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Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data

T0 review · 1 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Active label selection can push individualized threshold estimation to the parametric rate, beating the passive minimax rate when the conditional density is sufficiently smooth.

desk verdict A promising phase-transition result undermined by a failing RSC verification for most β in the claimed range. read the letter →

arxiv 2411.13763 v2 pith:OBPFCX3D submitted 2024-11-21 math.ST stat.MEstat.MLstat.TH

Jingyi Duan , Lehao Fu , Yang Ning This is my paper · ORCID
classification math.STstat.MEstat.MLstat.TH MSC 62F1262C2062G20
keywords activesubsamplingmeasurement-constrainedestimationindividualizedthresholdhigh-dimensionalM-estimationkernelsmoothingphasetransitionminimaxoptimalitysparsity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks which data points to label when labels are scarce but covariates are cheap, for the problem of estimating the optimal individualized threshold $\theta^*$ in a linear decision rule $X \gtrless \theta^{T}Z$. The authors propose a $K$-step active subsampling algorithm that starts with a uniformly sampled regularized M-estimator, then repeatedly samples only the observations whose $X-\hat\theta_{k-1}^TZ$ lies near zero---the most informative for the threshold---and refits. The central claim is a phase transition in $\beta$, the H\"older smoothness of the conditional density of $X$ given $(Y,Z)$: for $\beta>(1+\sqrt{3})/2$ the two-step estimator reaches the parametric rate $O_p((s\log d/N)^{1/2})$, strictly faster than the passive minimax rate $(s\log d/N)^{\beta/(2\beta+1)}$, and matches the newly formulated $N$-budget minimax lower bound up to a log factor. For $1<\beta\le(1+\sqrt{3})/2$ the same rate needs a fixed finite number of steps $>2$, and for $\beta=1$ only a near-parametric rate is attainable. A sympathetic reader should care because in settings like electronic health record studies the bottleneck is the cost of chart review, not the availability of covariates; the paper shows this bottleneck can be partially broken by adaptive label selection.

What carries the argument

The argument is carried by a zoom-in sampling rule. At each step $k\ge2$, the algorithm defines the active set $S_k=\{(X,Z): -b_{k-1}\le (X-\hat\theta_{k-1}^TZ)/\sqrt{1+\|\hat\theta_{k-1}\|_2^2}\le b_{k-1}\}$ and samples only from this thin band around the current estimated threshold, with probability $c_{n,k}$ proportional to the available budget. The loss is a smoothed surrogate $L_\delta$ built from a kernel of order $\lfloor\beta\rfloor$, whose kernel smoothing creates a bias of order $c_{n,k}\delta_k^\beta$ and a stochastic error of order $\sqrt{c_{n,k}K\log d/(n\delta_k)}$; balancing these gives $\delta_k\asymp(b_{k-1}s\log d/N)^{1/(2\beta+1)}$ and the per-step rate $\|\hat\theta_k-\theta^*\|_2\lesssim(b_{k-1}s\log d/N)^{\beta/(2\beta+1)}$. Since the active set has probability $\asymp b_{k-1}$, each iteration multiplies the rate by a power of the band width $b_{k-1}$, and the stability condition $b_{k-1}\ge C\max\{\delta_k,\|\hat\theta_{k-1}-\theta^*\|_2\sqrt{\log(N/(s\log d))}\}$ determines how small $b_{k-1}$ may be chosen. The phase transition occurs because for $\beta>(1+\sqrt{3})/2$ the first-step estimator already lands in the "fast convergence region" where $\|\hat\theta_1-\theta^*\|_2$ is at most order $\delta_2$, so one more step reaches the parametric rate; for smaller $\beta$ several steps are needed to reach that region, and for $\beta=1$ it is never reached.

