The previous post treated a sentence in Ciborowski and Nash’s reply to Pearce et al. as a live problem for the Sarclet zircon match. The sentence is still the least hedged claim in that paper. The question it raises is still the right question. What it is not, once the grains are tested rather than the histograms inspected, is evidence that the Altar Stone is not from northeast Scotland.
The claim
Ciborowski, T. J. R. and Nash, D. J. 2026. “Arithmetic Methods for Exploring Archaeological Source Provenance Using Geochemistry – A Reply to Pearce et al.” Journal of Archaeological Science: Reports 75: 106012. https://doi.org/10.1016/j.jasrep.2026.106012
In the course of a methods defence, discussing someone else’s data, they write:
“...the more valid conclusion that may be drawn from the U-Pb zircon data in Clarke et al. (2024) is that, even with five comparator analyses, none of the individual ‘Altar Stone’ samples look anything like the Orcadian Basin in terms of U-Pb zircon geochronology. This observation alone suggests that the Altar Stone is not from northeast Scotland.”
That is not a caveat about an arithmetic similarity method. It is a provenance conclusion. It is built on their Fig. 3: three sparse age histograms for the Altar Stone debitage thin sections (2010K.240, FN593, MS3) set against five histograms for Strachan et al. (2021)’s Orcadian Basin samples, all binned at 50 Myr. The eye is invited to see disagreement within each group, and therefore to treat the resemblance between the two pooled signatures in Clarke et al. (2024) as an artefact of averaging.
Clarke et al. (2026), “From Highlands to Henge,” does not answer this. Its Methods section states that it uses “the reported Altar Stone zircon U–Pb concordia dates from Clarke et al. (2024), which are compiled from three thin sections: MS3, 2010k.240 and FN593.” The celebrated Sarclet result (p = 0.96) is a match between one individual outcrop and that three-sample pool. The timeline rules out a considered rejection: Highlands-to-Henge was accepted on 2 May 2026; the Ciborowski and Nash reply was not accepted until 11 August 2026.
So the critique was unanswered in the journals. That much of the previous post stands. The natural next test, as that post said, was to rerun the Sarclet comparison three times — MS3 alone, FN593 alone, 2010K.240 alone — on the published grain lists. That test is sitting in the supplementary tables. This post reports it.
Why the question was fair
Pooling is not automatically wrong. If three fragments are pieces of the same sandstone, combining their zircon ages is the statistically honest thing to do: Clarke et al. (2024) recovered only 56 concordant grains across the three thin sections (24 from MS3, 17 from 2010K.240, 15 from FN593). Vermeesch (2004) is the usual reference for why that is a small sample. To be 95% sure of not missing a 5% age fraction in a worst-case population, 117 grains are wanted. Fifty-six is already thin; fifteen is a sketch.
Clarke et al. (2024) were explicit about the constraint, and about the three sections: “The total concordant analyses used in this work is thus 56 over 3 thin sections, each showing no discernible provenance differences.” They also noted that they analysed every zircon grain within the spatial limit of the technique in the sections. There is no larger Altar Stone zircon list waiting in a drawer. The stone itself is not available for destructive sampling.
The fair part of Ciborowski and Nash’s argument is therefore this: if the three fragments do disagree with one another, pooling them can manufacture a basin-level resemblance that no individual piece actually has. And if that is so, matching the pool to Sarclet does not tell you that any physical fragment of the Altar Stone looks like Sarclet. That is a real detrital-zircon methods worry. It is not settled by asserting, as Clarke et al. (2024) did, that the differences were not discernible. It is settled by testing them.
Visual comparison of n = 15 histograms is not that test.
What was done
The grain lists are the same ones used for the July 2026 independent audit of Clarke et al. (2026)’s Sarclet claim:
- Altar Stone: Clarke et al. (2024), Nature Supplementary Information 1, sheet “A) Zircon U–Pb.” Concordant grains defined as those with absolute discordance ≤ 10%, matching the published total of 56 (24 + 17 + 15). Age used: Concordia Age (Ma), as specified by Clarke et al. (2026).
- Orcadian Basin: Strachan et al. (2021), Supplementary Table B. Concordant grains are those classified by the authors as S or Y (detrital concordant / youngest detrital concordant). Age used: their Preferred Age (Ma). Locality counts: Sarclet 44, Braemore 42, Kirtomy 46, Portskerra 46, Watch Hill 34.
