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Pruning makes full-orbit binary pulsar searches tractable

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2026-07-09 01:45 UTC pith:3IE5BAA7

load-bearing objection Novel pruning algorithm for coherent binary pulsar search; sound framework but claims rest on simulated noise only the 1 major comments →

arxiv 2607.07700 v1 pith:3IE5BAA7 submitted 2026-07-08 astro-ph.HE astro-ph.IM

Coherent Signal Detection with Pruning -- I. Finding Short-Period Binary Pulsars in Circular Orbits

Pravir Kumar , Barak Zackay This is my paper
classification astro-ph.HE astro-ph.IM
keywords coherentorbitalsearchessensitivityaccelerationbeyondbinarycomputational
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper introduces Extreme Pruning (EP), a hierarchical search algorithm that progressively eliminates statistically implausible regions of parameter space across successive coherent integration stages. The central mechanism is a competition between polynomial growth of the search grid and exponential contraction of surviving noise candidates: because coherent signal power accumulates as the square root of integration time while noise candidates die off exponentially, pruning thresholds can be set so that the total computational cost converges to a finite bound rather than scaling polynomially with observation duration. A multi-pass ensemble strategy runs many cheap, aggressively pruned searches anchored at different data segments, treating each as an independent Bernoulli trial and combining them binomially to recover high overall detection probability at a fraction of the cost of a single high-sensitivity pass. Applied to circular-orbit binary pulsars, the method reduces computational complexity by up to ten orders of magnitude relative to unpruned hierarchical search, achieving greater than 90 percent detection probability at the sensitivity threshold while enabling, for the first time, fully coherent integration over an entire orbital period. The paper validates this on simulated data across constant-acceleration, constant-jerk, and full circular-orbit search regimes, and benchmarks a GPU implementation showing survey-scale feasibility.

Core claim

The core discovery is that the cost-sensitivity frontier for hierarchical coherent searches is strongly convex: per-pass detection probability can be driven very low (around 10 percent) at minuscule computational cost, and an ensemble of such cheap passes with well-separated anchor segments recovers ensemble detection probabilities exceeding 90 percent through binomial combination, because the early-stage pruning decisions across disjoint data segments behave as statistically independent trials. This converts a formally intractable ten-dimensional circular-orbit template enumeration into a bounded-complexity search whose cost is dominated by a characteristic pruning timescale rather than by总

What carries the argument

Extreme Pruning (EP): a hierarchical, multi-stage coherent search that (1) partitions the observation into base segments, (2) progressively accumulates and scores candidates on a refining parameter grid, (3) prunes candidates below stage-dependent thresholds optimized via Viterbi-style dynamic programming, and (4) runs an ensemble of such passes with different anchor segments, combining results binomially. A Polynomial Fast Folding Algorithm (P-FFA) provides the efficient base-segment initialization through dynamic programming with data reuse.

Load-bearing premise

The multi-pass ensemble strategy assumes that pruning runs with well-separated anchor segments behave as statistically independent Bernoulli trials. This independence is empirically validated for constant-acceleration and constant-jerk searches but shows modest deviations for the full circular-orbit search near the detection threshold, which the paper attributes to implementation-level discretization effects rather than a fundamental limitation.

What would settle it

If the effective number of independent pruning trials is substantially lower than the number of physically separated anchor segments (due to inter-run segment overlap or shared late-stage data), the ensemble detection probability would be systematically overestimated, particularly for high-dimensional searches.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Archival pulsar survey data (HTRU-S, PMPS, LOTAAS) can be reprocessed for compact binary systems at full coherent sensitivity for the first time, potentially discovering pulsars in orbits with periods of tens of minutes to a few hours that were invisible to acceleration-based searches.
  • Next-generation facilities like SKA can run fully coherent jerk or circular-orbit searches in near real-time on modest GPU clusters, preventing sensitivity loss at the search stage for the most compact binaries.
  • Globular cluster observations, which require few beams and narrow DM ranges, become prime targets for deep circular-orbit EP searches covering multiple orbital cycles, accessing ultra-compact and ultra-fast pulsar populations.
  • The pruning principle is general and applicable to other inference problems with structured phase models beyond pulsar searching.
  • A 3- to 5-fold sensitivity improvement over conventional acceleration searches translates directly to a cubed-to-fifth-power increase in searchable volume for compact binary pulsars.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The convexity of the cost-sensitivity frontier (Figure 12) suggests a natural economic interpretation: the marginal cost of an additional unit of detection probability diverges as probability approaches unity, meaning there is a well-defined optimal operating point that depends on the ratio of compute cost to scientific value of a missed detection.
  • The basis-transition strategy from polynomial to Cartesian circular-orbit coordinates (Section 6.3) implies that searches over multiple orbital cycles could scale as T-squared rather than T-to-the-tenth, which would make multi-orbit coherent integration dramatically cheaper than single-orbit searches per unit of phase coverage.
  • The phase-trap phenomenon near zero-acceleration orbital phases (Figure 18) suggests that an adaptive anchor-selection strategy that avoids seeding in these regions could recover the lost 5 percent of orbital phases without additional compute cost.
  • If the independence assumption holds more broadly, the multi-pass ensemble strategy could be applied to other hierarchical search problems in astronomy (e.g., gravitational wave template banks) where a single high-completeness search is prohibitively expensive.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 7 minor

