{"id":"6185abcd-a9e0-42fd-b119-0591f8dcc492","arxiv_id":"2505.05113","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For constant block times, the per-block expected arbitrage loss is approximately σ_b²/(2+1.7164 γ/σ_b), and fixed spacing asymptotically beats every other block-time distribution.","lead":"This paper derives a closed-form approximation for loss-versus-rebalancing, the expected arbitrage loss suffered by automated market maker liquidity providers, when blockchain blocks arrive at fixed intervals as on proof-of-stake chains. It further proves that fixed-interval block production gives the smallest asymptotic arbitrage loss among all block-time distributions with the same mean.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline constant depends on Lemma 3.1's auxiliary overshoot O: its printed definition is self-contradictory, and its convergence to the same limits as R is asserted, not proved; if o1,r1 differ by O(1), the 1.7164 coefficient changes.","rationale":"The reader's weakest_assumption identifies exactly the load-bearing point: Lemma 3.1's claims about the auxiliary overshoot O. The printed definition of O is self-contradictory, and the appendix proves convergence for R and L but merely asserts it for O. This is not a manufactured concern; it is the only place where the derivation of the headline ARB constant is under-supported. I considered whether a more central issue exists, such as the constant in Corollary 4.2's optimality theorem, but the OCR ambiguity there makes it hard to assess, and the Dirac-optimality argument via Jensen appears sound if the normalization is read as |ζ(1/2)|/√π. I also note independent support: the Monte Carlo validation in Table 2 confirms the ARB formula to <0.01% for ρb ≥ 1, which makes it likely that the intended Lemma 3.1 is true even though the proof is incomplete. By the strong Markov property at τρb, the eventual left overshoot on upper-crossing paths is the overshoot below -ρb of a centered walk started at 0, and by symmetry this converges to the same F as the right overshoot; so the gap is fixable. The verdict should remain CONDITIONAL: the paper's central quantitative claim is plausible and empirically supported, but the manuscript must correct the definition of O and supply a rigorous proof (or a precise citation) for the convergence of its first two moments before the result is fully established.","tokens_in":14194,"tokens_out":25876,"duration_ms":239637,"concrete_test":"Correct O to the intended eventual-left-overshoot variable O = -S_{τ0}1{τ=τρb}/p and run a Monte Carlo simulation of the Gaussian random walk with N(0,1) increments for ρb = 5, 10, 20, 40. For each path that hits +ρb before going negative, record the eventual negative overshoot H = -S_{τ0} at the first time S_n < 0 after the upper hit. Estimate o1 = E[H | τ=τρb] and o2 = E[H^2 | τ=τρb]. If o1-κ and o2-ω decay exponentially in ρb (so that r1-o1 and r2-o2 are exponentially small), Lemma 3.1 holds and the gap is a missing proof; if they converge to limits different from κ and ω, the constant 1.7164 in the headline formula is wrong.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.3 defines O = -Sτ 1{τ=τρb}/p. On the event {τ=τρb}, Sτ > ρb, so O is negative and O(ρb); substituting o1 = -(ρb+r1) and o2 = ρb^2+2ρb r1+r2 into (2.3)-(2.9) forces h1 = 0, making the printed identities algebraically inconsistent. The intended variable is evidently the eventual ladder height on upper-crossing paths, O = -S_{τ0}1{τ=τρb}/p, where τ0 is the first time S_n<0. Even with that correction, the appendix proof of Lemma 3.1 derives Lotov's convergence (6.1)-(6.3) for the right overshoot R and the left overshoot L, then states \"likewise o1 = κ + O(e^{-cρb})\" with no theorem for O. This gap is load-bearing: from (2.9), E[τ] = h2 + h1(ρb + r1 - o1) + O(1/ρb) + O(e^{-cρb}), and from (2.10), LVR = ℓσ_b^2 h2/2 + O(e^{-cρb}). If o1 differs from r1 by an O(1) amount, the constant in E[τ] shifts by h1(r1-o1), changing the 1.7164 coefficient in the headline ARB formula; if o2 differs from r2, the LVR leading constant is unaffected but the next-order correction changes.