Abstract
A match between a sighting report and a strain spike means nothing until we know how often such matches happen by pure chance. This paper adapts the time-slide method, used by professional gravitational-wave searches to estimate background, to the problem of pairing witness reports with detector data.
The idea is simple: shift every sighting timestamp by an offset that cannot be physical (hours or days), recount the coincidences, and repeat thousands of times. The shifted counts form an empirical background. A real effect must stand above it; a chance alignment will not.
We pair the method with environmental witness channels (seismometers, magnetometers, mains monitors) that veto spikes with mundane causes, and with a pre-registered analysis plan. We propose it as the standard significance test for every candidate RGL escalates, starting with the July 2026 anomaly cluster. This paper reports a method, not a result.
1. Introduction: the coincidence problem
Project Waveform made our timestamps precise. Precision alone does not tell us whether a match is meaningful. A low-cost strain array produces many transient spikes per day from traffic, wind, thermal drift and electronics. Some of them will land near a sighting by accident.
The expected number of chance coincidences is easy to state:
N_{\text{chance}} \approx N_{\text{reports}} \times R_{\text{spike}} \times 2\,\Delta tHere N_reports is the number of sighting reports, R_spike is the spike rate above threshold, and Δt is the matching window either side of the report. With 1,000 reports, 20 spikes per day and a ±5-minute window, about 139 matches appear from noise alone.
That formula assumes spikes and reports arrive at random, independently. They do not. Both cluster at night, on weekends, and in clear weather. Spike rates rise with wind; reports rise with clear skies and festivals. An analytic estimate will get the background wrong. We need one measured from our own data.
2. Method: time-slide background estimation
In professional searches, analysts shift one detector’s data against another’s by offsets far larger than light-travel time. Any coincidence that survives the shift cannot be astrophysical, so the shifted counts measure the background. We apply the same logic between two different kinds of record: witness reports and strain logs.
- Count the zero-lag coincidences. Pair each report with any above-threshold spike within ±Δt. Record the count N₀ and a ranking statistic per pair (Section 4).
- Slide. Shift every report timestamp by an offset τ, chosen as a whole number of days (±1, ±2 … ±k). Whole-day shifts keep each report at the same hour, so the night-time and weekly rhythms that drive both records are preserved.
- Recount. Count coincidences at each offset, giving N(τ).
- Build the background. The distribution of N(τ) over all offsets is the chance expectation, with diurnal and weekly structure already built in.
- Compare. The empirical p-value is the fraction of slides with a count at least as high as N₀.
With k = 500 days each way we get 1,000 background trials, enough to claim significance down to about p = 0.001. Offsets that land on detector downtime are dropped, not filled.
The same machinery works between detector sites. Sliding Site One against Site Two by minutes to hours tests whether a three-site ‘correlated spike’ is rarer than the sites’ shared weather and power grid would produce.
3. Witness channels and environmental vetoes
A strain spike is only an anomaly candidate if nothing ordinary explains it. Each detector site should log auxiliary channels on the same clock as the strain sensor. A spike that coincides with a loud auxiliary channel is vetoed before any sighting match is attempted.
| Witness channel | What it catches | Suggested hardware |
|---|---|---|
| 3-axis seismometer / geophone | Traffic, footsteps, quarry blasts, regional earthquakes | MEMS accelerometer or low-cost geophone |
| Fluxgate magnetometer | Geomagnetic storms, nearby vehicles, switching loads | Three-axis fluxgate, logged at ≥10 Hz |
| Mains voltage and frequency monitor | Grid transients shared by all sites on one network | Isolated mains logger |
| Temperature and pressure | Thermal drift, pressure fronts, door openings | Enclosure + outdoor sensors |
| Microphone | Aircraft, thunder, machinery | Calibrated SPL logger, envelope only |
| GNSS timing status | Clock faults that fake coincidences | Receiver lock and holdover flags |
Vetoes must be tuned before looking at sighting matches. The rule: a channel’s veto threshold is set so that it removes a stated fraction of spikes (for example 5%) on data with no reports nearby. The veto’s ‘use-percentage’ — the share of that channel’s own loud events that coincide with a strain spike — is reported for every channel.
Three-site correlations deserve special suspicion. Geomagnetic storms and the shared power grid are both continent-scale and arrive at all sites within seconds. A cluster that also shows up on every magnetometer is a space-weather event until proven otherwise.
4. Scoring a candidate: significance and odds
A count is crude. Each coincidence also gets a ranking statistic so that one strong, clean match outweighs several weak ones. We propose a simple product of three terms:
\rho = \frac{\text{SNR}_{\text{strain}}}{\text{SNR}_{\text{thr}}} \times w_{\text{time}} \times q_{\text{report}}- SNR_strain / SNR_thr: how far the spike clears the detection threshold.
