{"id":"550bcdf4-0646-4c7b-a3ef-decab89fb16f","arxiv_id":"2504.17274","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Edge-flipping a generalized random dot-product graph produces another such graph in one higher dimension, and a privacy-adjusted spectral embedding consistently recovers latent positions and persistence diagrams at near-minimax rates.","lead":"This paper studies how to recover hidden node positions from a graph after each edge has been independently flipped to protect privacy. It proves that a standard local privacy mechanism preserves the graph model within a known geometric distortion, and that an adjusted spectral embedding recovers positions and topological features at near-optimal rates.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3.3's stated condition nρ_n = ω(log n) is insufficient for the imported spectral bounds: the proof requires the effective sparsity n σ(ε)^2 ρ_n to grow faster than log^4 n, so the consistency range is overstated.","rationale":"The reader's weakest_assumption identifies the same point: the upper bound imports spectral concentration results into a non-Bernoulli shifted matrix without verifying their hypotheses. I agree and add precision: the concrete failure is the sparsity-regime condition. Theorem 3.3 states nρ_n = ω(log n), but the imported non-private bounds (Proposition B.1, from [56, Theorem 1]) explicitly require nρ_n = ω(log^4 n). The effective sparsity after edgeFlip is t_n = σ(ε)^2 ρ_n, so the needed condition is n t_n = ω(log^4 n), which is not implied by nρ_n = ω(log n) for fixed or large ε. The non-Bernoulli noise (variance depending on τ(ε)^2) compounds this, because the cited residual bounds were derived for graph noise whose variance scales with the signal. I examined the alleged Theorem 3.4 gap and found it less severe: the different O(p,q) alignments are handled by the T3 term, and the transformations inside the persistence diagrams differ by an orthogonal matrix, so the O(d) invariance argument appears valid there. The lower bound Theorem 3.2 is plausible. Since the central upper bound's stated regime is overclaimed, the manuscript should fix Theorem 3.3's assumption and proof before full acceptance; my recommendation does not change the reader's conditional verdict.","tokens_in":33400,"tokens_out":32687,"duration_ms":272752,"concrete_test":"Re-derive the residual bound in Appendix C.4 without invoking [56, Lemma 12] as a black box: track the explicit hypotheses of [56, Theorem 1] and [10, Propositions 6.3 & 6.5] for the matrix A = M_ε(A) − τ(ε)^2 11^T. In particular, verify (i) the log-power condition on the effective sparsity n t_n = n σ(ε)^2 ρ_n, and (ii) whether the entrywise variance (τ(ε)^2 + P_{ij})(1 − τ(ε)^2 − P_{ij}) satisfies the moment conditions used in those bounds. If the imported results require n t_n = ω(log^4 n), exhibit a parameter sequence with nρ_n = ω(log n) but n t_n = o(log^4 n), e.g., fixed ε and ρ_n = log^{3/2} n / n; this would show Theorem 3.3's stated condition is insufficient and the theorem must be restated with the stronger condition or supplied with new sparse-noise bounds.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing issue is the condition under which Theorem 3.3's upper bound holds. The theorem states that consistency of Algorithm 1 follows whenever nρ_n = ω(log n), but the proof in Appendix C.4 applies Rubin-Delanchy et al. (2022) and Cape et al. (2019) results that are stated for Bernoulli GRDPG adjacency matrices and require the average degree nρ_n = ω(log^4 n). After edgeFlip, the effective sparsity parameter of the privatized graph is t_n = σ(ε)^2 ρ_n ≤ ρ_n, so the stated assumption nρ_n = ω(log n) does not imply n t_n = ω(log^4 n); for example, ρ_n = log^{3/2} n / n with fixed ε gives nρ_n = ω(log n) but n t_n = o(log^4 n). Moreover, the matrix A = M_ε(A) − τ(ε)^2 11^T is not a Bernoulli GRDPG adjacency matrix: its entries have variance (τ(ε)^2 + P_{ij})(1 − τ(ε)^2 − P_{ij}) rather than P_{ij}(1−P_{ij}), and when τ(ε)^2 