Summary. This paper introduces Extreme Pruning (EP), a hierarchical search framework that combines progressive candidate elimination with the Polynomial Fast Folding Algorithm (P-FFA) to enable fully coherent searches for binary pulsars in circular orbits. The core idea is to prune statistically implausible parameter-space branches at intermediate integration stages, converting the polynomial scaling of template enumeration into a bounded asymptotic cost. A multi-pass ensemble strategy with well-separated anchor segments is used to recover high aggregate detection probability from low per-pass survival rates. The paper presents the mathematical framework (Sections 2–6), software implementation in LOKI (Section 7), and validation via signal injection in simulated white Gaussian noise (Section 5.5, Figure 15). The authors claim >90% detection probability at the sensitivity threshold and up to 10 orders of magnitude computational reduction relative to an unpruned hierarchical baseline.

Significance. The problem addressed is real and important: the compact-binary regime ($T_{obs} / P_{orb} sim 0.1$–$1$) is where scientific payoff is highest and where existing acceleration/jerk searches lose phase coherence. The EP framework, if it performs as described, would represent a genuine advance in making fully coherent circular-orbit searches computationally tractable. The paper ships a public C++20/CUDA implementation (LOKI) with Python bindings, which strengthens reproducibility. The complexity analysis (Section 2, Eqs. 1–4) is clean and the bounded-cost argument is well-constructed. The Viterbi-style threshold optimization (Section 5.4.2) is a thoughtful contribution. The multi-pass ensemble strategy (Section 5.5) is a clever exploitation of the convex cost–sensitivity frontier. However, the significance of the central claims is tempered by the fact that all validation is on simulated white Gaussian noise with no real telescope data, and the most demanding search configuration (full circular orbit) shows a measurable threshold shift that is not fully decomposed.

major comments (1)
  1. Section 5.5, Figure 15 (right column): For the full circular-orbit search, the empirical ensemble detection probability shows a rightward shift relative to the independent-trial binomial prediction of Eq. (70), with complete recovery requiring $Z gtrsim 12$ versus the nominal $Z_t = 10$ (a ~20% threshold penalty). The paper attributes this to 'accumulated discretization effects arising from finite phase tolerance ($eta$), residual phase transport errors, and higher-dimensional tiling losses' but does not decompose the individual contributions. This matters because the abstract claims '>90% detection probability at the sensitivity threshold.' If tiling gaps from the aggressive diagonal-only scheme (Section 5.2.4) dominate the shift, this is not an implementation-level artifact but a fundamental trade-off of the chosen tiling strategy, and the headline claim should be qualified accordingly
minor comments (7)
  1. Section 5.2.4: The paper adopts aggressive tiling as the operational default but states that sensitivity gaps 'must then be controlled empirically, for example by tightening the search tolerance $eta$.' It would help to state whether the $eta=1.0$ used in Figure 15 already reflects such tightening, or whether additional tightening was applied for the circular-orbit benchmark.
  2. Section 5.4.1, paragraph on Monte Carlo framework: The resampling/duplication procedure used to maintain trial populations introduces correlations that 'slightly increases the variance of the final $P_d$ estimates.' No quantitative bound on this variance inflation is given. A brief statement of the expected magnitude would strengthen the reader's confidence in the threshold optimization.
  3. Section 6.2.5, Figure 18(a): The phase-trap dropouts where $P_d$ collapses near zero are noted but their impact on the ensemble detection probability is not quantified. Since these affect <5% of anchor positions, a brief statement confirming that the multi-pass ensemble with $n_{run} = 16$–$32$ is not systematically degraded by these traps would be useful.
  4. Table 1: The 'EP Gain' column reports orders-of-magnitude reduction relative to an 'unpruned hierarchical baseline.' It would be helpful to clarify whether this baseline includes the P-FFA data-reuse speedup (Eq. 41) or is purely brute-force folding, as this affects interpretation of the gain factor.
  5. Section 8.1: The projected GPU-hours for archival reprocessing (e.g., 85M GPU-hours for HTRU-S circular-orbit search) are described as 'conservative upper bounds.' The assumptions behind these estimates (number of DM trials, frequency range) should be stated explicitly for each survey entry in Table 2.
  6. Abstract: The claim of '3- to 5-fold improvement in sensitivity' relative to conventional acceleration searches is not directly demonstrated in the validation section. This appears to follow from the extended coherent integration time rather than an explicit injection-recovery comparison. Consider qualifying this as a projected improvement.
  7. Section 3.3.2: The choice of $Z_alpha$ (Eq. 18) over the statistically optimal $Z_beta$ (Eq. 19) is stated as a computational convenience. Since sensitivity claims depend on the detection statistic, a brief quantification of the suboptimality of $Z_alpha$ for the duty cycles relevant to MSPs would be informative.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee's single major comment is well-taken: the threshold shift in the full circular-orbit search is not decomposed, and the abstract claim should be qualified. We agree to revise accordingly.