What would settle it

Check Assumption 3.5 numerically for a logistic-regression threshold model with $\beta=1.5$: compute the minimum sparse eigenvalue of $\nabla^2 R^{D_k}_{\delta_k}(\theta)$ over $\theta$ in the ball $\{\theta:\|\theta-\hat\theta_{k-1}\|_2\le R_{k-1}\}$; if it is not proportional to $c_{n,k}$ with high probability, the rate theorem's foundation fails. Alternatively, simulate the two-step algorithm with increasing $N$ and verify empirically whether the $\ell_2$ error tracks $(s\log d/N)^{1/2}$ rather than the passive rate.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that active label selection can convert a non-regular high-dimensional estimation problem into one that behaves like a regular parametric problem. Concretely, when the conditional density of $X$ given $(Y,Z)$ is $\beta$-smooth with $\beta>(1+\sqrt{3})/2$, the estimator produced by two iterations of the proposed algorithm satisfies $\|\hat\theta_K-\theta^*\|_2 = O_p((s\log d/N)^{1/2})$ with high probability, while the best passive estimator using $N$ i.i.d. labels has rate $(s\log d/N)^{\beta/(2\beta+1)}$. The same parametric rate is achieved for $1<\beta\le(1+\sqrt{3})/2$ by running $K=\lceil \log_{\beta/(2\beta+1)}(1-(\beta+1)/(2\beta^2))\rceil+1$ iterations, and for $\beta=1$ only $\|\hat\theta_K-\theta^*\|_2 = O_p((\log(N/(Ks\log d)))^{1/4}(Ks\log d/N)^{1/2})$ is obtained with $K=\lceil\log_3(\log N)\rceil$. The paper also defines an $N$-budget minimax risk over label-sampling distributions and proves the lower bound $(s\log(d/s)/N)^{1/2}$, showing the active estimator is minimax optimal up to logarithmic factors and that unlabeled covariates do not improve the rate.

Load-bearing premise

Assumption 3.5 — that the smoothed, selectively sampled risk is strongly convex and smooth on shrinking balls around each previous estimate — is the load-bearing condition; the paper verifies it only for a conditional mean model with Gaussian noise and assumes it for the general binary response and conditional mean classes used in the main theorems.

Editorial extensions

If this is right

  • If the density is $\beta$-smooth with $\beta>(1+\sqrt{3})/2$, two labeling rounds with budget split $N_1=N/8$, $N_2=7N/8$ give the same $\ell_2$ accuracy as a parametric estimator using $N$ labels; additional rounds do not improve the rate.
  • The $N$-budget minimax lower bound $(s\log(d/s)/N)^{1/2}$ implies that no sampling scheme in the permitted class can beat the proposed algorithm's rate by more than a log factor, and that the unlabeled pool adds no rate benefit once labels are actively selected.
  • For intermediate smoothness $1<\beta\le(1+\sqrt{3})/2$, the practical protocol should budget for more than two rounds; the required number of rounds is fixed and finite, independent of $N$.
  • When only Lipschitz smoothness ($\beta=1$) holds, the achievable rate carries an extra $(\log N)^{1/4}$ factor even with $K=\lceil\log_3(\log N)\rceil$ rounds, so the gain over passive sampling is only logarithmic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate practical reading: when analysts cannot verify that the conditional density is smoother than $1.37$-H\"older, running $K=2$ is still a safe default because the dominant improvement happens between the first and second iterate, and the second iterate's tuning is simpler.
  • The rate improvement implies a direct cost translation: for $\beta>(1+\sqrt{3})/2$, the same $\ell_2$ error as passive sampling with $N$ labels is reached with roughly $(s\log d)^{(1-1/(2\beta))}N^{1-1/(2\beta)}$-style fewer labels; in EHR chart-review budgets this converts into concrete dollar savings, though the paper does not quantify this.
  • The proof's reliance on a region-sampling class suggests a natural stress test: allow sampling probabilities that depend on $Z$ beyond the bounded-probability and sparse-eigenvalue constraints, and see whether the lower bound still holds; one would suspect it does, because the Fano construction already chooses $Z$ uniform on $[-1,1]$.
  • A testable extension the authors mention but do not pursue is Lepski-type adaptation to unknown $\beta$; the paper's own simulations fix $K=2$ and cross-validate the bandwidth, so an empirical study measuring achieved rates under unknown $\beta$ would tell whether the phase-transition recommendation is robust.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper studies measurement-constrained estimation of a high-dimensional individualized threshold parameter θ* in the M-estimation problem (1.2), where only N of n available units can be labeled. It proposes a K-step active subsampling algorithm that uses the current estimator to define an 'active set' of observations with X close to the current threshold, and focuses label acquisition there. The main theoretical claim is a phase transition in the Hölder smoothness β of the conditional density of X given (Y,Z): for β > (1+√3)/2, a two-step version attains the parametric l2 rate (s log d / N)^{1/2}, faster than the passive i.i.d. minimax rate (s log d / N)^{β/(2β+1)} and matching the paper's N-budget minimax lower bound up to logarithmic factors; for 1 < β ≤ (1+√3)/2 the same rate requires a finite K > 2 depending on β, and for β = 1 only a near-parametric rate with K = O(log log N) is obtained. The paper also gives implementation details, a data-driven version with cross-validation, simulations, and a diabetes readmission application.

