplying by the mean colour $\\delta\\vartheta_m = m$ gives the Gaussian, folding through the absolute value gives the half-normal, and summing an independent fair colour random walk over the random block $|N_t|$ gives the Brownian-time M-Wright law.","core_discovery":"The paper's central claim is that for the continuous-time stochastic XNOR process started from a homogeneous Bernoulli measure with magnetization $m \\in (0,1)$, the rescaled current $t^{-1/4}J_{\\rm hom}(t)$ converges weakly to a centered Gaussian with variance $\\sigma_m^2 = 2m^2(1-m^2)/((3+m^2)\\sqrt{\\pi})$; started from a biased domain wall, $t^{-1/4}J_{\\rm dw}(t)$ converges to the half-normal variable $|G_m|$ with the same scale parameter; and at $m=0$, $t^{-1/8}J_{\\rm hom}(t)$ converges to the M-Wright variable $X_0$ with scale $a_0 = 1/(\\sqrt{6}\\,\\pi^{1/4})$, representable as $B_{-G^{(0)}/2}$ with $G^{(0)}\\sim N(0, 2/(3\\sqrt{\\pi}))$. Each conjecture includes convergence of every fixed-order moment, not just weak convergence of the law.","pith_inferences":["A testable extension beyond the paper: any kinetically constrained hopping model whose zero-bond and gap sector reduces to the same constant-rate zero-range process with the same $\\phi$ should show the same variance coefficient $\\sigma_m^2$ after colour decoration, making the amplitude a fingerprint of the tracer sector rather than of the XNOR rule itself.","At $m=0$, a sharper test than the marginal density is conditional: conditionally on the tracer current $Q_t$, the rescaled spin current should be Gaussian with variance proportional to $|Q_t|/\\sqrt{t}$; this conditional structure is a direct consequence of the Brownian-time representation and could be checked in the same trajectories.","The paper leaves open the exact time-dependent magnetization profile for the domain wall; the same coordinate map should at least produce its asymptotic form, since the tracer and colour sectors are already separated."],"forward_implications":["For every fixed $r$, the domain-wall cumulants obey $\\kappa_r[J_{\\rm dw}(t)] = \\kappa_r(H_m)\\,t^{r/4} + o(t^{r/4})$, so after dividing by the variance scale $t^{1/2}$, all higher-order cumulants diverge in time.","At $m=0$ the current fluctuations occur on the $t^{1/8}$ scale and the variance grows linearly in $t^{1/4}$ with coefficient $\\mathrm{Var}(X_0) = a_0\\sqrt{2/\\pi}$.","No $t^{1/2}$ drift appears in the XNOR domain-wall current; the leading motion is already the $t^{1/4}$ half-normal fluctuation, in contrast to SSEP where a deterministic $t^{1/2}$ current dominates.","The three conjectures place stochastic XNOR in the same anomalous full-counting-statistics universality class as charged single-file systems, with model-specific amplitudes fixed by the parameter-free reduction to a tagged SSEP particle."],"supporting_citations":[{"why":"Establishes the $z=4$ subdiffusive time scale for random XNOR circuits, supplying the $t^{1/4}$ fluctuation scale used throughout.","marker":"[18]"},{"why":"Derives the emergent single-file tracer description and the normalized spin-correlation profile, the physical basis for identifying equal-spin pairs as conserved tracers.","marker":"[19]"},{"why":"Provided the domain-wall half-normal and zero-magnetization variance-mixture shapes that the paper adopts and supplies with explicit amplitudes.","marker":"[20]"},{"why":"Classical tagged-particle result giving the $t^{1/4}$ Gaussian limit for a tagged hole in one-dimensional SSEP, the first pillar of the reduction.","marker":"[27]"},{"why":"Tagged-particle and fractional Brownian motion limits in nearest-neighbor SSEP used to support the convergence of the auxiliary tracer current.","marker":"[28]"},{"why":"The AI-generated candidate proof that supplies the deferred uniform density-fluctuation estimate and the moment-convergence arguments; unverified but load-bearing for the derivation.","marker":"[22]"},{"why":"Exact SSEP current fluctuations for step initial data, used as the standard comparison baseline for the homogeneous and domain-wall limits.","marker":"[26]"}],"fun_headline_variants":["No-fit XNOR current laws: Gaussian, half-normal, M-Wright","Exact XNOR current limits: Gaussian, half-normal, M-Wright","XNOR current exact law trio: Gaussian, half-normal, M-Wright","XNOR current distributions pinned without fitting"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes that the number of equal-spin pairs in the region swept out by a moving marker differs from the average density times the marker displacement by an error that is negligible on the main fluctuation scale, and this uniform density-fluctuation bound is deferred to an unverified companion manuscript.","fun_headline_variants_meta":{"raw":{"variants":["No-fit XNOR current laws: Gaussian, half-normal, M-Wright","Exact XNOR current limits: Gaussian, half-normal, M-Wright","XNOR current exact law trio: Gaussian, half-normal, M-Wright","XNOR current distributions pinned without fitting"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001344,"raw_usage":{"total_tokens":5457,"prompt_tokens":941,"completion_tokens":4516,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":557,"completion_tokens_details":{"reasoning_tokens":4441}},"tokens_in":557,"tokens_out":4516,"duration_ms":27117,"temperature":1.0,"reasoning_tokens":4441,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:17:13.622410+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the residual $E_t$ from Eq. (32) in a simulation that also records the tagged zero-bond displacement: for homogeneous $0<m<1$ and for the domain wall, the ratio $|E_t|\\,t^{-1/4}$ should converge to zero in probability. If instead it stays bounded away from zero, the identity $N_t = -\\delta Q_t + o_P(t^{1/4})$ fails and all three conjectures lose their derivation. Independently, at $m=0.5$ the ratio $\\mathbb{E}[(t^{-1/4}J_{\\rm hom}(t))^2]/\\sigma_m^2$ should approach 1; the paper's own data show it about 16.6% above the target at $t=16384$, so longer runs with $L\\ge1024$ to $t\\gtrsim 10^5$ would settle whether the amplitude is correct.","supporting_citations":[{"cited_title":"Emergent tracer dynamics in constrained quantum systems","cited_arxiv_id":"2205.07901","evidence_quote":"Derives the emergent single-file tracer description and the normalized spin-correlation profile, the physical basis for identifying equal-spin pairs as conserved tracers."},{"cited_title":"The motion of a tagged particle in the simple symmetric exclusion system on Z,","cited_arxiv_id":null,"evidence_quote":"Classical tagged-particle result giving the $t^{1/4}$ Gaussian limit for a tagged hole in one-dimensional SSEP, the first pillar of the reduction."},{"cited_title":"On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion","cited_arxiv_id":"0711.0017","evidence_quote":"Tagged-particle and fractional Brownian motion limits in nearest-neighbor SSEP used to support the convergence of the auxiliary tracer current."},{"cited_title":"Current fluctuations in the stochastic XNOR hopping process (An AI-generated candidate proof)","cited_arxiv_id":null,"evidence_quote":"The AI-generated candidate proof that supplies the deferred uniform density-fluctuation estimate and the moment-convergence arguments; unverified but load-bearing for the derivation."},{"cited_title":"Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition","cited_arxiv_id":"0902.2364","evidence_quote":"Exact SSEP current fluctuations for step initial data, used as the standard comparison baseline for the homogeneous and domain-wall limits."}],"review_version":1}