dominates t_n the noise is dense. The proof does not verify that the cited residual bounds (e.g., [56, Lemma 12] and [10, Props 6.3 & 6.5]) remain valid for this shifted, non-Bernoulli noise. Consequently, the claimed rate O(log n / √(n σ(ε)^4 ρ_n^2)) is not established in the stated regime; the paper's own Proposition B.1 and the introduction both indicate the denser regime ω(log^4 n) is required. This directly affects the central near-minimax consistency claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies latent-position recovery from generalized random dot-product graphs (GRDPGs) under ε-edge local differential privacy, using the edgeFlip mechanism. The central theoretical contribution is Theorem 3.1, which states that edgeFlip maps a GRDPG with signature (p,q) and sparsity ρ_n to another GRDPG with signature (p+1,q), sparsity 1, and latent positions φε(x) = τ(ε) ⊕ σ(ε)ρ_n^{1/2}x. Building on this closure property, the authors prove a minimax lower bound for latent-position estimation under ε-edgeLDP (Theorem 3.2), propose a privacy-adjusted spectral embedding (Algorithm 1), and claim near-minimax optimal consistency in Theorem 3.3 under nρ_n = ω(log n). They then extend the result to persistence diagrams (Theorem 3.4) and illustrate the methods on synthetic and real-world data.","tokens_in":33786,"tokens_out":12772,"duration_ms":123983,"significance":"If the main theorems hold, the paper is a substantial contribution: it moves private graph inference from stochastic block models to the much richer GRDPG class, gives a clean geometric interpretation of edgeFlip, and provides the first minimax lower bound for latent-position estimation under local edge DP, together with a topological-data-analysis downstream application. The closure argument in Theorem 3.1 is elegant and checkable, and the lower-bound proof via Le Cam's lemma is a credible technical core. The paper also ships reproducible code and experiments with clearly described settings. However, the central upper-bound proof in Theorem 3.3 imports spectral concentration results under conditions that are not verified, and the stated density regime conflicts with the proof's own requirements; these issues must be resolved before the near-minimax optimality claim is established.","major_comments":[{"comment":"Theorem 3.3 is stated under nρ_n = ω(log n), but the proof imports Proposition B.1 and the results of [56, Theorem 1] and [2, Theorem 4], whose stated condition is nρ_n = ω(log^4 n). After edgeFlip the relevant sparsity scale of the privatized graph is t_n = σ(ε)^2 ρ_n ≤ ρ_n, so the theorem's assumption does not imply n t_n = ω(log^4 n); for example, with fixed ε and ρ_n = log^{3/2} n / n, we have nρ_n = ω(log n) but n t_n = o(log^4 n). The introduction's last paragraph and Proposition B.1 both state the ω(log^4 n) regime, so either Theorem 3.3's assumption must be strengthened to nσ(ε)^2 ρ_n = ω(log^4 n) or its equivalent, or a new argument must be supplied that works under nρ_n = ω(log n). As written, the consistency range and the near-minimax optimality claim are overstated.","section":"Section 3.3 / Appendix C.4, Eq. (32)"},{"comment":"The matrix A = Mε(A) − τ(ε)^2 1_n1_n^T is not a Bernoulli GRDPG adjacency matrix, yet the proof applies [41, Theorem 5.2], [56, Lemma 12], and [10, Propositions 6.3 and 6.5] to it. These results are stated for graphs whose entries are independent Bernoulli with expectation P; here A has entries taking values 1−τ² and −τ², with variance (τ²+σ²ρ P_ij)(1−τ²−σ²ρ P_ij), which differs from P_ij(1−P_ij). When τ² is non-negligible, the noise has a dense component that does not vanish with ρ_n. The proof does not verify the effective-sparsity condition n max_ij P_ij = nσ(ε)^2 ρ_n ≫ log^c n needed for the imported spectral bounds, nor the corresponding row-wise eigenvector perturbation assumptions. Since this is the sole route to Eqs. (32)–(35), the high-probability bound in Theorem 3.3 is not established as written.","section":"Appendix C.4, Step 1 