The statistic is a two-sample Kolmogorov–Smirnov test (scipy.stats.ks_2samp, two-sided). That is the same point-estimate KS used in the July audit, not Clarke et al.’s uncertainty-weighted Monte Carlo variant (Guynn and Gehrels 2010), which is why the pooled Sarclet p-value here is 0.865 rather than the published 0.96. The gap is documented; it does not change pass/fail at p = 0.05, and it does not change the ranking of localities. A p-value above 0.05 means the test cannot reject the hypothesis that the two age lists were drawn from the same parent. It is not a proof of identity, especially at these sample sizes. It is the right instrument for Ciborowski and Nash’s claim, which is a claim of dissimilarity.
The July audit already showed that, on the pooled Altar Stone list, Sarclet, Braemore, Kirtomy and Portskerra are all statistically indistinguishable from the Altar Stone, and that Braemore matches at least as well as Sarclet under every discordance threshold tested. This post asks a different question: do the three fragments still look like one another, and does each of them still look like Sarclet, once the pool is taken apart?
The three fragments do not disagree with each other
Ciborowski and Nash’s Fig. 3A is drawn so that 2010K.240, FN593 and MS3 appear to have different shapes. FN593 in particular looks younger: its mean concordia age is 1310 Ma against 1516 Ma for MS3 and 1490 Ma for 2010K.240. That offset is real. It is also what a 15-grain subsample of a Mesoproterozoic-dominated sandstone is allowed to do.
| Pair | D | p | At p = 0.05 |
|---|---|---|---|
| MS3 vs 2010K.240 | 0.292 | 0.290 | indistinguishable |
| MS3 vs FN593 | 0.292 | 0.345 | indistinguishable |
| 2010K.240 vs FN593 | 0.267 | 0.529 | indistinguishable |
Clarke et al. (2024)’s “no discernible provenance differences” survives a formal test of the same 56 grains. The histograms “looking different” is sampling noise. There is no statistical licence, on these lists, to treat the three fragments as internally inconsistent groups whose disagreements are being smoothed away by pooling.
Each fragment still matches Sarclet
That was the test that would have carried the aggregation critique through into the specific result this blog has used. It does not.
Figure 1. Cumulative U–Pb age distributions for the three Altar Stone thin sections, the pooled 56-grain list, and Strachan et al. (2021) Sarclet (RS-ORS-18-17). Concordant grains only. The three fragments scatter around the Sarclet curve; they do not peel away from it. FN593’s younger mean is visible as a steeper early rise, and is still within what a 15-grain draw from the same parent can produce.
Figure 2. Each fragment against Sarclet and Braemore, the two strongest Caithness matches in the July audit. No panel shows a fragment sitting off both curves.
Fragment n Mean age (Ma) vs Sarclet p vs Braemore p MS3 24 1515.5 0.445 0.691 2010K.240 17 1490.2 0.600 0.694 FN593 15 1309.9 0.610 0.271 Pooled 56 1452.7 0.865 0.889 All three fragments remain indistinguishable from Sarclet. Two of the three are a closer match to Braemore than to Sarclet — the same ranking the July audit found on the pool. FN593, the fragment whose histogram looks most unlike the others, is if anything the closest of the three to Sarclet on this test (p = 0.610).
The full fragment-by-locality matrix is below. A p-value above 0.05 means the test cannot reject a shared parent. The only fail in the whole table is 2010K.240 versus Kirtomy, at p = 0.049 — a hair below the line, with n = 17. FN593 versus Watch Hill (p = 0.051) sits a hair above it. That is not a pattern of three samples pointing in different directions. It is a pattern of three small samples sitting inside the same Caithness neighbourhood.
Sample Braemore Kirtomy Portskerra Sarclet Watch Hill MS3 0.691 0.093 0.514 0.445 0.456 2010K.240 0.694 0.049 0.680 0.600 0.389 FN593 0.271 0.549 0.079 0.610 0.051 Pooled 0.889 0.266 0.293 0.865 0.163 FN593 is worth a separate sentence on identity rather than on ages. It is excavated debitage from a Roman context at Stonehenge (SH08 Context 16). Bevins et al. (2023, Table 1) give FN593 as the corrected designation: the same piece was mislabelled FN573 in Ixer et al. (2019) and in Bevins et al. (2020, 2022). It is not a purposive sample from the monolith. 2010K.240 is the 1844 underside piece. MS3 is further debitage, from near Stone 1 in Hawley’s excavations. If one of these were a different sandstone, the three-way split is exactly where that would have shown up. It does not.