- w_time: a timing weight, 1 at zero offset and falling linearly to 0 at the edge of the ±Δt window.
- q_report: the Project Waveform quality grade, from 1.0 (second-level, device-verified time) to 0.2 (verbal recollection).
The time slides then give a background distribution of the loudest ρ per slide. A candidate’s false-alarm rate is how often the background produces a ρ that high. This is the number we publish, in plain units: ‘one per N years of reports at this rate’.
When the false-alarm rate is low, a mundane explanation still has to be weighed. We report the odds as a ratio of how well each hypothesis predicts the full data, including the witness channels — not just whether noise can be ruled out.
5. Worked illustration (hypothetical numbers)
The numbers below are invented to show how the test reads. They are not RGL data.
Assume 1,200 graded reports over two years, 15 spikes per day surviving vetoes, and a ±3-minute window. The analytic estimate is 1,200 × 15 × 6 / 1,440 ≈ 75 chance matches. Now suppose 1,000 whole-day slides give a mean of 74 and a standard deviation of 11, wider than pure randomness because both records cluster at night.
| Scenario | Zero-lag matches | Slides at or above it | Empirical p | Reading |
|---|---|---|---|---|
| A | 79 | 334 of 1,000 | ≈ 0.33 | Fully consistent with chance |
| B | 96 | 31 of 1,000 | ≈ 0.03 | Interesting; check vetoes and repeat on new data |
| C | 128 | 0 of 1,000 | < 0.001 | Strong excess; now rule out shared causes |
Scenario A is where most honest analyses will land, and it is worth publishing: it tells the community the matches were noise. Scenario C does not prove anything exotic. It proves the two records are linked, which could still mean a shared trigger such as storms that both shake the sensors and draw people outside.
6. Applying it to the July 2026 cluster: pre-registered plan
The four nights of correlated three-site spikes in late July are the first case this test will be run on. We commit to the plan below before computing any result, and will publish the outcome whichever way it falls.
- Freeze the inputs. Archive the strain logs, auxiliary channels and report database as of today, with checksums.
- Fix the parameters. Threshold, Δt = ±3 minutes, k = 500 days each way, and the ρ definition from Section 4. No changes after the first look.
- Check space weather first. Compare the cluster nights against the planetary Kp index and the nearest geomagnetic observatory record (Tihany, Hungary). Any site magnetometer showing the same timing is noted.
- Check the grid and seismic record. Mains logs from all three sites, plus public regional seismic bulletins for the same windows.
- Run inter-site slides. Slide each site against the others by 1 to 24 hours in 10-minute steps to measure how often three-site ‘clusters’ appear by chance.
- Run report slides. Only then pair surviving spikes with field reports.
- Publish everything. Code, parameters, background distributions and the final p-value, including if it is unremarkable.
The decision rule is set now: a false-alarm rate below one per 10 years of operation, after vetoes, escalates the cluster to Project Tesseract. Anything weaker is filed as a documented null.
7. Limitations and what would falsify an anomaly
The method is only as strong as its honesty about what it cannot do.
- Shared causes survive slides. If weather drives both spikes and sightings on the same night, a whole-day shift breaks the link and the zero-lag excess looks real. Witness channels and weather covariates are the only defence.
- Reports are not independent. A widely shared video produces dozens of reports of one event. Reports within one hour and 50 km are merged before counting.
- Tuning on the answer. Any parameter changed after seeing the zero-lag result invalidates the p-value. Pre-registration is part of the method, not an extra.
- Sensitivity is unknown. Our sensors have no confirmed astrophysical detection. Professional detectors are many orders of magnitude more sensitive, so a spike we see that they do not is far more likely local than astrophysical.
An anomaly claim is falsified if any of these hold: the excess disappears once weather covariates are included; the matching spikes are flagged by a witness channel; the excess does not repeat in a fresh, independently collected dataset; or it appears equally at sites far from the reports.
8. Conclusion and open data commitments
Every sighting–strain match RGL reports from now on will carry a time-slide false-alarm rate. Project Waveform made our timestamps trustworthy; this method makes our coincidences measurable.
We will release the slide code, the veto definitions and the background distributions alongside each candidate. Anyone running a sensor and a report log can apply the same test to their own data, and we invite them to.
References
- Abbott, B. P. et al. (LIGO Scientific and Virgo Collaborations), ‘GW150914: First results from the search for binary black hole coalescence with Advanced LIGO’, Physical Review D 93, 122003 (2016) — time-slide background estimation in practice.
- Gravitational Wave Open Science Center — public event catalogs and strain data.
- NOAA Space Weather Prediction Center: Planetary K-index — geomagnetic activity record.
- Relative Gravity Labs, Project Waveform — intake and timestamp protocol.