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies loss-versus-rebalancing (LVR) for automated market makers under general block-time distributions, focusing on deterministic (constant) block times. The authors model the log-price as a resetting random walk on the no-arbitrage interval, decompose long-run average arbitrage loss as the product of the probability of an arbitrage trade and the expected loss conditional on a trade, and use Wald identities and ladder-height / overshoot results to derive closed-form asymptotic expressions. For constant block times the central formula is ARB = ℓσ_b² / (2 + √(2π) γ/(|ζ(1/2)|σ_b)) + exponentially small error, with numerical Monte Carlo support for ρ_b = γ/σ_b ≥ 1. For general block-time distributions the paper claims a universal first-order trade probability and that the Dirac (constant) block-time distribution asymptotically minimizes LVR among distributions with fixed mean.","tokens_in":14506,"tokens_out":24234,"duration_ms":234291,"significance":"If the mathematical derivation can be made fully rigorous, the contribution is significant for the DeFi literature: it provides the first analytical LVR formula for fixed-interval blockchains, gives a closed-form coefficient (1.7164) that can be used in practice, and identifies a design principle (constant block times minimize asymptotic arbitrage losses). The paper is commendable for being parameter-free: the constants come from cited external results (Lai, Chang–Peres, Lotov, Spitzer, Wald), not from fitting, and the Monte Carlo experiments are used only as validation. The decomposition Ptrade × LVR and the universality result for Ptrade are appealing and potentially useful beyond the specific constant-time case. However, the correctness of the headline coefficient currently rests on a proof gap and on an algebraically inconsistent definition of an auxiliary overshoot, so the central claim cannot yet be considered established.","major_comments":[{"comment":"The definition O = -S_τ 1{τ=τρ_b}/p is algebraically inconsistent with the surrounding identities. On the event {τ=τρ_b}, S_τ > ρ_b, so O is negative and of order ρ_b, not a positive O(1) overshoot. Substituting this definition into (2.3) and using (2.5) forces h1 = 0, which contradicts h1 > 0. The intended object is presumably the eventual ladder height on paths that first hit the upper barrier, i.e. O = -S_{τ0} 1{τ=τρ_b}/p, where τ0 is the first time the walk is negative. This correction must be made and the identities re-derived with the corrected definition.","section":"Section 2.3, definition of O and equations (2.3)–(2.4)"},{"comment":"The proof does not establish the claimed convergence for the auxiliary overshoot O. The stated consequence of Lotov's theorem, (6.1), gives the limiting distribution of the upper overshoot R and of the left overshoot L = -S_τ conditional on {τ=τ0}. It does not give the distribution of -S_{τ0} conditional on {τρ_b < τ0}, which is what the corrected O requires. The sentence 'likewise o1 = κ + O(e^{-cρ_b})' is asserted without a theorem. This gap is load-bearing: in (2.9) the denominator contains r1 + o1 and the numerator contains r2 - o2, and in (2.10) the correction term is proportional to h1(r2 - o2)/(ρ_b + r1 + o1). If o1 differs from r1 by an O(1) amount, E[τ] acquires an O(1) shift and the constant in the headline ARB formula changes; if o2 differs from r2, the leading LVR constant is unchanged but the stated exponentially small error is not justified. A proof of the convergence of O to the same limit F (or an explicit argument showing the difference is exponentially small) is required.","section":"Section 6, proof of Lemma 3.1 (convergence of o1, o2)"},{"comment":"The 'good event' argument is not coherent as written. Event B is defined as {τρ_b < τ0 and ∃ n0 ≥ τρ_b : S_{n0} ∈ [ρ_b/4, 3ρ_b/4]}; the overshoot S_{τρ_b} occurs at or before n0, and restarting the walk at n0 via the strong Markov property cannot control the