and Lemma B.3"},{"comment":"The map φε is defined inconsistently between Theorem 3.1 and the appendix. Theorem 3.1 uses φε(x) = τ(ε) ⊕ σ(ε)ρ_n^{1/2}x, but Appendix B.1 defines φε(x) = τ(ε) ⊕ σ(ε)x, and Lemma B.3 accordingly computes E[Mε(A)_ij] = σ(ε)^2 X_i^T I_{p,q} X_j + τ(ε)^2, omitting the ρ_n factor. Appendix C.4 invokes Lemma B.3 while using the ρ_n-containing form of the expected adjacency P. The proof needs a consistent definition of φε and corrected lemmas, or an explicit statement that the ρ_n-free version is used only for the noise bound and not for the spectral separation step.","section":"Appendix B.1, Lemma B.3, and Appendix C.4"}],"minor_comments":[{"comment":"The rate O(log n / √(n σ(ε)^4 ρ_n^2)) can diverge when nσ(ε)^4ρ_n^2 = o(log n), so the theorem should either state explicitly the consistency condition nσ(ε)^4ρ_n^2 = ω(log n) or clarify that consistency is claimed only in that regime.","section":"Section 3.3, Theorem 3.3"},{"comment":"The proof of Theorem 3.4 concludes with W∞(D̂_n, D_n) = O(log n / √(σ² n ρ_n)), which does not match the stated rate O(log n / √(n σ⁴ ρ_n²)) in Theorem 3.4; in addition, the quantity T1 is written as ‖qρ_n qX − XQ_n^{-1}‖_{2,∞}, where a missing −1/2 exponent on qρ_n appears likely. Please correct the normalization and reconcile the final rate with the theorem statement.","section":"Appendix C.5, final displayed equation"},{"comment":"The estimator qρ_n is defined as an average of qA_ij, which can be negative or exceed 1 for finite samples, yet the algorithm's return statement claims qρ_n ∈ [0,1]; specify a clipping or truncation step if one is intended.","section":"Algorithm 1, Step 2"},{"comment":"The notation table entry for ΔX is incomplete, reading 'ΔX = for ξ∼ P'; it should define ΔX = n^{-1}X^TX as in Appendix A.","section":"Appendix, Table 1"}],"recommendation":"major_revision","confidential_remarks":"The core closure idea is attractive and the lower-bound argument appears sound, but the upper-bound proof relies on transferring spectral concentration results to a shifted, non-Bernoulli matrix without verifying their conditions. The mismatch between the stated ω(log n) regime and the ω(log^4 n) regime acknowledged in the introduction is load-bearing; I believe a careful revision that states the correct sparsity condition and either proves or properly imports the needed spectral bounds could make the paper publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one for the closure theorem, but don't take the headline rates at face value. The paper shows that applying the edgeFlip local privacy mechanism to a GRDPG yields another GRDPG in one higher dimension, with a simple affine distortion of the latent positions. That is a short computation, but it is the right idea: it turns private graph inference into an ordinary embedding problem on a slightly different model. The minimax lower bound under ε-edgeLDP looks solid, and the proof via Le Cam and chi-square follows standard machinery without obvious holes. The privacy-adjusted spectral embedding is the natural estimator, and the claimed near-minimax rate is believable in the right density regime. The citation pattern is fine; the overlap with the co-author's prior SBM paper is properly framed as related work, not as a load-bearing reference.\n\nThe soft spots are concentrated in the upper bound and the topological section. Theorem 3.3 states consistency when nρ_n = ω(log n), but the proof imports spectral embedding bounds from Rubin-Delanchy et al. and Cape et al. that need the effective average degree nσ(ε)^2ρ_n to grow faster than log^4 n. The introduction itself says the denser regime is needed, so the theorem statement is internally inconsistent. This is not cosmetic: for ρ_n = log^{3/2} n / n and fixed ε, the theorem's condition holds but the imported bounds do not apply. Also, the centered matrix A = M_ε(A) − τ(ε)^2 11^T is a shifted Bernoulli matrix with variance structure different from a pure GRDPG, and the proof does not verify that the cited residual bounds survive that shift. I suspect both are fixable with a careful matrix concentration argument and a corrected theorem statement, but as written the upper bound is not proved in its claimed range.