Significance. If the results hold, the phase transition is significant: it shows that active subsampling can overcome the slow non-regular rate of threshold M-estimators and achieve parametric accuracy in high dimension under a label budget, with a matching lower bound in a carefully defined class of adaptive sampling mechanisms. The proposed algorithm is concrete and computationally practical, and the N-budget minimax framework (the class Q_N(P(β,s))) is a useful formalization for measurement-constrained active estimation. The paper ships no code, but the simulations and real-data analysis illustrate the potential practical value.

major comments (1)
  1. [Section A.7, Eq. (A.76); Theorem 2] The verification of Assumption 3.5 in Section A.7 is incompatible with the tuning of Theorem 2 over a substantial part of the claimed range. Proposition A.4 requires condition (A.76), namely s M_n^3 √s / δ_k^3 · (s log d / N)^{β/(2β+1)} = o(1). Theorem 2 sets δ_k = c_1 (s log d / N)^{1/(2β)} for every k ≥ 2. Substituting gives s^{3/2} M_n^3 (s log d / N)^{β/(2β+1) - 3/(2β)}. The exponent is negative for all β < (3+√15)/2 ≈ 3.436, which includes the entire interval (1+√3)/2 < β ≤ 3.436 covered by Theorem 2. Since s log d = o(N), the left-hand side diverges as N grows, so (A.76) fails. This matters because Theorem 1 (and hence Theorem 2) passes through Assumption 3.5, and the appendix's verification is the only concrete evidence that this load-bearing condition holds for a nontrivial model. The paper therefore does not currently establish the parametric-rate claim for the conditional mean model on the advertised range of β, and the phase-transition threshold (1+√3)/2 is not supported by the provided verification.
minor comments (4)
  1. [Section 1.3 / Definition 3.1] The notation is nonstandard: ⌊β⌋ is defined as the greatest integer strictly less than β. In standard usage, floor(β) is the greatest integer ≤ β. For integer β this changes the kernel order l from β to β-1. If the intended definition is l = ⌈β⌉-1, please state that explicitly.
  2. [Lemma A.3] The statement of Lemma A.3 writes θ_j = c√s (s log(d/s)/N)^{1/2} ω_j, but the proof and equation (A.33) imply θ_j = c (s log(d/s)/N)^{1/2} ω_j / √s. This is a typo, but it affects the displayed form of the hypotheses in the lower-bound construction and should be corrected.
  3. [Section 1] The text states that for 1 < β ≤ (1+√3)/2 the required number of iterations K is strictly greater than 2. At the endpoint β = (1+√3)/2, the formula in Theorem 3 gives K = ⌈log_{β/(2β+1)}(1 - (β+1)/(2β^2))⌉ + 1 = 2, so the statement 'strictly greater than 2' is false at that boundary. Please qualify the statement to reflect the endpoint behavior.
  4. [Section 5] The simulations set δ1 = δ2 = 1 and use a Gaussian kernel, whereas the theory (Theorems 2–4) assumes a compactly supported kernel of order l with bandwidths δ_k → 0 that are specific functions of s, d, N, and n. The text explains the practical choice, but it would be helpful to comment explicitly on the gap between the implemented bandwidth and the theoretical regime, and on whether the simulation results should be interpreted as supporting the theoretical rates or only the algorithm's practical performance.

