Data-Quality Segments and Analysis Readiness

Analysis-ready data are defined by an explicit set operation on time intervals, not by a vague statement that a detector was “on.” Acquisition, observing intent, interferometer state, calibration validity, hardware injections, environmental disturbances, and analysis-specific vetoes answer different questions. Their intersection—and the processing support required around it—determines which samples may enter a stated result.

Required background. Probability and Inference for Gravity supplies conditional samples, selection effects, and live-time denominators.

Helpful background. Gravitational Radiation and Waveforms supplies signal duration and detector-response requirements. Computational Relativity supplies interval algorithms, provenance, and reproducible software tests.

Segment algebra in absolute time

Represent every state as a union of half-open GPS intervals,

$$S=\bigcup_k[t_k^{\rm start},t_k^{\rm stop}).$$

Half-open intervals assign a shared boundary to exactly one neighbor and make duration additive. Let $A$ be valid acquisition, $O$ the declared astrophysical observing state, $C$ valid calibration, and $Q_\alpha$ the quality conditions required by analysis $\alpha$. Let $H_\alpha$ contain hardware-injection or special-operation intervals excluded by that analysis. A basic readiness set is

$$R_\alpha=A\cap O\cap C\cap Q_\alpha\cap H_\alpha^{\,c},$$

where the complement is taken inside the declared analysis span. Additional masks may remove event-specific disturbances or require a network coincidence,

$$R_\alpha^{\rm net}=\bigcap_{I\in\mathcal N_\alpha}R_{\alpha,I}.$$

All sites use the same absolute GPS coordinate before intersection. Geometric signal delays are waveform-response terms and do not shift data-quality segments.

The live time is the measure

$$T_\alpha=\mu(R_\alpha) =\sum_k(t_k^{\rm stop}-t_k^{\rm start})$$

after intervals are sorted, merged, and made disjoint. Deadtime must name its denominator. A veto occupying $100\,\mathrm{s}$ has very different meaning relative to one hour of observing time and one month of wall time.

What the ingredients mean

Each factor in $R_\alpha$ has a distinct evidential role.

Ingredient	Establishes	Does not by itself establish
Data acquisition	Required samples and timing metadata exist	Optical lock or valid strain calibration
Observing state	Detector was in the declared astrophysical operating mode	Absence of glitches or calibration problems
Calibration validity	The strain response is valid to its stated scope	Stationary or Gaussian noise
Hardware-injection state	Known test signals or special excitations are identified	Safety of every auxiliary channel
Environmental/instrument flag	A documented condition occurred	Relevance to every analysis or frequency
Analysis veto	A prespecified contamination rule applies	Universal unusability of the interval

Some conditions require full time exclusion; others affect only a band, channel, or class of analyses. A narrow instrumental line may be irrelevant to a burst search outside that band but central to a continuous-wave search. Calibration uncertainty may be propagated rather than vetoed when the response remains valid but imperfect. Readiness is therefore indexed by analysis, detector, data release, and sometimes frequency.

Tier or category labels are not timeless semantics. Their definitions can change between releases, and a compact bit mask may combine several conditions. Use the flag name and documentation belonging to the exact dataset rather than assuming that an identically numbered category means the same thing in another epoch.

Processing support shrinks usable intervals

A sample can belong to $R_\alpha$ yet be unusable near a segment edge because filtering, whitening, resampling, or a time–frequency transform needs surrounding data. If a processing operator requires $p_-$ seconds before and $p_+$ seconds after each retained sample, the effective set is an erosion

$$R_\alpha^{\rm core} =\bigcup_k [t_k^{\rm start}+p_-,\,t_k^{\rm stop}-p_+),$$

discarding intervals that become empty. A symmetric filter has $p_-=p_+$; a causal filter may not. A transform requiring blocks of duration $T$ and stride $\Delta T$ also admits only block origins whose complete support lies in $R_\alpha$.

Padding must come from valid data even if it is discarded afterward. Filling a gap with zeros, copying edge samples, or reflecting data changes the filter transient and can fabricate coherent structure. If such a boundary rule is unavoidable, record it and verify it with injections near the edge.