The five Orcadian samples do not “disagree with each other” either
Ciborowski and Nash’s second limb is that Strachan et al. (2021)’s five Old Red Sandstone samples, “separated by 1000s of metres of stratigraphy and from across 100s of km²,” record mutual dissimilarities, “likely the product of a changing sedimentary input into the evolving basin.” Changing input across a basin is expected geology. It is not, by itself, a reason to distrust a match to one of those samples. And on a KS test, the five samples mostly do not disagree:
Pair D p At p = 0.05 Braemore vs Sarclet 0.127 0.825 same Braemore vs Portskerra 0.135 0.753 same Kirtomy vs Sarclet 0.176 0.419 same Braemore vs Kirtomy 0.214 0.221 same Braemore vs Watch Hill 0.238 0.196 same Portskerra vs Sarclet 0.233 0.142 same Portskerra vs Watch Hill 0.266 0.101 same Sarclet vs Watch Hill 0.273 0.092 same Kirtomy vs Portskerra 0.304 0.028 different Kirtomy vs Watch Hill 0.367 0.007 different Eight of ten pairs cannot reject a shared parent. The two that can both involve Kirtomy. That is a modest, geographically intelligible amount of intra-basin variation. It is not five signatures pointing at five different places. It is also why matching a pooled Altar Stone list to a pooled “Orcadian Basin” signature, as Clarke et al. (2024) first did, is the weaker comparison, and why matching it to individual outcrops, as Clarke et al. (2026) then did, is the stronger one. Ciborowski and Nash are right that the 2024 basin-level pool is a blunt instrument. They are not right that taking it apart removes northeast Scotland.
What this does not show
Three limits, all real.
Uncorrected pairwise tests. This post reports 28 pairwise KS comparisons (3 fragment pairs, 15 fragment-versus-locality, 10 locality pairs) at α = 0.05 with no multiple-comparison correction. Three of those 28 fall at or below 0.05 — 2010K.240 versus Kirtomy, Kirtomy versus Portskerra, Kirtomy versus Watch Hill — which is about what chance would produce across that many tests even if every list were drawn from the same parent. The argument does not rest on those three rejects. It rests on the failure of Ciborowski and Nash’s dissimilarity claim: the three fragments do not reject one another, and none of them rejects Sarclet. Those are the tests the critique asked for. Naming the multiple-testing issue does not change them.
Low power. A 15-grain list cannot strongly prove identity. Failure to reject a shared parent at n = 15 versus n = 44 is weaker than a high-n match, and would often fail to detect a moderate difference. That limit cuts one way: it stops anyone from reading p = 0.610 as “FN593 is Sarclet.” It does not cut the other way. Ciborowski and Nash’s claim was the stronger one — “none look anything like.” A KS test of the same grains they plotted does not support that claim. You cannot look at n = 15 histograms and declare dissimilarity when the formal test says p = 0.61.
Sarclet is not unique. The July audit already found that Braemore matches the pooled Altar Stone at least as well as Sarclet at every discordance threshold from 5% to 20%, and that Watch Hill, present in the same Strachan et al. (2021) dataset and unmentioned by Clarke et al. (2026), also clears p = 0.05. The three-way split does not change that. The group-level result is a Caithness neighbourhood (Sarclet, Braemore, Kirtomy, Portskerra), not a single harbour. Formation identity is still not facies identity: Sarclet and Braemore are mapped as Lower Old Red Sandstone, while the Altar Stone’s published description is of a flagstone-like facies developed principally in the Middle ORS. That distinction was in the screening paper and remains the reason East Caithness is a search area, not a quarry identification.