distribution of S_{τρ_b} conditional on B. Similarly, the use of A for the left overshoot is unclear. This part of the proof therefore does not achieve the uniform-in-x convergence needed for the moment asymptotics. The proof of Lemma 3.1 must be reworked so that the conditioning events actually determine the overshoot variable whose distribution is being bounded.","section":"Section 6, equations (6.2)–(6.3) and the events B and A"},{"comment":"There is an internal inconsistency in the constant relating h2 to the Riemann zeta function. Corollary 3.1 and Table 1 use h2 = |ζ(1/2)|/√π, leading to LVR = ℓσ_b²|ζ(1/2)|/(2√π) and to the headline denominator with √(2π)γ/(|ζ(1/2)|σ_b). In contrast, equation (4.4) yields h2 = |ζ(1/2)|/√(2π) for the constant block-time case, and equations (4.1)–(4.2) use |ζ(1/2)|/√(2π), while Table 1's 'General' row uses |ζ(1/2)|/√π. These differ by a factor of √2. The authors must correct the coefficient in (4.4) and align (4.1)–(4.2) with Table 1, and then verify that the definition of Cµ is consistent. This affects the general-distribution LVR formula and the Dirac-optimality statement. Relatedly, in Corollary 4.1 the text states that 'by Lemma 4.1 ... h2 ... are all bounded constants,' but Lemma 4.1 only bounds r1, r2, o1, o2; a separate argument for the finiteness of h2 is needed.","section":"Section 4, equations (4.1), (4.2), (4.4), and Table 1"}],"minor_comments":[{"comment":"There are several typos: 'bl ocks', 'Los s-versus-rebalancing', 'theoretical expression for ρb = γ σb smaller than 5' in the Table 2 caption, and missing labels for the panels in Figure 1.","section":"Throughout"},{"comment":"The displayed second Wald identity writes Var(X1)E[τ] + (E[X1])²E[τ²] = E[Sτ²]; with E[X1]=0 this is fine, but the E[τ²] term is unnecessary and may confuse readers. The simplified identity Var(X1)E[τ] = E[Sτ²] is what is used.","section":"Section 2.3, Wald identities"},{"comment":"Reference [3] is duplicated in the bibliography (the Ethereum Foundation documentation appears twice), and references [5] and [19] have the same title; please check whether they are distinct works or a duplicate entry.","section":"References"},{"comment":"The SDE in the final remark has a missing parenthesis or an ambiguous grouping; please rewrite the expression so that the denominator and the drift term are unambiguous.","section":"Section 5, item (3)"},{"comment":"The proof uses notation such as P(R1 ≥ x | τ0 ≥ τρ_b) without defining R1, and the displayed decomposition of the conditional probability is difficult to follow. A cleaner conditioning argument would help, especially since the same domination is needed for O under the corrected definition.","section":"Appendix, proof of Lemma 4.1"}],"recommendation":"major_revision","confidential_remarks":"The paper contains a promising and potentially publishable idea, but the current manuscript is not yet verifiable: the central lemma's proof has a genuine gap, the auxiliary overshoot O is misdefined, and there are internal inconsistencies in the zeta-constant between Section 3 and Section 4. These are not mere cosmetic issues; they directly affect the headline closed-form coefficient. I would encourage the editor to send the revised version back to a referee familiar with Lotov's boundary-crossing theorems, since the main question is whether the 'leftover' overshoot O indeed converges to the same limit as the right overshoot. The authors should be asked to provide a complete proof or an explicit citation for that step, and to reconcile the constant discrepancy before the paper can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe short version: this paper gives the first closed-form LVR formula for constant block times—the empirically dominant setting for proof-of-stake chains—and a clean optimality result for the Dirac block-time law. The formula is plausible, the Monte Carlo table supports it, and the paper deserves a serious referee. But don't accept it as is: Lemma 3.1 has a typo in the definition of O and a missing convergence proof.