Template bank for sub solar mass compact binary mergers in the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA

Aaron Viets; Alexander Pace; Alvin K. Y. Li; Amanda Baylor; Anarya Ray; Becca Ewing; Bryce Cousins; Chad Hanna; Cody Messick; Cort Posnansky

REVIEW 1 major objections 5 minor 98 references

Template bank for sub solar mass compact binary mergers in the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA

T0 review · 1 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A 3.45-million-template bank covers sub-solar-mass mergers across LIGO-Virgo-KAGRA's fourth observing run.

desk verdict Solid, workmanlike template-bank paper with a real validation gap at the lowest masses; worth a peer review. read the letter →

arxiv 2412.10951 v2 pith:IHSPIUEN submitted 2024-12-14 gr-qc

Chad Hanna , James Kennington , Wanting Niu , Shio Sakon , Divya Singh , Shomik Adhicary , Pratyusava Baral , Amanda Baylor

show 33 more authors

Kipp Cannon Sarah Caudill Bryce Cousins Jolien D. E. Creighton Becca Ewing Heather Fong Richard N. George Patrick Godwin Reiko Harada Yun-Jing Huang Rachael Huxford Prathamesh Joshi Soichiro Kuwahara Alvin K. Y. Li Ryan Magee Duncan Meacher Cody Messick Soichiro Morisaki Debnandini Mukherjee Alexander Pace Cort Posnansky Anarya Ray Surabhi Sachdev Stefano Schmidt Urja Shah Ron Tapia Leo Tsukada Koh Ueno Aaron Viets Leslie Wade Madeline Wade Zach Yarbrough Noah Zhang

This is my paper · ORCID

classification gr-qc PACS 04.30.-w04.80.Nn

keywords gravitationalwavestemplatebanksub-solarmasscompactbinariesmanifoldalgorithmmatchedfilteringprimordialblackholesLIGO-Virgo-KAGRAlow-latencysearch

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

The paper claims that the GstLAL pipeline now has template banks capable of searching for gravitational waves from compact binaries with a component below one solar mass throughout the fourth observing run, both in low latency and offline. To build them, the authors extend the geometric manifold placement algorithm down to component masses of 0.2 solar masses with two fixes: a neighborhood-based metric estimation for the unstable low-mass region and a boundary-padding step that adds a marginal bank along the low-mass edge. Simulated-signal tests (SBank) show that 90% of test signals spanning the archive bank's design space have a match of 97.42% or higher, and that the low-latency bank recovers 90% of its primary target signals at match 0.99. If these results hold, the search can place new constraints on primordial black holes and other exotic sub-solar-mass objects, and can issue low-latency alerts for potentially electromagnetically-bright low-mass mergers.

What carries the argument

The load-bearing machinery is the manifold treebank algorithm, a geometric placement method that tiles the intrinsic parameter space into hyperrectangular regions, each containing one template at its center, using a Fisher-information mismatch metric to decide when a region is too large. Two additions make it work at low masses: neighborhood metric estimation, which replaces a failed pointwise metric evaluation with the metric at a random nearby point inside a mismatch hyperellipsoid (up to a maximum number of attempts); and boundary padding, which unions the main bank with a smaller marginal bank extending past the low-mass boundary to raise fitting factors for extremal signals. The bank's efficacy is then tested with SBank, which computes the fitting factor of simulated signals against the bank.

What would settle it

Generate simulated 0.2–0.4 $M_\odot$ signals and match them against templates constructed with the same 128-second duration truncation used in the bank, computing fitting factors directly rather than via the raised-cutoff proxy used by SBank; if the 90th-percentile match in the low-low region falls below the quoted 97.77% by more than the statistical uncertainty, the claimed efficacy is not reproduced.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that two new template banks deliver sufficient coverage for sub-solar-mass (SSM) searches in O4. The archive bank contains 3,452,006 templates covering primary masses 0.2–10 $M_\odot$, secondary masses 0.2–1 $M_\odot$, mass ratios 1–10, and aligned spins up to 0.9 (above 0.5 $M_\odot$) or 0.1 (below), built with IMRPhenomD waveforms, a 45 Hz lower cutoff, a 128-second maximum duration, and a 96.5% minimum match; the low-latency bank uses 1,069,651 templates with component masses 0.5–10 and 0.5–1 $M_\odot$ and spins up to 0.3. In bank simulations, 90% of signals in the low-low, high-low, and high-high regions reach matches of 97.77%, 98.08%, and 96.79% respectively, and 90% of BNS-like signals reach about 95.8% for chirp masses below roughly 2.4 $M_\odot$, while the bank does not recover NSBH signals above that chirp mass. The paper also claims two methodological advances: mismatch-neighborhood metric estimation, which samples nearby points when the Fisher metric has negative eigenvalues at very low masses, and boundary padding, which merges a low-mass-edge marginal bank with the main bank at the cost of up to roughly 30% more templates.

