Torthaí na dtástálacha · Pre-registered test results
Each test was written down with its data, comparison (null) model and pass rule before scoring (prereg/tests_v1.json). The code that reads compass directions from the monument records, and the scoring code, were frozen and published first (commit c244e8f, with an addendum fixing the details). Everything was then run once on 9 Oct 2026 (results commit ab7fb46). Every result is shown here, including the nulls. T4’s headline number was seen in a pipeline check before the freeze, so it is listed separately as exploratory. Log: TEST_LOG.md.
| Test | Question | n | Observed | Chance (mean, 95% range) | p | Holm p | Robustness | Verdict |
|---|---|---|---|---|---|---|---|---|
| T1 | Wedge tombs face the midwinter-sunset bin | 51 | 37.3% in the SW bin | 6.2% (0.0%–13.7%) | < 0.0001 | 0.0005 | Cork + Kerry excluded: holds | Supported |
| T2 | Passage tombs at solar/lunar declinations | 36 | score 0.142 | 0.092 (0.057–0.131) | 0.0062 | 0.019 | Brú na Bóinne excluded: holds | Supported |
| T3 | Stone rows at lunar standstills | 119 | 6 rows | 5.9 random · 6.2 hill targets | 0.620 | 1.000 | Cork/Kerry vs rest: fails | Not supported |
| T5 | Pair/row axes at horizon peaks | 245 | 58.8% hit a peak | 59.7% (53.9%–65.3%) | 0.653 | 1.000 | thresholds 0.3°, 1.0°: fails | Not supported |
| Test | Question | n | Observed | Chance (mean, 95% range) | p | Holm p | Robustness | Verdict |
|---|---|---|---|---|---|---|---|---|
| T4 | Passage-tomb intervisibility | 216 | 83.8% see another tomb | 34.8% (26.9%–43.1%) | 0.0010 | 0.0040 | none named: holds | Exploratory signal |
We found a signal, but because we saw it before the freeze, it doesn’t count as a clean pre-registered test.
p = one-sided Monte Carlo p value (10,000 random draws; T4: 1,000). The smallest possible values are 1/10,001 and 1/1,001. Holm p is adjusted for running five tests. “Supported” (confirmatory) requires Holm p < 0.05, an effect in the stated direction, and passing the named robustness check. T4 is labelled exploratory because its primary result was seen before the freeze.
Facing directions of the 51 wedge tombs (area ∝ count). The SW bin (gold) holds the midwinter sunset at every site.
19 of 51 wedge tombs (37.3%) face the south-west bin that holds the winter-solstice sunset. Random directions would put about 3 there (6.2%). p < 0.0001, Holm p = 0.0005. The real horizon gives the same bin. The mean direction is 248° (WSW), with strong concentration (R̄ = 0.68). With Cork and Kerry left out (n = 31), it is still 32.3% (p < 0.0001).
What it shows: wedge tombs that say which way they face overwhelmingly face SW to W, as the NMS scope note says (“invariably … westerly”). What it does not show: that the builders aimed at the midwinter sunset. A SW–W preference is also consistent with the afternoon or setting Sun in general, with slope, or with prevailing weather. Only 51 of the 309 records with a compass phrase say “faces”, “opens to” or “entrance at”, so this sample may not represent all wedge tombs.
Each tick is one tomb’s declination through its own real horizon. The gold bands are the 7 targets ±1.5°: solstices, equinox, and the Moon’s major and minor standstills.
20 of 36 tombs fall within 1.5° of a target. The summed density score is 0.142, against 0.092 for random directions (95% range up to 0.131). p = 0.0062, Holm p = 0.019. With Brú na Bóinne left out (n = 22): p = 0.0066. Two checks added after scoring point the same way: without the two surveyed axes, p = 0.014; keeping only one tomb per 2 km cluster (n = 17), p = 0.007.
Read this with care. The national survey of passage tombs (NMS 2024, Prendergast: 136 surveyed tombs) found no overall clustering (global p = 0.896). Our sample is smaller (36), comes from compass phrases in text (each ±11°), and covers the tombs whose descriptions happen to say which way they open. The larger, measured survey should carry more weight. Our result is a reason to look again, not a reversal.
6 of 119 stone rows point (at their lower-horizon end) within 1.5° of a major or minor standstill declination. Random directions give 5.9 on average (p = 0.547), and directions aimed at horizon peaks give 6.2 (p = 0.620). There is no excess. Cork/Kerry is slightly above chance (+0.75) and the rest is below (−0.61).
What it means: on SMR compass data, this does not replicate Ruggles’s lunar preference for the Cork–Kerry rows. Compass phrases are much coarser than his theodolite surveys, so a weak real pattern could be hidden. This is a null result, not proof of absence.
We found a signal, but because we saw it before the freeze, it doesn’t count as a clean pre-registered test.
