# Test rules: re-run of Piassi et al. (2026), written before the multi-event test was run

Written on 2026-11-01 by the wave-1 verifier, before any sudden commencement other than 10 May 2024 was computed. Saved so the page can say so. What had been looked at by then: the preprint's full text; the 10 May 2024 records of the paper's 12 stations and of the other public low-latitude stations (one table of A, V and PA by local time); one day of SJG and SMS in March 2015, for file formats; Ebre's annual lists as printed, with no statistic computed from them. These rules are not changed after the results are seen. Any later addition is marked "added after the results" in `report.md`.

## What the paper's numbers fixed (from the 10 May reproduction, which came first)

The paper does not give its window `W_SSC`, its `N_pre`, its wavelet or its filter (preprint, section 2.4, PDF pp. 9-10). On 10 May 2024 these settings reproduce its Tables 4 and 6 from the public one-minute files, and they are now frozen:

- **H:** EMBRACE's H column; `sqrt(X² + Y²)` for INTERMAGNET stations reporting XYZ; H directly if HDZ. Fill values dropped. No wavelet denoising: its settings are not stated.
- **`A`:** the largest H from T to T+12 min, minus the mean of the 60 one-minute values before T (T−60 to T−1). (Paper's equation 1, on raw rather than denoised H.)
- **`V`:** the largest |H(k) − H(k−1)| for k from T to T+12 min. (Equations 2-3.)
- **`Pc5`:** H over T−120 to T+120 min, band-passed at 1.6-7 mHz by a second-order Butterworth band-pass run forward and backward (60 samples of odd-reflection padding), then the band-passed maximum minus the lowest value before it. (Equations 4-5.)
- **`PA`:** the sum of |H(k) − H(k−1)| for k from T−119 to T+120 min. (Equation 6.)
- **`R`:** Southern value divided by Northern value (Equations 7-10).
- **T** is the listed onset, floored to the minute. On 10 May 2024 the paper's T is 17:04; Ebre's provisional list gives 17:05. The reproduction uses 17:04; the multi-event test uses the list, 17:05, for every event alike.

## Events

Ebre Observatory's annual lists of rapid variations (`ssc_YYYY_d.txt` to 2022, `ssc_YYYY_p.txt` for 2023-26), every entry from January 2013, when SMS's public record begins, to the last listed (August 2026).

- Kept: type SSC or SI. Dropped: SI− (a negative impulse, a different test).
- **Event size:** the mean of the five amplitudes the list prints for the event.
- **Primary set:** size of at least 20 nT. Sensitivity sets: at least 15 nT, at least 30 nT, and SSC only at 20 nT.
- 10 May 2024 stays in the sets, and its rank is reported. Medians are also given without it.

## Stations

- **The paper's five pairs:** SMS-SJG, ASC-GUI, HBK-PAG, GAN-ABG, KDU-KNY.
- **The band:** every other public station, in INTERMAGNET through BGS's GIN or in EMBRACE, with a dip latitude of 12° to 30° in magnitude in IGRF-14 at 2024.36 (away from the electrojet and the auroral zones). A station enters the band table only with at least 5 near-noon events.
- **Data exclusion, per station and event:**
  - less than 95% of the 241 samples, or less than 90% of the 60 baseline samples, or fewer than 12 of the 13 samples of the amplitude window;
  - any single |H(k) − H(k−1)| above 500 nT;
  - a frozen channel: 15 or more consecutive identical values within the 241 samples (see the amendment below);
  - for `R_A`: `A` of 3 nT or less at either station, or an amplitude-window maximum below the baseline.
  - Gaps up to 5 minutes are linearly interpolated for `Pc5` only.
- Every exclusion is counted and reported.