Circularity Check

1 steps flagged · score 4.0 of 10

Rates are not fitted, but the appendix's verification of the load-bearing RSC/RSM assumption invokes Theorem 2's own rate conclusions, making that support circular.

  1. self definitional [Section A.7 (verification of Assumption 3.5), opening paragraph; Assumption 3.5 in Section 3.1]
    "Recall that in Theorem 2, we showed that with high probability, ∥ bθ1 − θ∗∥2 ≲ (s log d/N)^{β/(2β+1)} and ∥ bθk − θ∗∥2 ≲ (s log d/N)^{1/2} for 2 ≤ k ≤ K. ... Therefore, it suffices to verify Assumption 3.5 on the set Ω = {θ : ∥θ − bθk−1∥2 ≲ (s log d/N)^{β/(2β+1)}} at the kth iteration for any 2 ≤ k ≤ K."

    Assumption 3.5 is one of the assumptions under which Theorem 2 is proved (Theorems 2-4 are stated under Assumptions 3.1-3.5). The appendix's 'detailed verification' of Assumption 3.5 chooses the localized set Ω_{k-1} using the rates of bθ_{k-1} that are exactly the conclusions of Theorem 2 (for k≥2, the parametric rate; for k=2, the bθ1 rate from Theorem 1). Thus the RSC/RSM premise is justified by the same theorem that requires it. A simultaneous-induction reformulation could repair this, but as written the verification is not independent. Separately, Proposition A.4's condition (A.76) is incompatible with Theorem 2's δ_k ≍ (s log d/N)^{1/(2β)} tuning for β in ((1+√3)/2, (3+√15)/2), so the appendix does not establish the condition under the theorem's own tuning in that regime.

full rationale

The main rate derivation (Theorem 1 to Theorems 2-4) is not circular: the master rate comes from balancing kernel bias cn,kδ^β with stochastic error sqrt(cn,kK log d/(nδ_k)) via λ_k and δ_k, and the parametric rate follows algebraically from bk−1 = Δ^{1/(2β)} satisfying bk−1 ≥ Cδ_k and the event W_{k−1}; the phase-transition threshold (1+√3)/2 is the feasibility condition for that choice. The N-budget lower bound is an independent hypothesis-construction argument with θ_j at the target scale, not fitted to the upper bound. Self-citations to Feng et al. (2022) for path-following lemmas and the k=1 RSC base case are load-bearing but external published support, so they do not by themselves make the argument circular. The circularity I do find is localized to Section A.7: the paper says it verifies Assumption 3.5, but the verification uses Theorem 2's rate bounds, which are proved under Assumption 3.5. Because Assumption 3.5 is the load-bearing condition through which all upper-bound rates pass, this circular verification is material; the honest reading is that Theorems 2-4 are valid conditional implications, while the claimed verification of the condition for the conditional mean model is not self-contained. There is also a non-circular correctness gap: condition (A.76) fails under Theorem 2's tuning for a large part of the claimed β-range. Score 4 reflects a central claim with independent content and one partially circular support step, not a derivation that reduces to its inputs.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The upper-bound theorems rest on Assumptions 3.1-3.5 plus scale conditions, and the lower bound relies on a constrained sampling class. No new physical or statistical entities such as new particles or latent variables are introduced. The theory's tuning parameters depend on unknown beta and s, leaving a gap between the formal rates and the practical CV-based implementation.