Zircon is not the whole Scottish case. Even if the three-way split had gone the other way, “not from northeast Scotland” would not follow from “this zircon comparison is weaker than advertised.” Clarke et al. (2024) also have Laurentian-facing detrital ages, mid-Ordovician apatite and rutile overprinted by Grampian (~460 Ma) magmatism, and Lu–Hf. Bevins et al. (2020, 2023, 2024) have the mineralogical package — diagenetic baryte, calcite cement, tosudite, scarce K-feldspar — that already pushed the stone out of Anglo-Welsh ORS and off Mainland Orkney. The Ba/Rb stream-sediment screen does not use the zircon data at all. Ciborowski and Nash’s sentence asks one comparison to carry a conclusion that several independent lines are already carrying.
The rest of the reply, in this light
Two other Altar Stone points in the same paper should be kept in their place.
Ciborowski and Nash replot Bevins et al. (2023) pXRF data to argue that sample 2010K.240 does not sit on the in-situ Altar Stone array for P, Zn, Mn, K and Ca, and that Bevins et al. did not discuss Mn, Zn or P despite treating Mn and Zn as usable provenance indicators elsewhere. Bevins et al. (2023) had already attributed the Ca offset to leaching of calcite cement, the Fe offset to an Fe-oxide film on the exposed upper surface, and the Ba–Sr range to variable baryte. Those are arguments about a recumbent, partly buried, partly weathered slab, not a confession that 2010K.240 is a different rock. The unused Mn–Zn–P plots are a fairer, narrower jab than the zircon sentence. They are not a disproof of the 1844 label, and they are not a disproof of the petrography: baryte, kaolinite, calcite cement, and the heavier elements still match. The zircon result above is consistent with 2010K.240 being what the label says it is. It cannot prove the label; it can stop the ages being used as if they already disproved it.
Bevins et al. (2024), Was the Stonehenge Altar Stone from Orkney?, is not a rival “not Scotland” paper. It excludes the sampled Mainland Orkney formations on K-feldspar, tosudite and baryte. That removes the islands. It leaves Caithness and the rest of the mainland basin where Clarke et al. (2024, 2026) put them.
What this means for the East Caithness screen
Section 3.5 of the screening paper cited Clarke et al. (2026)’s Sarclet result as independent corroboration: two methods sharing no data, assumptions, or statistical framework, converging within about 10 km. The previous post said that corroborating value now rested on a comparison whose Altar Stone side had not been tested sample-by-sample, and that §3.5 should be caveated accordingly.
The caveat that survives is the one the July audit already required: Sarclet is one of several statistically indistinguishable Caithness matches, not a unique p = 0.96 pin, and the Altar Stone side of Clarke et al. (2026) is still a 56-grain pool. The caveat that does not survive is the one Ciborowski and Nash’s sentence would have forced — that the zircon convergence might be an aggregation artefact, and that the independent-convergence argument might need to be withdrawn.
It does not need to be withdrawn. The three-way split, now run on the published grains, does not pull the fragments apart from one another or off Sarclet and Braemore. The stream-sediment result never depended on the zircon data being sound. The zircon result, tested the way the critique asked, still points at the same stretch of East Caithness coast.
State of the debate
Year Paper Main development 2024 Clarke et al., Nature Orcadian Basin proposed as Altar Stone source, via pooled zircon, apatite and rutile. Three thin sections described as showing no discernible provenance differences (n = 56). 2024 Bevins et al., JAS Rep. Mainland Orkney excluded on mineralogy (K-feldspar, tosudite, baryte). Mainland basin left open. June 2026 Clarke et al., J. Quaternary Sci. Sarclet identified as strongest individual-outcrop zircon match (p = 0.96); Altar Stone side left pooled. Braemore, Kirtomy and Portskerra also compatible. June 2026 Pearce et al., JAS Rep. Comment on Ciborowski and Nash’s arithmetic similarity method. Does not itself address the Altar Stone zircon pooling. July 2026 Daw, sarsen.org East Caithness Ba/Rb screen; cites Sarclet as independent corroboration. Independent KS audit: group-level match real; Sarclet not uniquely strongest. September 2026 Ciborowski & Nash, JAS Rep. Reply to Pearce et al. Side argument: disaggregated zircon histograms “look nothing like” the Orcadian Basin, therefore not northeast Scotland. September 2026 This post Three-way KS split of the published grains: fragments indistinguishable from each other; each indistinguishable from Sarclet and Braemore. Aggregation artefact not found. “Not from northeast Scotland” does not follow. Bottom line
The aggregation worry was legitimate and, in the journals, unanswered. The observation it was built on does not survive a formal test of the same grains. That is the opposite of a kill-shot on northeast Scotland, and it is the opposite of a reason to retire the zircon convergence.