Load-bearing premise

The claimed match values assume that the SBank simulations, which cannot apply the 128-second maximum waveform duration that actually truncates the bank's templates, are a faithful proxy for the templates' true coverage; if raising the low-frequency cutoff (to 75/55/45 Hz by mass region) does not fully compensate for the up-to-16% SNR loss at 0.2 $M_\odot$, the quoted matches overstate the bank's effectiveness at the lowest masses.

Editorial extensions

If this is right

The offline bank lets GstLAL search O4 archive data for mergers with component masses down to 0.2 $M_\odot$, covering the same SSM parameter space as the previous O3 search and enabling updated rate upper limits on primordial black hole and dissipative dark matter binaries.
The low-latency bank makes GstLAL's SSM search real-time for the first time, so a detected low-mass merger can trigger electromagnetic follow-up while the signal is still fresh.
The two manifold enhancements remove the low-mass barrier for geometric bank placement, so future banks tuned to new noise curves or mass ranges can be regenerated in minutes rather than weeks.
Combining the offline SSM bank with the BNS/NSBH/BBH bank raises the 90th-percentile match for high-high edge signals from 96.79% to 97.14%, so events at the boundary between search classes are not lost.
A 90th-percentile match of at least 96.5% (the minimum-match design choice) implies that template spacing alone misses no more than roughly 10% of signals in the designed space, assuming the duration-cutoff caveat is accounted for.

Reading between the lines

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

The 128-second duration cutoff can cost up to 16% optimal SNR for 0.2 $M_\odot$ systems, and the SBank tests use raised low-frequency cutoffs rather than the truncation itself; a dedicated injection study with truncated templates would likely show lower real-world sensitivity at the very lowest masses than the quoted matches suggest.
The same neighborhood-estimation and boundary-padding recipe should transfer to other long-duration, low-chirp-mass searches, including eccentric binaries or ultralight subsolar objects, whenever the waveform approximant's smoothness degrades.
If O4 produces no SSM detections, the population model attached to the low-latency bank (built with an uninformative prior so all templates carry equal weight) can feed joint constraints with the O3 SSM upper limits into primordial black hole abundance limits.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The short version: this paper is a solid, incremental contribution to the GstLAL template-bank toolkit. It delivers two new banks for sub-solar-mass searches in O4 and extends the manifold algorithm down to 0.2 solar masses with two new tricks. The validation is extensive but has a real gap at the lowest masses, and the authors mostly but not fully own up to it.

What's new: first manifold-based bank for component masses down to 0.2 Msun, plus two modifications to the geometric placement code: neighborhood metric estimation to handle numerical failures in the low-mass region, and boundary padding to improve recovery at the low-mass edge. The banks are concrete products, and the simulations use SBank, an independent program, with about 300k injections. That's real evidence, and the paper credits the prior manifold work rather than overselling.

The main soft spot is the duration cutoff. SBank can't apply the 128-second truncation that manifold applies, so the validation uses raised low-frequency cutoffs (75/55/45 Hz per mass region) as a proxy. That proxy doesn't capture the SNR loss from the truncation. For a 0.2+0.2 system, their own Section III reports nearly 16% SNR loss due to the cutoff. That implies the actual fitting factor for the lowest-mass corner is about 0.84, not the 97%+ reported for the low-low region. So the 'sufficient efficacy' claim overstates what is directly tested. The paper does disclose this in Section V, so it's not hidden, but the abstract and conclusion don't carry the caveat.

There's also a mild circularity in the boundary padding: the padding width was chosen by iterating until the bank's own simulations showed good recovery. That doesn't invalidate the result, but it means the quoted matches are partially tuned. Finally, the conclusion misstates the spin bounds compared to Table I — it says the smaller component has |s|<=0.05, but Table I uses |s|<=0.1 for the low-mass regime and |s|<=0.9 for the high-mass regime. Minor.

Bottom line: worth reading if you work on template banks or SSM searches, and worth citing for the algorithmic extensions. It deserves peer review, with a request to either directly validate the truncated templates or soften the efficacy claim for the lowest masses. I'd send it out.