read point-by-point responses

  1. Referee: Section 5.5, Figure 15 (right column): For the full circular-orbit search, the empirical ensemble detection probability shows a rightward shift relative to the independent-trial binomial prediction of Eq. (70), with complete recovery requiring Z ≳ 12 versus the nominal Z_t = 10 (a ~20% threshold penalty). The paper attributes this to 'accumulated discretization effects arising from finite phase tolerance (η), residual phase transport errors, and higher-dimensional tiling losses' but does not decompose the individual contributions. This matters because the abstract claims '>90% detection probability at the sensitivity threshold.' If tiling gaps from the aggressive diagonal-only scheme (Section 5.2.4) dominate the shift, this is not an implementation-level artifact but a fundamental trade-off of the chosen tiling strategy, and the headline claim should be qualified accordingly.

    Authors: The referee is correct on both counts: (1) we did not decompose the individual contributions to the threshold shift, and (2) the abstract claim '>90% detection probability at the sensitivity threshold' is not adequately qualified given the observed ~20% threshold penalty for the full circular-orbit search. We will revise the manuscript to address both issues. revision_made = 'yes' On the decomposition: we agree that attributing the shift to a generic list of effects without quantifying their relative contributions is insufficient. In the revised manuscript, we will add a controlled ablation study using the existing injection framework, isolating each contribution by toggling them independently: (a) varying η (1.0 → 0.5 → 0.25) to isolate grid discretization losses, (b) switching between time-domain and Fourier-domain folding to isolate phase-shift quantization, and (c) switching between aggressive and quadrature tiling (Section 5.2.4) to isolate tiling-gap losses. This will directly show which effects dominate. On the tiling concern specifically: the referee raises a legitimate point about whether the aggressive diagonal-only tiling is a fundamental design trade-off rather than a mere implementation artifact. We acknowledge that our current characterization of the shift as 'implementation-level' is not fully supported without the decomposition. The aggressive tiling scheme was adopted as the operational default because it is the only strategy that maintains bounded computational cost across all anchor segments (Section 5.2.4, Figure 7); the quadrature alternative inflates the branching factor by orders of magnitude and is therefore not a drop-in replacement. If the ablation confirms that tiling gaps are the dominant contributor, we will state this explicitly and frame它— revision: no

Circularity Check

0 steps flagged

No circularity found: derivation chain is self-contained with independent validation