83.8% of the 216 passage tombs can see at least one other passage tomb within 10 km over the real terrain, against 34.8% for random points on similar ground near each cemetery. p = 0.0010 (the floor for 1,000 draws), Holm p = 0.0040. Of the tombs that see another, 87.8% see a higher one (chance: 60.6%). For comparison, Prendergast (2016) found 52 of 132 tombs directed at other tombs, 49 of them higher.
| Pair separation | Real pairs intervisible | Random pairs |
|---|---|---|
| 0–1 km | 615 / 861 (71.4%) | 35.2% |
| 1–3 km | 207 / 464 (44.6%) | 13.5% |
| 3–10 km | 567 / 908 (62.4%) | 6.4% |
The caveat, stated before scoring: passage tombs come in tight cemeteries, and the random points do not keep that clustering, so part of the gap is just that real tombs have more near neighbours. The distance table (added after the T4 result had been seen, so it is descriptive only) shows that even at 3–10 km, real pairs see each other far more often than random pairs (62% against 6%). Tombs sit on summits and ridges, and that siting makes them visible. Disclosure: T4 does not use compass data, and its headline number was seen during a code check before the freeze. The code was not changed afterwards.
58.8% of 245 axes (126 pairs, 119 rows) have a horizon peak of at least 0.5° prominence in one of their two bearing bins. Random directions on the same horizons give 59.7%, so p = 0.653. At 0.3° the figures are 80.0% against 76.5% (p = 0.092), and at 1.0° 40.8% against 37.7% (p = 0.153). No evidence that the axes target hills.
T6b was written down after T6 had already stopped. The survey’s own summary, that Connacht wedge tombs concentrate towards the south-west and west, was already known. The test asks for the gallery axis on each published plan, clockwise from that plan’s north arrow, to the nearest degree, and then applies the same winter-solstice test as T1. The stop rule is the same: fewer than 30 usable bearings, and the test is not scored.
A bearing here would be a measurement of a drawing published in 1964 (Mayo), 1972 (Galway, Roscommon and Leitrim) or 1989 (Sligo). It would be a reading of that sheet, with the sheet’s own north arrow. The plans were opened. No degree was stored. Two readings are required, the second from marked endpoints, and the freeze leaves the degree blank when those ends cannot be placed. Line detection on the scans selected scale bars, frames and section lines, and no visual degree could be tied to a marked pair of points. Tombs with both readings: 0. No tomb was dropped for a difference above 5°, because no pair exists.
Volume V states that the arrow is true north. Volumes II and III do not say whether an arrow is true or magnetic, so an unlabelled arrow in those volumes is excluded. No plan was classed as magnetic, so no declination was applied. Usable corrected bearings with a unique monument match: 0, under the stop of 30. There is no share and no p-value. The compass rose is omitted: it plots a scored sample, and the scored sample is empty. Sligo plans that do have a unique match number 22. That is still under 30, even before the blank degrees, and the Mayo, Galway, Roscommon and Leitrim plans stay out under the north rule.
What it shows: the 79 definite Connacht wedge tombs from T6 were taken to the published plans, matched to SMR numbers where the frozen join allowed it (63 unique matches), and the test stopped with an empty scored sample. What it does not show: a facing direction, a midwinter-sunset alignment, or a field compass reading. The per-tomb sheet is t6b_bearings.csv. The write-up is T6b_outcome.md. Freeze: 9f124a8.
Descriptive only. These four rows are class wedge in the monument table. The bearing is blank where the plan was not read to the nearest degree. Roevehagh and Caherfurvaus have no plan in these volumes.
GA095-078---- · survey Ga. 18
Plans located: Fig. 11 and Fig. 16, Volume III figures PDF, pages 23 and 33. Page 23 names Lavally (Ga. 18). Page 33 names Lavally (Ga. 18), after Westropp.
Unspecified. Volume III states no true-or-magnetic convention, and neither plan is labelled. Plan bearing: no degree was read.
GA095-141---- · not on the survey list used for T6b
No plan in Volumes II, III or V. The name is not in those texts, and the tomb is not one of the 14 Galway wedge tombs on the survey list.
No arrow in these volumes. Plan bearing: no degree was read.
GA112-009---- · survey Ga. 31
Plan located: Fig. 69, Volume III figures PDF, page 124. The caption names Doorus Demesne (Ga. 31).
Unspecified. Volume III states no true-or-magnetic convention, and the plan is not labelled. Plan bearing: no degree was read.
GA096-173---- · not on the survey list used for T6b
No plan in Volumes II, III or V. The name is not in those texts, and the tomb is not one of the 14 Galway wedge tombs on the survey list.
No arrow in these volumes. Plan bearing: no degree was read.
Data: NMS Sites and Monuments Record (CC BY 4.0), NI SMR (OGL v3), Copernicus GLO-30 DEM (© DLR e.V. 2010–2014 and © Airbus Defence and Space GmbH 2014–2018, provided under COPERNICUS by the European Union and ESA). Code: scripts/.