Referee Report

1 major / 5 minor

Summary. This paper describes the construction and validation of two template banks for GstLAL's O4 subsolar-mass compact-binary searches. The offline bank covers m1 ∈ [0.2, 10] M⊙, m2 ∈ [0.2, 1] M⊙, mass ratio up to 10, spin-aligned, with a low-frequency cutoff of 45 Hz, a maximum waveform duration of 128 s, and 3,452,006 templates; the low-latency bank covers m1 ∈ [0.5, 10] M⊙, m2 ∈ [0.5, 1] M⊙, |χeff| < 0.3, and 1,069,651 templates. Methodologically, the paper introduces two modifications to the manifold geometric placement algorithm: neighborhood metric estimation to handle metric failures at very low masses, and boundary padding to improve coverage near the low-mass boundary. Efficacy is assessed with SBank simulations in three mass/spin regions and with BNS/NSBH injection sets. The headline results are 90th-percentile matches of 97.77%, 98.08%, and 96.79% in the low-low, high-low, and high-high regions, respectively, for the offline bank.

Significance. The banks are a practical deliverable for an ongoing search, and the paper's methodological additions (neighborhood metric estimation and boundary padding) address genuine numerical problems in applying manifold to low masses. The validation uses large, independent SBank simulation sets and standard fitting-factor definitions, which is a strength. However, the claimed 'sufficient efficacy' for the offline bank's lowest-mass corner is not directly supported: the simulations cannot apply the 128 s duration cutoff, and the paper's proxy (raised flow cutoffs) does not measure the SNR loss that the cutoff imposes on real signals. If that gap can be closed by direct simulation or by an analytic correction, the paper would be a solid instrument paper; as it stands, the central claim is only partially demonstrated.

major comments (1)

[Section V, Table II and Section III] The central efficacy claim for the offline bank is not directly established for the low-low mass region because the SBank simulations do not apply the 128 s maximum-duration cutoff that manifold uses in template placement. The paper concedes this: 'the bank simulation test below cannot reflect the SNR loss due to this duration cutoff in our templates.' Raising the flow cutoff to 75/55/45 Hz per region (Table II) does not fix the problem, because the simulated signals themselves are generated with the raised cutoff; the test therefore measures the bank's coverage of signals that begin at 75/55/45 Hz, not the recovery of full 45 Hz signals by the duration-truncated templates actually used in the search. This is quantitatively important: for m_i = 0.2 M⊙, Section III reports up to 16% optimal-SNR loss from the cutoff, implying that the overlap between a full-band signal and the truncated template at the same parameters is at most about 0.84, well below the 96.5% minimum match and the quoted 97.77% low-low 90th percentile. I recommend either (1) running SBank or an equivalent code with the actual 128 s-truncated templates against full-band flow = 45 Hz injections for the low-low region, or (2) presenting a separate calculation that multiplies the geometric match by the duration-cutoff overlap and then restating the efficacy claim for that corner of parameter space.

minor comments (5)

[Section VI] The spin range stated in the conclusion ('−0.9 to 0.9 in the larger component and −0.05 to 0.05 in the smaller component') is inconsistent with Table I and Section III, which specify |s_i,z| < 0.1 for masses ≤ 0.5 M⊙ and |s_i,z| < 0.9 for masses > 0.5 M⊙; please correct.
[Section IV C] The boundary-padding width is effectively a free parameter tuned on simulation results ('we stopped widening once a significant majority of simulated signals near the original boundary achieved match values above 95%'); the paper should report the final padding width and discuss the possible optimistic bias from tuning on the same type of validation used in Section V.
[Introduction and Section II] There are typographical errors that should be corrected: 'independet' and 'power spectral densitys' in Section II, 'dipassive' in the Introduction, 'Paramter' in Table IV, and 'culster' in the Acknowledgments.
[Section V.2 and Appendix B] For the BNS/NSBH simulations, the paper reports 90th-percentile matches as low as 0.70 and 0% for NSBH, which is expected because these lie outside the target space; however, the text should more clearly state that these numbers are not efficacy claims for the bank's design region but rather characterize a serendipitous detection capability, to avoid misinterpretation.
[Section III] The statement that a minimum match of 96.5% 'ensures that no more than approximately 10% of astrophysical signals can be missed' is imprecise: the minimum match is a per-template worst-case design value, and the fraction of signals below a given fitting factor depends on the signal population and the match distribution; consider rephrasing.