free parameters (4)
  • Active set half-width b_{k-1} = c3(s log d/N)^(1/(2 beta)) in Theorem 2; cross-validated in Algorithm 3
    The size of the sampling window controls the rate gain; the theory gives a formula depending on unknown beta, while the practical algorithm tunes b by cross-validation.
  • Bandwidth delta_k = c1(s log d/N)^(1/(2 beta+1)) in the first step and b-dependent values later; set to 1 in simulations
    Balances kernel bias and stochastic error; the theoretical optimal value depends on beta and N, but the implementation fixes delta=1 and does not reproduce the theoretical tuning.
  • Regularization parameter lambda_k = c2 sqrt(N log d/(n^2 b_{k-1} delta_k)); tuned by 5-fold CV in practice
    The lasso penalty must dominate the gradient stochastic error; the optimal value is theory-dependent and in practice is chosen by CV.
  • Smoothness parameter beta = assumed known in all theorems; not estimated
    The phase transition thresholds, the number of steps K, and all tuning formulas depend on beta. The paper only suggests Lepski adaptation as future work, so the main theorems do not cover the practical case of unknown beta.
assumptions (7)
  • domain assumption Assumption 3.1: theta* is s-sparse with ||theta*||_0 <= s and ||theta*||_2 <= C.
    Needed for lasso-type rates and restricted strong convexity; bounded norm avoids degeneracy.
  • domain assumption Assumption 3.2: Z is bounded or sub-Gaussian, P(Y=1) is bounded away from 0 and 1, and sparse eigenvalues of E[ZZ^T | Y=y] are bounded.
    Used for concentration inequalities and for controlling the plug-in error of the previous estimator in the active set.
  • domain assumption Assumption 3.3: The conditional density f(x|y,z) is beta-Holder at x = theta*^T z with beta >= 1, with upper and lower bounds in a neighborhood of the threshold.
    Determines the bias order delta^beta and drives the phase transition in beta.
  • standard math Assumption 3.4: The kernel K is of order l = floor(beta), symmetric, bounded, with finite moment conditions.
    A standard kernel assumption used to control higher-order bias in the smoothed gradient.
  • ad hoc to paper Assumption 3.5: Restricted strong convexity and restricted smoothness of the subsampled smoothed risk on localized balls hold with constants proportional to the sampling probability.
    This is the load-bearing high-level condition. The paper does not verify it from primitive assumptions for the general model; Section A.7 verifies it only for a conditional mean model.
  • domain assumption Sample size conditions (3.11), (3.13), (3.19): the pool size n must be large relative to the budget N, e.g. N <= C n^(2 beta/(2 beta+1)) (s log d)^(1/(2 beta+1)).
    Needed to keep the active-set sampling probabilities c_{n,k} below 1 and to ensure enough points fall into each active set.
  • domain assumption For the lower bound, the sampling class Q_N(P(beta,s)) imposes conditional independence, budget E sum Q_i <= N, and a sparse eigenvalue bound on the sampled design.
    Formalizes the measurement-constrained sampling mechanism; the N-budget minimax lower bound applies within this class.

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Cite this review

Pith. "Pith review of Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data." pith.science (2026). https://pith.science/paper/OBPFCX3D

@misc{pith2026241113763,
  author       = {Pith},
  title        = {Pith review of: Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OBPFCX3D}},
  note         = {Machine review of arXiv:2411.13763}
}
abstract