\n\nThe persistence diagram section has a subtler issue: for p,q > 0 the latent positions are identifiable only up to O(p,q), and persistence diagrams are not invariant to indefinite orthogonal transformations. So Dgm(X) as an estimand is not well-defined unless q = 0. The proof also seems to contain a rate in the final line that does not match the theorem statement. This part needs more thought before it can be trusted.\n\nFor the right reader—statisticians working on private network inference or TDA on graphs—the core idea is valuable and the experiments are honest. I would send it to peer review, but it needs major revision on the density condition and the topological claims.","headline":"A genuinely nice closure result for private GRDPGs, with an upper-bound proof that overstates its density regime and a TDA section that needs more care.","tokens_in":34304,"tokens_out":8843,"would_cite":true,"duration_ms":77092,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62C20","62H12","05C80"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper proves that edgeFlip, a standard local edge-differential-privacy mechanism, maps generalized random dot-product graphs to the same model class with one extra latent dimension, and that a privacy-adjusted spectral embedding then…","keywords":["local differential privacy","generalized random dot-product graphs","edgeFlip","spectral embedding","latent position estimation","minimax rates","persistence diagrams"],"falsifier":"Simulate $A\\sim G(P,\\rho_n;p,q)$ with $n\\rho_n=\\log^{2.5} n$ (so $n\\rho_n=\\omega(\\log n)$ but $n\\rho_n=o(\\log^4 n)$), privatize with edgeFlip at a fixed $\\varepsilon$, run Algorithm 1, and measure $d_{2,\\infty}(\\hat X/\\sqrt{\\hat\\rho_n},X)$ across increasing $n$. If the error does not track $O\\bigl(\\log n/\\sqrt{n\\sigma(\\varepsilon)^4\\rho_n^2}\\bigr)$ and instead levels off, the spectral-concentration step imported from non-private GRDPG bounds is the failing link in the stated regime.","tokens_in":33170,"feed_emoji":"🔒","tokens_out":8907,"duration_ms":83368,"temperature":0.7,"pith_summary":"The paper is trying to establish that a standard local-differential-privacy mechanism for graphs, edgeFlip, does not destroy the latent geometry encoded in the graph; it transforms a generalized random dot-product graph into another such graph with one extra latent dimension. This closure lets a privacy-adjusted spectral embedding recover the original latent positions consistently and nearly optimally in the $\\ell_{2,\\infty}$ metric, with a matching lower bound up to a $\\sqrt{\\log n}$ factor. The same convergence rate carries over to persistence diagrams, so topological features such as clusters and loops can be recovered privately. A sympathetic reader should care because most prior private-graph work stopped at community detection in stochastic block models, while this paper extends the argument to a substantially richer nonparametric family.","feed_headline":"Edge flipping preserves graph geometry for private recovery","feed_subtitle":"A standard local-DP flip maps the graph model onto itself in one extra dimension, enabling near-optimal latent-position recovery.","key_machinery":"The central object is the edgeFlip mechanism together with the geometric closure map $\\varphi_\\varepsilon$. edgeFlip flips each edge with probability $\\pi(\\varepsilon)=1/(e^\\varepsilon+1)$; writing $\\sigma(\\varepsilon)=\\sqrt{(e^\\varepsilon-1)/(e^\\varepsilon+1)}$ and $\\tau(\\varepsilon)=\\sqrt{1/(e^\\varepsilon+1)}$, the privatized edge probabilities become $\\tau(\\varepsilon)^2+\\sigma(\\varepsilon)^2\\rho_n X_i^T I_{p,q} X_j$, which are exactly inner products in $\\mathbb{R}^{d+1}$ after appending the constant coordinate $\\tau(\\varepsilon)$ and scaling the original