Circularity Check

1 steps flagged · score 5.0 of 10

Partial circularity: boundary-padding width is tuned against the same SBank match simulations later quoted as validation, while the other mass regions remain independent.

fitted input called prediction [Section IV C (Boundary Enhancement) and Section V 1 (Simulation studies in the template bank space)]
"The process for finalizing a choice of padding-constraints, which were used to produce the marginal bank, was iterative, balancing the increase in number of templates against the performance of bank simulations along the low mass boundary. ... We stopped widening the padding once the bank's performance was sufficient – specifically, when a significant majority of simulated signals near the original boundary achieved match values above 95%. ..."

The padding constraints (the width of the marginal bank) are a tunable input to bank construction. They were adjusted iteratively until the bank's own SBank simulations at the low-mass boundary reached a target ('a significant majority ... match values above 95%'). The same SBank match simulations are then reported in Section V 1 as evidence of efficacy, and the low-low region's high matches are explicitly attributed to the padding ('over-density of templates ... as a result of the padding procedure'). Hence the boundary performance is not an independent prediction of the method; it is the objective function used to terminate the padding search.

full rationale

The bank efficacy is primarily measured with the independent SBank match calculator against standard LAL waveform injections, so the core validation is not circular in the sense of reusing manifold's own placement metric. The manifold algorithm and its prior uses are cited from the authors' own papers ([1, 2, 28, 73]), but these citations support computational efficiency and design conventions rather than a uniqueness claim, and the match values are computed by an external program. However, one element of the validation is self-referential: the boundary-padding constraints were iteratively widened until the bank's own simulations at the low-mass boundary reached a target match (Section IV C), and the resulting low-low simulation results are then presented as evidence of efficacy (Section V 1). The final 90th-percentile match is not literally the stopping rule and the other mass regions were not padded, so the circularity is partial. The paper also explicitly flags a limitation: 'the bank simulation test below cannot reflect the SNR loss due to this duration cutoff in our templates' (Section V), which weakens the directness of the lowest-mass validation but is a coverage shortfall, not a circular reduction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim depends on design choices (padding width, duration cutoff, flow cutoffs) and domain assumptions (waveform model, metric local-constancy, PSD representativeness) that are not derived or externally benchmarked. No new physical entities are introduced.

free parameters (5)

Boundary padding width / marginal bank extent = Not quantified; roughly 30% (about 500,000) additional templates
Chosen iteratively until simulated signals near the low-mass boundary reached match > 95% (Section IV C), so the padding is tuned to the validation set.
SBank simulation flow cutoffs for low-low / high-low / high-high regions = 75 Hz / 55 Hz / 45 Hz (Table II)
Hand-selected to approximate the effect of the 128 s maximum duration cutoff in bank simulations (Section V).
Minimum match = 0.965 (offline), 0.97 (low-latency)
Design choice setting template density and hence bank size; chosen to balance missed fraction (~10%) and template count.
Maximum waveform duration = 128 s
Chosen as a power of two near BNS durations; causes up to 16% SNR loss for 0.2 M_sun systems (Section III).
Spin restrictions = |s| < 0.1 for m <= 0.5 M_sun, < 0.9 above; low-latency |s| < 0.3
Chosen for computational cost and consistency with previous SSM searches (Section III, Appendix B); not derived from first principles.

assumptions (5)

domain assumption IMRPhenomD accurately represents the gravitational waveforms of sub-solar-mass binary mergers within the search band.
Used for both template generation and injection; waveform systematic errors are not quantified (Sections III and V).
domain assumption The match metric and its Fisher-information approximation define a Riemannian metric that is locally constant on the template placement scale.
Foundation of the manifold method; the new neighborhood estimation assumes g(p) ≈ g(qn) inside the mismatch hyperellipsoid (Section IV B and Appendix A).
domain assumption The one-week O4a PSD (starting Dec 29, 2023) is representative of detector sensitivity for the search's use during O4.
The bank placement and validation both use this PSD; if O4b sensitivity differs substantially, coverage could be suboptimal (Sections II and III).
domain assumption Minimum match 96.5% implies that no more than ~10% of astrophysical signals are missed by the bank.
Standard geometric-bank relation (Owen 1996, ref [32]); assumes the mismatch distribution is as expected from the covering.
ad hoc to paper Raising the flow cutoff in SBank simulations approximately reproduces the effect of the 128 s duration cutoff applied by manifold.
Needed because SBank lacks the duration-cutoff feature; the paper itself notes the simulation cannot reflect the SNR loss (Section V).