Versioned flags and event-level judgment

Online state flags are available promptly but may be revised when calibration or detector-characterization information improves. Offline derived products can therefore differ from low-latency selections. Reproducibility requires the release and minor version, not only a GPS interval and detector name.

Candidate assessment may identify a localized glitch not captured by a broad segment flag. Any event-level gate, exclusion, or alternate model should be documented separately from the baseline live-time calculation. Changing the selection after inspecting a candidate can bias false-alarm estimates or population inference unless the background is recomputed under the same rule.

Current catalog methods distinguish search data selection, candidate-level data quality, and parameter-estimation treatment; see LVK Collaboration 2026, §§3–5, PDF. The distinction is essential: a candidate can remain analyzable with a glitch model even when one detector–time region is unsuitable for an unmodified stationary likelihood.

A reproducible readiness query

For public data, record:

• dataset and minor version, detector, GPS analysis span, sample rate, and file checksums;
• exact state-vector bits or named segment products and their documented semantics;
• calibration-validity rule and uncertainty treatment;
• hardware-injection, environmental, and instrumental masks;
• analysis-specific vetoes, category definitions, padding, and frequency restrictions;
• interval-library version, endpoint convention, query code, and final segment checksum;
• wall time, single-detector live time, network coincident live time, and every denominator used.

The public contract here is frozen to the GWOSC O4 technical details and API documentation available on 2026-08-18. A later release may revise files, flags, or caveats and must be queried anew.

Test an implementation first on hand-constructed intervals containing overlaps, touching endpoints, zero-duration entries, gaps, and nested vetoes. Verify commutativity and associativity of union and intersection, De Morgan identities inside the declared span, and agreement between bit-mask and segment-list representations. On public data, compare the computed live time with an independently obtained official summary when one exists, while preserving enough detail to diagnose a discrepancy.

Refine segment rounding, padding, sample rate, PSD window, gate support, and calibration samples. Report intervals lost to each requirement rather than only the final total. This is a computational evidence prescription; it does not claim that a current collaboration segment database was reproduced for this page.

Common pitfalls

Using wall time as analyzed live time. Gaps, nonobserving state, calibration invalidity, vetoes, and edge erosion must be removed before the denominator is formed.

Treating all flags as universal vetoes. Relevance depends on signal duration, frequency, search statistic, and available mitigation.

Rounding interval endpoints independently. Floating-point or sample-index rounding can create overlaps and one-sample holes. Convert with one declared rule and test exact boundary cases.

Exercises

1. Intersect and measure segments. Inside $[0,20)$ seconds, let $A=[0,10)\cup[12,20)$, $O=[2,18)$, $C=[0,8)\cup[9,20)$, and a veto $V=[6,7)\cup[14,16)$. Find $R=A\cap O\cap C\cap V^c$ and its live time.

Solution

First,

$$A\cap O\cap C =[2,8)\cup[9,10)\cup[12,18).$$

Removing $V$ gives

$$R=[2,6)\cup[7,8)\cup[9,10)\cup[12,14)\cup[16,18).$$

The durations are $4+1+1+2+2=10$ seconds.

2. Account for filter support. A symmetric conditioning filter requires $2$ seconds of valid padding on each side. Apply it to the readiness set from Exercise 1. Which core intervals remain?

Solution

Eroding each component by $2$ seconds on both sides leaves only

$$[2+2,6-2)=[4,4),$$

which is empty; all shorter components also become empty. Thus no interval supports this filter under a component-by-component strict-validity rule. The result illustrates why fragmented live time can be unusable for long-support processing even when its total duration is nonzero. A different padding source would require an explicit, justified boundary policy.

References

• Gravitational Wave Open Science Center. “API Documentation.” Version available 2026-08-18. Official documentation.
• Gravitational Wave Open Science Center. “O4 Technical Details.” Version available 2026-08-18. Official documentation.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “GWTC-5.0: Methods for Identifying and Characterizing Gravitational-Wave Transients.” arXiv:2605.27224 (2026). Open PDF.