full rationale

The paper's derivation chain is self-contained and does not exhibit circularity. The central claims rest on three pillars: (1) the pruning concept (Section 2), derived from the statistical separation of H0 and H1 distributions under coherent integration — a standard signal-processing argument; (2) the threshold optimization (Section 5.4.2), which uses Monte Carlo simulations of pruning dynamics under known noise (H0: Gaussian) and signal (H1: known injection) models to calibrate stage-dependent thresholds via Viterbi-style dynamic programming — this is standard calibration against a known forward model, not fitting to the target result; (3) the multi-pass ensemble strategy (Section 5.5), whose binomial prediction P_ensemble = 1-(1-P_d)^{n_run} (equation 70) is validated against 50 independent signal injections per configuration (Figure 15), with the paper honestly reporting a ~20% threshold shift for the circular-orbit case and attributing it to discretization effects rather than claiming perfect agreement. The complexity reduction claim (up to 10 orders of magnitude) follows directly from the algorithm's structure: exponential pruning of noise candidates versus polynomial expansion of the search grid, quantified by counting surviving candidates under the calibrated thresholds. The thresholds are calibrated on simulated H0/H1 models and applied to independent validation injections — the prediction (binomial ensemble probability) is not forced by construction. The only in-preparation self-citation (D. Gazith et al. 2026) concerns the Kadane-based boxcar scoring optimization, which is a minor implementation detail not load-bearing for any central claim. No uniqueness theorems are invoked, no ansatz is smuggled through self-citation, and no result is renamed from a known empirical pattern.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 3 invented entities

The free parameters are design choices (eta, P_d, n_run, C_max) rather than fitted constants, and the paper is transparent about this. The key domain assumptions (white Gaussian noise, constant signal amplitude) are standard in pulsar search but represent real limitations. The independence assumption for multi-pass pruning is the most ad hoc axiom and is only partially validated. No new physical entities are postulated; the invented entities are algorithmic constructs validated on simulated data.

free parameters (6)
  • eta (phase tolerance) = 1.0-2.0 in benchmarks
    Controls grid density vs. computational cost trade-off; chosen by hand, not derived from data
  • P_d (per-pass detection probability) = 0.05-0.10
    Set to achieve target ensemble sensitivity; optimized via Viterbi DP but the target itself is a design choice
  • n_run (number of ensemble passes) = 16-32
    Chosen to achieve P_ensemble > 0.9; not derived from first principles
  • C_max (candidate buffer limit) = ~10^7
    Set by available memory hardware; affects achievable P_d
  • T_seg (base segment duration) = T_obs/128
    Determined by P-FFA termination level; chosen for computational tractability
  • Z_t (detection threshold) = 8.2-10.0
    Calibrated from enumeration volume and false-alarm budget; not a fitted constant but a survey design parameter
axioms (6)
  • domain assumption Noise is white and Gaussian after pre-processing
    Invoked in Section 2 (equation 1-2) and Section 5.4.1 for threshold calibration; real pulsar data has red noise and RFI
  • domain assumption Signal amplitude is constant over the observation
    Invoked in equation 1 for S/N ~ sqrt(t) scaling; pulsars exhibit scintillation and profile variations
  • domain assumption Orbits are circular
    Stated in Section 3; motivated by spider system astrophysics but excludes eccentric systems
  • domain assumption Sky position is known to within beam uncertainty
    Section 3; standard assumption for pulsar searches but limits blind survey applicability
  • ad hoc to paper Pruning runs with separated anchors are statistically independent
    Section 5.5, equation 70; validated empirically for polynomial searches but approximate for circular orbits
  • domain assumption Phase errors accumulate as random walk across merge stages
    Section 4.3.1; assumes uncorrelated nearest-neighbor offsets which may not hold for structured grids
invented entities (3)
  • Extreme Pruning (EP) algorithm independent evidence
    purpose: Hierarchical candidate elimination for binary pulsar search
    Validated via injection-recovery tests on simulated data (Figure 15); code is public
  • Polynomial FFA (P-FFA) independent evidence
    purpose: Generalized fast folding for polynomial phase models
    Benchmarks on simulated data (Figure 20); recovers standard FFA scaling for k_max=0
  • Phase debt mechanism no independent evidence
    purpose: Tracks deferred phase rotations in hierarchical accumulation
    Described in Section 5.3 but not independently validated; correctness depends on implementation

pith-pipeline@v1.1.0-glm · 62954 in / 3426 out tokens · 680267 ms · 2026-07-09T01:45:04.581831+00:00 · methodology

0 comments
read the original abstract

Detecting pulsars in short-period binary systems, which are unparalleled laboratories for fundamental physics and tests of general relativity, is a prime objective of radio astronomy. Their rapid orbital motion, however, presents a formidable computational challenge. Conventional searches are therefore limited to simplified signal models (e.g., constant acceleration) that remain valid for only short integrations ($\lesssim 4$-$10$% of an orbital period). This fundamental limitation severely degrades search sensitivity, placing much of the faint, relativistic pulsar population beyond the reach of current surveys. We present a novel hierarchical search framework based on extreme pruning that overcomes these limitations by progressively eliminating improbable regions of parameter space across successive coherent integration stages. The algorithm achieves $>90$% detection probability at the sensitivity threshold, with near-unity recovery for stronger signals, while reducing the computational complexity of full circular-orbit searches by up to 10 orders of magnitude relative to an unpruned hierarchical baseline. The resulting efficiency enables, for the first time, fully coherent integration over an entire orbital period and beyond. Compared to conventional acceleration searches, the proposed method delivers a 3- to 5-fold improvement in sensitivity, dramatically increasing the discovery potential for high-value targets such as pulsar-black hole binaries.