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Cite this review

Pith. "Pith review of Template bank for sub solar mass compact binary mergers in the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA." pith.science (2026). https://pith.science/paper/IHSPIUEN

@misc{pith2026241210951,
  author       = {Pith},
  title        = {Pith review of: Template bank for sub solar mass compact binary mergers in the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IHSPIUEN}},
  note         = {Machine review of arXiv:2412.10951}
}

abstract

Matched-filtering searches for gravitational-wave signals from compact binary mergers employ template banks which are a collection of modeled waveforms described by unique intrinsic parameters. We present two banks designed for low-latency and archive sub-solar mass (SSM) searches in data from the fourth observing run of LIGO-Virgo-KAGRA, and demonstrate the efficacy of the banks via simulated signals. Further, we introduce a set of modifications to the geometric, manifold algorithm that allow the method to work for exceedingly low component masses necessary for SSM bank production. The archive search bank contains a total of $3,452,006$ templates, and covers a mass parameter space of $0.2$ to $10\ M_\odot$ in the larger component and $0.2$ to $1.0\ M_\odot$ in the smaller component, the spin parameter space of $-0.9$ to $0.9$ for masses above $0.5$ $M_\odot$ and $-0.1$ to $0.1$ for masses below $0.5$ $M_\odot$, and the mass ratio parameter space of $1$ to $10$. The PSD used was from a week of the first half of the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA, and the low frequency cutoff was set to $45$ Hz with a maximum waveform duration of $128$ seconds. The bank simulations performed using SBank have shown that the banks presented in this paper have sufficient efficacy for use in their respective searches.

Figures

Figures reproduced from arXiv: 2412.10951 by the authors.

**Figure 2.** FIG. 2: Schematic representation of the bounded [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3: Simulations of signal recovery for low mass [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (14 more)

**Figure 4.** Figure 4: FIG. 4: Plots for simulated signals in the “low-low” region. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5: Plots for the simulated signals in the “high-low” region. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6: Plots for the simulated signals in the “high-high” region. For purposes of visually presenting the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7: Plots for BNS simulated signals with low-spins. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8: Plots for BNS simulated signals with high-spins. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: FIG. 9: Plots for NSBH simulated signals with low-spins. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: FIG. 10: Plots for NSBH simulated signals with high-spins. For purposes of visually presenting the mismatches, [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

**Figure 11.** Figure 11: FIG. 11: Template placement in the O4 low-latency [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: FIG. 12: Plots for the SSM-BBH injections. (a) shows that 90% of the injections are recovered with a match [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

**Figure 13.** Figure 13: FIG. 13: Plots for the BNS-LOW injections. (a) shows that 90% of the injections are recovered with a match [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

**Figure 14.** Figure 14: FIG. 14: Plots for the BNS-HIGH injections. (a) shows that 90% of the injections are recovered with a match [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]

**Figure 15.** Figure 15: FIG. 15: Plots for the NSBH-LOW injections. (a) shows that only 10% injections are recovered with a mismatch [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]

**Figure 16.** Figure 16: FIG. 16: Plots for the NSBH-HIGH injections. (a) shows that only 10% injections are recovered with a mismatch [PITH_FULL_IMAGE:figures/full_fig_p014_16.png]

**Figure 17.** Figure 17: FIG. 17: Template weights corresponding to the [PITH_FULL_IMAGE:figures/full_fig_p014_17.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Metric evaluation fails at a point p, detected by the presence of negative eigenvalues in the metric gij

[2] [2]

A hyperellipsoid of maximum mismatch centered at p is determined using a reference metric

[3] [3]

A point qi is randomly sampled from within the hyperellipsoid, so that qi is “nearby” to p

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Metric estimation is attempted at qi

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surrounded

Finally, we use the metric g(qn) for the neighbor- hood by associating g(p) ≈ g(qn). Where the reference metric in Step 2 is produced by a general estimate at the beginning of the treebank algo- rithm and succeeded in each iteration of splitting by the metric of the parent hyperrectangle. C. Boundary Enhancement Another principal assumption of the manifol...

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Classical and Quantum Gravity 32, 074001 (2015)

work page 2015

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(Section V 1.)

Assess the effectualness of the template bank by us- ing simulated signals that span the template bank parameter space. (Section V 1.)