coordinates by $\\sigma(\\varepsilon)\\rho_n^{1/2}$. Algorithm 1 reverses this distortion by forming $\\tilde A=\\sigma(\\varepsilon)^{-2}(M_\\varepsilon(A)-\\tau(\\varepsilon)^2 11^T)$, estimating $\\rho_n$ from the average privatized edge, and taking the adjacency spectral embedding. The extra dimension is the geometric footprint of the privacy noise.","core_discovery":"The central claim is Theorem 3.1: if $(A,X)\\sim G(P,\\rho_n;p,q)$ is a generalized random dot-product graph, then after edgeFlip the privatized graph satisfies $(M_\\varepsilon(A),\\varphi_\\varepsilon(X))\\sim G(\\varphi_{\\varepsilon\\#}P,1;p+1,q)$, where $\\varphi_\\varepsilon(x)=\\tau(\\varepsilon)\\oplus\\sigma(\\varepsilon)\\rho_n^{1/2}x$ appends one constant coordinate and scales the original latent positions. Consequently, Algorithm 1 achieves $d_{2,\\infty}(\\hat X/\\sqrt{\\hat\\rho_n},X)=O\\bigl(\\log n/\\sqrt{n\\sigma(\\varepsilon)^4\\rho_n^2}\\bigr)$ with high probability when $n\\rho_n=\\omega(\\log n)$, while Theorem 3.2 shows that no $\\varepsilon$-edgeLDP mechanism can beat $\\Omega\\bigl(\\sqrt{\\log n/(n\\sigma(\\varepsilon)^4\\rho_n^2)}\\bigr)$ in the regime $\\varepsilon<3\\rho_n/8$. Theorem 3.4 extends the same rate to the bottleneck distance between persistence diagrams. Together these results say that, up to logarithmic factors, edgeFlip is an optimal privacy mechanism for this problem and the privacy-adjusted spectral embedding is an optimal estimator.","pith_inferences":["An implicit consequence of the closure theorem is that edgeFlip can act as a reusable privacy layer for any downstream estimator that is equivariant under the GRDPG's symmetries and Lipschitz in the $d_{2,\\infty}$ metric, not just for spectral and topological methods.","The same geometric lens suggests a route to private graphon estimation: for exchangeable latent-position models whose edge probabilities are bilinear in latent features, edgeFlip should correspond to appending a constant spike coordinate, which may turn existing graphon estimators into privacy-adjusted estimators at the cost of the sparsity penalty identified here.","A testable extension is to check whether the sparsity amplification $\\rho_n\\mapsto\\rho_n^2$ is forced by local privacy or by edge privacy itself; if central edge DP avoids the amplification, then the local-DP requirement, rather than edge confidentiality per se, is the source of the extra statistical cost."],"forward_implications":["After edgeFlip, the privatized graph is itself a GRDPG with effective sparsity $\\sigma(\\varepsilon)^2\\rho_n$ and one additional latent dimension, so standard GRDPG inference tools can be applied once the $\\tau(\\varepsilon)^2$ offset is subtracted and the scale is corrected.","The minimax lower bound shows that local edge privacy reduces the effective sample size from $n$ to $\\sigma(\\varepsilon)^4 n$ and amplifies sparsity from $\\rho_n$ to $\\rho_n^2$; consequently, consistent latent-position recovery is possible only when $\\sigma(\\varepsilon)^4\\rho_n^2=\\tilde{\\Omega}(1/n)$, which can be read as a phase-transition boundary for private estimation.","Algorithm 1's rate matches the non-private minimax rate after replacing $\\rho_n$ by $\\sigma(\\varepsilon)^4\\rho_n^2$, up to the same $O(\\sqrt{\\log n})$ gap that already appears in the best-known non-private GRDPG bounds.","Persistence diagrams computed from the privacy-adjusted embedding converge to those of the latent positions at the same rate as the embedding itself, so private recovery of connected components, loops, and other topological features is achieved under $\\varepsilon$-edgeLDP."],"supporting_citations":[{"why":"Establishes the GRDPG spectral-embedding consistency theorem and the convex-combination characterization that Theorem 3.1 extends to edgeFlip.","marker":"[56]"},{"why":"Provides the non-private minimax rate and the $d_{2,\\infty}$ metric against which the private lower and upper bounds are compared.","marker":"[62]"},{"why":"Supplies the