## Tests

1. **Same pair, other events.** For SMS/SJG: the median of `R_A`, `R_V`, `R_Pc5` and `R_PA` with a bootstrap 95% interval (2,000 resamples of events, seed 20261101); the share of events above 1; the rank of 10 May 2024.
   - If the enhancement is a persistent property of the pair, medians stay above 1 and 10 May is unremarkable.
   - If it is special to the great storm, medians are near 1 and 10 May is an outlier.
2. **Same local time, the other pairs.** The paper's pairs sat at different local times on 10 May (its Table 1). For each pair, the local time LT is the mean of its stations' solar local times at T.
   - Near noon is LT from 11 up to 15 h, a band centred close to SMS-SJG's 13.1 h on 10 May.
   - The test reports each pair's median `R` near noon and in the band at the local time it had on 10 May (±2 h), with n.
   - If the paper's contrast is a contrast of place, the other pairs stay below 1 near noon and SMS/SJG stays above them. If it is a contrast of local time, the other pairs rise toward SMS/SJG near noon, and SMS/SJG falls when it is away from noon.
3. **Season.** May is northern summer and southern winter. `R_A` near noon is split into May-August (southern winter), November-February (southern summer) and the rest. If the larger Northern response in the paper's other pairs is seasonal, it should reverse in November-February.
4. **Same local time and same season for every pair, by fit.** For each pair separately, least squares on all its events: ln R = a + b₁ cos(2π(LT−13.1)/24) + b₂ sin(2π(LT−13.1)/24) + c₁ cos(2π(d−131)/365.25) + c₂ sin(2π(d−131)/365.25), with d the day of the year. The fitted R at LT 13.1 and d = 131, exp(a + b₁ + c₁), is the pair's ratio on the same local time and season as 10 May. Bootstrap 95% interval as in test 1.
5. **Trend: is the enhancement "starting"?** For SMS/SJG, the same fit with an added term e × (year − 2020); e with a bootstrap 95% interval, in percent per decade. Also the median `R_A` in 2013-2017, 2018-2022 and 2023-2026. "Starting to become enhanced" predicts e > 0, with recent years above earlier ones. Beside it, the change in F(SJG)/F(SMS) in IGRF-14 over the same years, which is what a simple weak-field scaling would predict.
6. **Is it SMS, or SJG, or the region?** Relative amplitude `A_rel` = `A` / event size, near noon at the station's own solar local time (11 up to 15 h), for every band station.
   - The median per station (at least 5 events), against the station's F and dip latitude: Spearman's rank correlation of median `A_rel` with F, and the South American weak-field stations beside the rest.
   - The same with `V`.
   - Split by season where n allows.
   - SMS against its neighbours (PIL, VSS, JAT, SJC, CXP, CHI): the median ratio over shared events, near noon and at all local times.
   - SJG against other Northern band stations in the same way.
7. **Quiet-day control.** The five days of lowest Ap in each of January, April, July and October 2024 (GFZ), dropping any day with a listed SC. On each: `PA` over 15:05-19:04 UT, the same UT window as 10 May, and the day's H range, at SMS and SJG; the median ratios. If the ratios match the 10 May ratio, the paper's `R_PA` says little about the sudden commencement.
8. **Filtering.** SJG's one-second record on 10 May 2024 resampled to one minute three ways (instantaneous, 60-second mean, INTERMAGNET-style Gaussian), to bound how much of `R_V` and `R_PA` could come from different one-minute products at the two networks.
9. **Induction.** The step ratio ΔZ/ΔH at each paper station: ΔH and ΔZ each the mean of T+3 to T+7 minus the mean of T−5 to T−1, with the median over events where the event's ΔH is at least 10 nT. It is a rough sign of coastal and ground-conductivity effects, not a correction.

## Amendment, made before any multi-event result was read

The first version of the rule for a frozen channel was "more than 5% of consecutive samples exactly equal". Running the reproduction showed that it excludes SMS on 10 May 2024 itself: EMBRACE reports H to 0.1 nT, and 17 of that window's 240 steps (7.1%) are real zeros during the quiet hour before the event. The rule measures reporting resolution, not a stuck instrument, and it would have thrown out mainly SMS. It was replaced by the run-length rule above. No multi-event statistic had been read when this was changed: the metrics job was still downloading, and its first output file was discarded.

## What the test cannot do

No test here separates an ionospheric effect from a ground-conductivity effect at SMS. The re-run uses raw H where the paper denoises `A`. Local time and season are coarse controls, and the Southern and Northern stations of a pair are never at exactly the same local time.