\n\nWhat's genuinely new: Milionis et al. only covered Poisson arrivals. Here the constant-time case yields ARB = ℓσ_b²/(2 + 1.7164γ/σ_b) plus an exponentially small error, and Section 4 shows that constant spacing asymptotically minimizes LVR among all block-time distributions with fixed mean. That second result is a useful design principle. The Ptrade × LVR decomposition is inherited from [8], but applying two-barrier Gaussian random-walk asymptotics is the right tool, and the numerical validation is honest and convincing.\n\nWhere it's soft. First, the printed definition O = -Sτ 1{τ=τρb}/p is wrong: on that event Sτ > ρb, so O is large and negative, and the identities (2.3)–(2.9) would force h1 = 0. The intended object is the eventual ladder height on the upper-crossing path, O = -S_{τ0}1{τ=τρb}/p. The algebra works with that reading, but the text needs fixing.\n\nSecond, Lemma 3.1 asserts exponential convergence of o1,o2 to the same κ,ω as r1,r2. The appendix proves that for the right overshoot from Lotov's theorem and says 'likewise' for O. That 'likewise' is doing a lot of work. You need a separate argument—condition on the walk returning to the strip after the upper crossing, then apply the barrier asymptotics. It's probably true, but it's not written.\n\nOne correction to the stress test: if o1,r1 differ by O(1), the 1.7164 coefficient does not change. That coefficient comes from h1 and h2 only. What changes is the additive '+2' in the denominator and the error order: exponential becomes algebraic (O(σ_b/γ) relative). The leading asymptotics survive.\n\nEverything else holds up: the h2 expression from Lai/Spitzer, the Jensen argument for Dirac optimality, and the general-distribution bounds in Lemma 4.1 (sketchy but plausible).\n\nBottom line: worth a careful referee. Send it back for a corrected O definition and a real proof of Lemma 3.1's 'likewise' step. If that lands, this is a solid contribution to the LVR/DeFi literature.","headline":"Genuinely new and likely correct, but the proof of the key overshoot lemma is incomplete and the definition of O is typo'd; worth refereeing after a fix.","tokens_in":15052,"tokens_out":11986,"would_cite":true,"duration_ms":108499,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60G50","60J05","91G80"],"pacs":[],"model":"deepseek-v4-flash","headline":"For automated market makers on fixed-interval chains, per-block arbitrage loss is given by a closed-form formula, and constant spacing is asymptotically the best possible block-time law.","keywords":["loss-versus-rebalancing","automated market maker","constant block time","arbitrage","random walk","ladder heights","Riemann zeta function","proof of stake"],"falsifier":"A direct numerical check of the overshoot identities: simulate the Gaussian random walk on $[0,\\rho_b]$ and estimate the right overshoot moments $r_1,r_2$ and the auxiliary 'leftover' overshoot moments $o_1,o_2$ as defined in Section 2; for $\\rho_b$ from 1 to 8, test whether $r_1-o_1$ and $r_2-o_2$ decay like $e^{-c\\rho_b}$. Alternatively, rerun the paper's Monte-Carlo protocol at $\\rho_b=\\gamma/\\sigma_b\\in\\{0.5,1,2,3,4,5\\}$ and check that measured $\\overline{\\mathrm{ARB}}$ tracks $\\ell\\sigma_b^{2}/(2+1.7164\\,\\gamma/\\sigma_b)$ to the reported sub-0.01% accuracy; a fixed offset in the overshoot moments would appear as a wrong $O(1)$ constant.","tokens_in":13965,"feed_emoji":"📉","tokens_out":17498,"duration_ms":143781,"temperature":0.7,"pith_summary":"The paper aims to give automated market maker (AMM) liquidity providers a quantitative handle on arbitrage losses when blocks arrive at fixed intervals, the regime used by most proof-of-stake chains. It derives a closed-form expected loss per block, $\\overline{\\mathrm{ARB}} = \\ell\\sigma_b^{2}/(2+\\sqrt{2\\pi}\\,\\gamma/(|\\zeta(1/2)|\\,\\sigma_b)) + O(e^{-c\\gamma/\\sigma_b})$, and reports large Monte-Carlo simulations showing the approximation is quasi-exact across practical parameter ranges. It also establishes the factorization $\\mathrm{ARB}=P_{\\mathrm{trade}}\\times\\mathrm{LVR}$ and proves that, among all block-time distributions with a fixed mean, constant spacing uniquely minimizes the asymptotic loss-versus-rebalancing. If correct, the results turn LVR into a computable function of a few observables and give a design principle for block scheduling.","feed_headline":"Constant block spacing minimizes AMM arbitrage losses","feed_subtitle":"For proof-of-stake chains, a closed-form arbitrage-loss formula says fixed slot times are the optimal scheduling rule.","key_machinery":"The engine is a discrete-time Markov chain whose state is the log-price inside the no-arbitrage interval $[0,\\rho_b]$ with $\\rho_b=\\gamma/\\sigma_b$, reset to 0 whenever an arbitrage occurs. Stopping the underlying random walk at its first boundary crossing, the expected time to an arbitrage and the conditional loss are expressed through the ladder height $H$ (the size of the walk's first descent below zero) and the overshoot variables $R$ and $O$. The central identities are the stopped-random-walk relations $E[\\tau]=h_2+h_1(\\rho_b^2+2\\rho_b r_1+r_2-o_2)/(\\rho_b+r_1+o_1)$ and $\\mathrm{LVR}=\\ell\\sigma_b^{2}[h_2/2+h_1(r_2-o_2)/(2(\\rho_b+r_1+o_1))]$. For Gaussian increments $h_1=1/\\sqrt{2}$ and $h_2=|\\zeta(1/2)|/\\sqrt{\\pi}$, and the boundary-crossing estimate supplies $r_1,o_1\\to\\kappa=|\\zeta(1/2)|/\\sqrt{2\\pi}$ and $r_2,o_2\\to\\omega=1/4+\\kappa^2$ exponentially fast; the collapse of this ratio to $\\rho_b$ is what produces the explicit coefficient $1.7164$ in the headline formula.","core_discovery":"In the deterministic block-time model, with log-price increments $N(0,\\sigma_b^2)$ per block, the long-run per-block arbitrage loss is $\\overline{\\mathrm{ARB}} = \\ell\\sigma_b^{2}/(2+\\sqrt{2\\pi}\\,\\gamma/(|\\zeta(1/2)|\\,\\sigma_b)) + O(e^{-c\\gamma/\\sigma_b})$, numerically $\\approx \\ell\\sigma_b^{2}/(2+1.7164\\,\\gamma/\\sigma_b)$. The companion statements are $P_{\\mathrm{trade}} = 1/(\\gamma/(\\sqrt{2}\\sigma_b)+|\\zeta(1/2)|/\\sqrt{\\pi}) + O(e^{-c\\gamma/\\sigma_b})$ and $\\mathrm{LVR} = \\ell\\sigma_b^{2}|\\zeta(1/2)|/(2\\sqrt{\\pi}) + O(e^{-c\\gamma/\\sigma_b})$. Extended to arbitrary block-time laws, the paper shows that the asymptotic arbitrage probability $P_{\\mathrm{trade}} = \\sqrt{2}\\sigma_b/\\gamma + O(\\sigma_b/\\gamma)$ is universal, while the asymptotic LVR is minimized only by constant block spacing. Hence, among all distributions with the same mean block time, the Dirac law, that is constant block spacing, gives liquidity providers the strongest protection against arbitrage.","pith_inferences":["The same stopped-random-walk machinery should extend to fee-paying AMMs: fees shift or widen the no-arbitrage interval, and the overshoot identities should quantify how fees trade off against arbitrage loss.","A testable prediction is that blockchains with jittered or variable slot times impose higher adverse selection on liquidity providers than fixed slots with the same average; comparing measured LVR across chains that changed their slot schedule would isolate this effect.","Since asymptotic trade frequency is distribution-free, any reduction in LVR from changing block timing must come from shrinking the conditional loss per arbitrage; protocol designers could therefore optimize that second factor directly."],"forward_implications":["On proof-of-stake chains with fixed slot times, the formula gives LPs a closed-form adverse-selection cost per block from three observable inputs: per-block volatility, spread, and liquidity density.","Holding average block time fixed, replacing Poisson arrivals with constant spacing reduces per-block LVR by up to roughly 17.4% in the fast-block regime.","The asymptotic probability that a block contains an arbitrage trade is universal, so changing the block-time distribution changes the size of the loss per trade, not the frequency of trades.","Constant block spacing uniquely minimizes both asymptotic LVR and total arbitrage among all block-time distributions with a fixed mean, giving a scheduling principle for consensus