alignment-matrix and second-moment concentration lemmas used in the proof of Theorem 3.3.","marker":"[2]"},{"why":"Supplies the operator-norm tail bound for the privatized adjacency matrix used in Lemma B.3.","marker":"[41]"},{"why":"Provides the two-to-infinity perturbation bounds that control the embedding error in Theorem 3.3.","marker":"[10]"},{"why":"Contributes the edge-LDP chi-squared divergence argument that Theorem 3.2 adapts to latent-position estimation.","marker":"[42]"},{"why":"Introduces the edgeFlip-based edge-LDP community detection setting whose SBM analysis the present work generalizes.","marker":"[28]"},{"why":"Is the source of the edgeFlip randomized-response definition used in the paper.","marker":"[32]"}],"fun_headline_variants":["Edge flip preserves geometry for private recovery","Private graphs keep latent structure under edge flip","Optimal latent recovery from privatized dot-product graphs","Edge privacy does not distort latent positions","Geometry survives local differential privacy on edges"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The upper-bound proof assumes that spectral-concentration results proven for ordinary Bernoulli adjacency matrices carry over to the recentered privatized matrix $M_\\varepsilon(A)-\\tau(\\varepsilon)^2 11^T$, including a sparsity regime $n\\rho_n=\\omega(\\log n)$ that may be too sparse for those results; the paper itself notes that its introduction relies on the denser $\\omega(\\log^4 n)$ regime.","fun_headline_variants_meta":{"raw":{"variants":["Edge flip preserves geometry for private recovery","Private graphs keep latent structure under edge flip","Optimal latent recovery from privatized dot-product graphs","Edge privacy does not distort latent positions","Geometry survives local differential privacy on edges"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000175,"raw_usage":{"total_tokens":1285,"prompt_tokens":945,"completion_tokens":340,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":561,"completion_tokens_details":{"reasoning_tokens":275}},"tokens_in":561,"tokens_out":340,"duration_ms":3657,"temperature":1.0,"reasoning_tokens":275,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:46:08.079502+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate $A\\sim G(P,\\rho_n;p,q)$ with $n\\rho_n=\\log^{2.5} n$ (so $n\\rho_n=\\omega(\\log n)$ but $n\\rho_n=o(\\log^4 n)$), privatize with edgeFlip at a fixed $\\varepsilon$, run Algorithm 1, and measure $d_{2,\\infty}(\\hat X/\\sqrt{\\hat\\rho_n},X)$ across increasing $n$. If the error does not track $O\\bigl(\\log n/\\sqrt{n\\sigma(\\varepsilon)^4\\rho_n^2}\\bigr)$ and instead levels off, the spectral-concentration step imported from non-private GRDPG bounds is the failing link in the stated regime.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the GRDPG spectral-embedding consistency theorem and the convex-combination characterization that Theorem 3.1 extends to edgeFlip."},{"cited_title":"Minimax rates for latent position estimation in the generalized random dot product graph","cited_arxiv_id":"2307.01942","evidence_quote":"Provides the non-private minimax rate and the $d_{2,\\infty}$ metric against which the private lower and upper bounds are compared."},{"cited_title":"and Rinaldo, A","cited_arxiv_id":null,"evidence_quote":"Supplies the operator-norm tail bound for the privatized adjacency matrix used in Lemma B.3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the two-to-infinity perturbation bounds that control the embedding error in Theorem 3.3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contributes the edge-LDP chi-squared divergence argument that Theorem 3.2 adapts to latent-position estimation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the edgeFlip-based edge-LDP community detection setting whose SBM analysis the present work generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Is the source of the edgeFlip randomized-response definition used in the paper."}],"review_version":1}