Figures

Figures reproduced from arXiv: 2607.07700 by Barak Zackay, Pravir Kumar.

Figure 1
Figure 1. Figure 1: Statistical snapshot of the pruning process at an intermediate stage. The noise distribution (H0, gray) is shifted from zero due to the maximization over search parameters (look-elsewhere effect). The signal distribution (H1, blue) separates to higher values as integration time increases. The pruning threshold Z𝑡 (red dashed line) acts as a filter: the gray shaded region represents pruned candidates (elimi… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the bottom-up, breadth-first P-FFA merge. An ob￾servation of duration 𝑇obs is partitioned into eight equal segments. Fold￾ing profiles are initialized at stage 0 on the coarsest parameter grid. Each subsequent stage coherently combines profiles from adjacent segments in a level-synchronous manner, halving the number of segments at each step until profiles spanning the full observation on the f… view at source ↗
Figure 3
Figure 3. Figure 3: Convergence analysis of P-FFA sensitivity for injected pulsar signals. Each panel shows the recovered significance or (𝑆/𝑁 ) 2 fraction 𝑅 = (Zdetected/Zinjected ) 2 , as a function of pulsar duty cycle, for two simulated test cases in white Gaussian noise. Panel (a–b): Pulsar with an intrinsic period of 10 ms. Panel (c–d): Same period (10 ms), but with a constant acceleration of 100 m s−2 . Coloured lines … view at source ↗
Figure 4
Figure 4. Figure 4: Schematic of the hierarchical merging step of the EP algorithm for the edge-forward scheme (𝑞 = 0). An observation of duration 𝑇obs is partitioned into eight equal segments. Folding profiles are initialized at stage 0 on the base grid for each segment. Each subsequent stage coherently adds the next segment to the accumulated profile states, refining the grid as the coherent span increases, until the profil… view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the pruning procedure used in the EP algorithm. Each node represents a surviving candidate after scoring at a given stage, and each branch corresponds to refinement onto the finer parameter grid of the next stage. Candidates falling below the stage-specific threshold are pruned, so that only high-significance branches are propagated forward. key operations: refining each surviving parameter no… view at source ↗
Figure 6
Figure 6. Figure 6: Grid tiling problem in the Taylor basis, illustrated as a 2D projection in the acceleration–jerk (𝑑2–𝑑3) plane; the actual search space could be higher-dimensional, so tiling inefficiencies compound with dimension. Panel (a): At reference epoch 𝑡𝑠, an axis-aligned search tile is subdivided into finer orthogonal child cells. Panel (b)–(d): Advancing the epoch to 𝑡𝑠 + Δ𝑡 introduces off-diagonal coupling in t… view at source ↗
Figure 7
Figure 7. Figure 7: Cumulative grid size, expressed as the product of branching factors 𝐵(𝑠), for different reference-frame, basis, and tiling strategies. The example assumes a circular-orbit search (𝑃orb ≥ 𝑇obs) over an 18-min observation divided into 128 segments (𝜂 = 1.0, 𝑁𝑏 = 64). Fixed grid strategies are shown for both the best-case midpoint reference (𝑞 = 64; dotted lines) and the worst-case edge reference (𝑞 = 0; dash… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of three heuristic threshold schemes for a circular-orbit search (𝑃orb ≥ 𝑇obs) over an 18-min observation divided into 128 segments (𝜂 = 1.0, 𝑁𝑏 = 64, target S/N = 10). Panel (a): Stage-wise (S/N) 2 thresholds. The Bound scheme (green) increases thresholds linearly with stage. The Trials-aware scheme (magenta) adapts to per-stage false-alarm probability in later stages. The Constant Load scheme … view at source ↗
Figure 9
Figure 9. Figure 9: Schematic representation of the threshold-optimization problem. Blue curves indicate the family of possible threshold paths through stage￾wise S/N space. The objective is to identify the optimal sequence {Z𝑡,𝑠 } (red path) that minimizes computational cost while achieving the desired detection probability. The full search space grows exponentially with the number of stages; eight stages are shown here for … view at source ↗