protocols."],"supporting_citations":[{"why":"Introduces loss-versus-rebalancing as the adverse-selection cost of AMM liquidity provision, the quantity the paper computes.","marker":"[7]"},{"why":"Provides the Poisson block-time LVR benchmark and the ARB = Ptrade x LVR decomposition that the paper generalizes.","marker":"[8]"},{"why":"Supplies the boundary-crossing theorem for Gaussian random walks that yields exponential convergence of the overshoot moments used in Lemma 3.1.","marker":"[14]"},{"why":"Provides the fluctuation-theory result fixing the first ladder-height moment h1 = 1/sqrt(2) for centered random walks.","marker":"[10]"},{"why":"Provides the formula for the second ladder-height moment h2 in which the Riemann zeta value enters.","marker":"[6]"},{"why":"Supplies the stopped-random-walk identities connecting the expected stopping time and stopped second moment to overshoot statistics.","marker":"[11]"}],"fun_headline_variants":["Constant block times give AMM LPs best arbitrage protection","Fixed block intervals minimize AMM arbitrage loss","Closed-form LVR formula proves constant block spacing optimal","Dirac law beats all block-time distributions for AMM LPs","Deterministic block time: best shield for liquidity providers"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is Lemma 3.1: the auxiliary 'leftover' overshoot moments $o_1,o_2$ converge exponentially fast to the same limits $\\kappa,\\omega$ as the right overshoot moments $r_1,r_2$; the appendix derives the $r$ convergence from a cited boundary-crossing theorem and states the $o$ convergence 'likewise', but if an $O(1)$ difference between them survives, the $1.7164$ constant changes.","fun_headline_variants_meta":{"raw":{"variants":["Constant block times give AMM LPs best arbitrage protection","Fixed block intervals minimize AMM arbitrage loss","Closed-form LVR formula proves constant block spacing optimal","Dirac law beats all block-time distributions for AMM LPs","Deterministic block time: best shield for liquidity providers"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000408,"raw_usage":{"total_tokens":2186,"prompt_tokens":1082,"completion_tokens":1104,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":698,"completion_tokens_details":{"reasoning_tokens":1023}},"tokens_in":698,"tokens_out":1104,"duration_ms":7644,"temperature":1.0,"reasoning_tokens":1023,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:16:09.428198+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct numerical check of the overshoot identities: simulate the Gaussian random walk on $[0,\\rho_b]$ and estimate the right overshoot moments $r_1,r_2$ and the auxiliary 'leftover' overshoot moments $o_1,o_2$ as defined in Section 2; for $\\rho_b$ from 1 to 8, test whether $r_1-o_1$ and $r_2-o_2$ decay like $e^{-c\\rho_b}$. Alternatively, rerun the paper's Monte-Carlo protocol at $\\rho_b=\\gamma/\\sigma_b\\in\\{0.5,1,2,3,4,5\\}$ and check that measured $\\overline{\\mathrm{ARB}}$ tracks $\\ell\\sigma_b^{2}/(2+1.7164\\,\\gamma/\\sigma_b)$ to the reported sub-0.01% accuracy; a fixed offset in the overshoot moments would appear as a wrong $O(1)$ constant.","supporting_citations":[{"cited_title":"C., Roughgarden, T., & Zhang, A","cited_arxiv_id":null,"evidence_quote":"Provides the Poisson block-time LVR benchmark and the ARB = Ptrade x LVR decomposition that the paper generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the boundary-crossing theorem for Gaussian random walks that yields exponential convergence of the overshoot moments used in Lemma 3.1."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the fluctuation-theory result fixing the first ladder-height moment h1 = 1/sqrt(2) for centered random walks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the formula for the second ladder-height moment h2 in which the Riemann zeta value enters."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the stopped-random-walk identities connecting the expected stopping time and stopped second moment to overshoot statistics."}],"review_version":1}