Measurement-constrained problems frequently arise in modern applications such as electronic health record studies. In such problems, despite the availability of large datasets, collecting labeled data can be highly costly or time-consuming, allowing only a small portion of the data to be labeled within a given budget. This raises a critical question: which data points are most beneficial to label given the budget constraint? We study this question in the context of estimating an optimal individualized threshold under a measurement-constrained M-estimation framework. In particular, our goal is to estimate a high-dimensional parameter $\theta$ in a linear threshold $\theta^TZ$ for a continuous variable $X$ such that the discrepancy between whether $X$ exceeds the threshold $\theta^TZ$ and a binary outcome $Y$ is minimized. In the measurement-constrained setting, we propose a novel $K$-step active subsampling algorithm to estimate $\theta$, which iteratively samples the most informative observations in the dataset and solves a regularized M-estimator. Our theoretical analysis reveals a sharp phase transition phenomenon with respect to $\beta$, the smoothness of the conditional density of $X$ given $Y$ and $Z$. Please see the paper for the full abstract.

Figures

Figures reproduced from arXiv: 2411.13763 by the authors.

Figure 1
Figure 1. ∥θb − θ ∗∥ in ℓ1 and ℓ2 norms under the logistic regression. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the label budget is used in the first step for both two-step sampling methods. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p028_1.png] view at source ↗
Figure 2
Figure 2. ∥θb− θ ∗∥ in ℓ1 and ℓ2 norms under the conditional mean model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the label budget is used in the first step for both two-step sampling methods. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_2.png] view at source ↗
Figure 3
Figure 3. ∥θb− θ ∗∥ in ℓ1 and ℓ2 norms under the binary response model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the label budget is used in the first step for both two-step sampling methods. References Balcan, M.-F., Broder, A. and Zhang, T. (2007). Margin based active learning. In Interna￾tional Conference on Computational Learning Theory. Springer. Balcan, M.-F. and Long, P. (2013). Active… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: ∥θb − θ ∗∥ in ℓ1 and ℓ2 for logistic regression. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the label budget is used in the first step for both two-step sampling methods. where we used the fact that (Xi , Zi) ⊥ H¯ i−1. Since the sparse e…
Figure 5
Figure 5. Figure 5: ∥θb − θ ∗∥ in ℓ1 and ℓ2 for conditional mean model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the label budget is used in the first step for both two-step sampling methods. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p074_5.png]
Figure 6
Figure 6. Figure 6: ∥θb − θ ∗∥ in ℓ1 and ℓ2 for binary response model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the label budget is used in the first step for both two-step sampling methods. 74 [PITH_FULL_IMAGE:figures/full_fig_p074_6.png]
Figure 7
Figure 7. Figure 7: ∥θb−θ ∗∥∞ and prediction error for logistic regression. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the total budget of labeled data is used in the first step for both two-step sampling methods. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_…
Figure 8
Figure 8. Figure 8: ∥θb − θ ∗∥∞ and prediction error for conditional mean model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the total budget of labeled data is used in the first step for both two-step sampling methods. 75 [PITH_FULL_IMAGE:figures/full_fig_…
Figure 9
Figure 9. Figure 9: ∥θb − θ ∗∥∞ and prediction error for binary response model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/8 of the total budget of labeled data is used in the first step for both two-step sampling methods. (a) (b) [PITH_FULL_IMAGE:figures/full_…
Figure 10
Figure 10. Figure 10: ∥θb−θ ∗∥∞ and prediction error for logistic regression. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the total budget of labeled data is used in the first step for both two-step sampling methods. 76 [PITH_FULL_IMAGE:figures/full_fig_p076…
Figure 11
Figure 11. Figure 11: ∥θb − θ ∗∥∞ and prediction error for conditional mean model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the total budget of labeled data is used in the first step for both two-step sampling methods. (a) (b) [PITH_FULL_IMAGE:figures/ful…
Figure 12
Figure 12. Figure 12: ∥θb − θ ∗∥∞ and prediction error for binary response model. LR: ℓ1 penalized logistic regression; PF: path-following algorithm. 1/5 of the total budget of labeled data is used in the first step for both two-step sampling methods. 77 [PITH_FULL_IMAGE:figures/full_fig_…

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    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.senten...

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.