Figure 10
Figure 10. Figure 10: Viterbi-optimized threshold schemes for the same configuration as [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of Viterbi-optimized schemes (solid blue tones) with the heuristic schemes of [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ensemble pruning cost 𝐿 = 𝐶total/𝑃𝑑 versus cumulative de￾tection probability 𝑃𝑑 for the same search configuration as [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Schematic illustration of multi-pass pruning redundancy. The figure shows a subset of the search tree with initial branching pattern [4, 7, 1, 3] (additional branches omitted for clarity). Orange dashed lines indicate pruned nodes; green lines show survivors. Panel A: Full unpruned tree. Panels B–D: Three pruning runs anchored at segments 𝑞 = 0, 64, and 127. Each run traverses a distinct path through para… view at source ↗
Figure 15
Figure 15. Figure 15: Comprehensive validation of the EP framework ensembles for constant-acceleration (left), constant-jerk (centre), and full circular-orbit (right) searches as a function of injected signal significance Z. Bottom panels: Measured ensemble detection probability for 𝑛run = {1, . . . , 32} pruning passes, obtained from 50 independent signal injection per configuration. Faint curves show the prediction of the in… view at source ↗
Figure 16
Figure 16. Figure 16: illustrates the orbital geometry and these quantities. Kepler’s third law gives 𝑥 = sin 𝑖 𝑐 𝐺 1/3𝑚𝑐 (𝑚𝑝 + 𝑚𝑐) 2/3 Ω −2/3 orb , (78) where 𝑚𝑝 and 𝑚𝑐 are the pulsar and companion masses, respec￾tively. Substituting equation (77) into the generic phase model in equation (6) yields the circular-orbit phase model Φ(𝑡; 𝚲circ). The parameter vector 𝚲circ = { 𝑓int, 𝑥, Ωorb, 𝜓} defines a four-dimensional search sp… view at source ↗
Figure 17
Figure 17. Figure 17: Physical constraints on the polynomial search space in the snap (𝑑4) versus acceleration (𝑑2) plane for circular Keplerian orbits. The dashed box shows the full hyper-rectangular search region derived from 𝑃 min orb = 1 h, 𝑚𝑐,max = 10 𝑀⊙, and 𝑚𝑝,min = 1.2 𝑀⊙. The gray hatched quadrants (Q1 and Q3) are strictly unphysical, corresponding to unbound orbits. The pink and orange shaded regions are excluded by … view at source ↗
Figure 18
Figure 18. Figure 18: Dependence of detection probability and pruning-path autocorrelation on the anchor segment in the hierarchical EP search for a tuned threshold scheme targeting S/N = 10. Panel (a): Injection recovery performance for a circular-orbit search (𝑃orb ≥ 𝑇obs) over an 18-min observation divided into 𝑀 = 128 segments (𝜂 = 1.0, 𝑁𝑏 = 64). A signal with S/N = 15 was injected into 𝑛trials = 100 independent noise real… view at source ↗
Figure 19
Figure 19. Figure 19: Frequency chunking and folding-bin allocation used in P-FFA and EP searches. The main panel shows folding bins 𝑁𝑏 as a function of trial period. The dotted curve indicates the maximum limit 𝑏max, while the dashed curve shows the ideal continuous scaling corresponding to a constant physical bin width 𝑡𝑊. Solid curves show the discrete binning schemes adopted for different geometric growth factors 𝑔. The in… view at source ↗
Figure 20
Figure 20. Figure 20: Wall-clock runtime of the P-FFA search pipeline as a function of the tolerance parameter 𝜂 (panels a–b) and the number of samples 𝑁𝑠 (panels c–d), for constant-period (panels a, c) and constant-acceleration (panels b, d) searches per DM trial. Panels (a) and (b) correspond to SKA1-mid-like configurations with 𝑁𝑠 = 2 25 and 2 23, respectively. Panels (c) and (d) show scaling with 𝑁𝑠 at fixed 𝜂 = 1.0 and 2.… view at source ↗
Figure 21
Figure 21. Figure 21: Wall-clock runtime of the EP search pipeline for four survey configurations per DM trial. Top row (panels a–d): tolerance scan at fixed time-series length; bottom row (panels e–h): scaling with the number of samples 𝑁s at fixed tolerance. From left to right, the columns show a 5× inflated constant￾acceleration search, a jerk search, a snap search, and a fully coherent circular-orbit search. In panels (a)–… view at source ↗

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