Ciborowski and Nash’s sentence is the overreach. The histograms were the wrong instrument. The grains, taken one sample at a time, still look like Caithness.
Methods, for anyone who wants to rerun it
Two-sample Kolmogorov–Smirnov tests were computed in Python with scipy.stats.ks_2samp (two-sided). Altar Stone ages: Concordia Age (Ma), grains with |Disc (%)| ≤ 10 from Clarke et al. (2024) SI 1. Orcadian ages: Preferred Age (Ma), grains grouped S or Y in Strachan et al. (2021) Supplementary Table B. Locality codes: RS-ORS-18-14 Watch Hill, 18-15 Kirtomy, 18-16 Portskerra, 18-17 Sarclet, 18-18 Braemore. Cumulative plots are empirical distribution functions, not kernel density estimates, so that each step is a grain. The extracted grain lists used here are those already archived with the July 2026 Clarke et al. (2026) KS audit.
References
- Bevins, R. E., Pearce, N. J. G., Pirrie, D., Ixer, R. A., Hillier, S., Turner, P. and Power, M. 2023. “Assessing the authenticity of a sample taken from the Altar Stone at Stonehenge in 1844 using portable XRF and automated SEM-EDS.” Journal of Archaeological Science: Reports 49: 103973. https://doi.org/10.1016/j.jasrep.2023.103973
- Bevins, R. E., Pearce, N. J. G., Hillier, S., Pirrie, D., Ixer, R. A., Andò, S., Barbarano, M., Power, M. and Turner, P. 2024. “Was the Stonehenge Altar Stone from Orkney? Investigating the mineralogy and geochemistry of Orcadian Old Red sandstones and Neolithic circle monuments.” Journal of Archaeological Science: Reports 58: 104738. https://doi.org/10.1016/j.jasrep.2024.104738
- Ciborowski, T. J. R. and Nash, D. J. 2026. “Arithmetic methods for exploring archaeological source provenance using geochemistry – A reply to Pearce et al.” Journal of Archaeological Science: Reports 75: 106012. https://doi.org/10.1016/j.jasrep.2026.106012
- Clarke, A. J. I., Kirkland, C. L., Bevins, R. E., Pearce, N. J. G., Glorie, S. and Ixer, R. A. 2024. “A Scottish provenance for the Altar Stone of Stonehenge.” Nature 632: 570–575. https://doi.org/10.1038/s41586-024-07652-1
- Clarke, A. J. I., Veness, R. L. J., Kirkland, C. L., Clark, C. D., Gandy, N., Emery, A., Bradley, S. L., Ely, J. C. and Ignéczi, Á. 2026. “From Highlands to Henge: Refining the Provenance and Transport Pathways of Stonehenge’s Altar Stone.” Journal of Quaternary Science 41: 888–895. https://doi.org/10.1002/jqs.70080
- Daw, T. 2026. “A Multi-Element Geochemical Screen, Verified Against Bedrock Geology, for the Source of the Stonehenge Altar Stone Within the Orcadian Basin.” sarsen.org, 2 July 2026. https://www.sarsen.org/2026/07/a-multi-element-geochemical-screen.html
- Daw, T. 2026. “Not From Northeast Scotland At All.” sarsen.org, 3 September 2026. https://www.sarsen.org/2026/09/not-from-northeast-scotland-at-all.html
- Guynn, J. and Gehrels, G. 2010. “Comparison of detrital zircon age distributions using the K-S test.” University of Arizona LaserChron Center.
- Pearce, N. J. G., Bevins, R. E., Ixer, R. A. and Pirrie, D. 2026. “Arithmetic approaches alone are inadequate in defining similarity: A comment on Ciborowski and Nash 2026.” Journal of Archaeological Science: Reports: 105874. https://doi.org/10.1016/j.jasrep.2026.105874
- Strachan, R. A., Olierook, H. K. H. and Kirkland, C. L. 2021. “Evidence from the U-Pb-Hf signatures of detrital zircons for a Baltican provenance for basal Old Red Sandstone successions, northern Scottish Caledonides.” Journal of the Geological Society 178: jgs2020-241. https://doi.org/10.1144/jgs2020-241
- Vermeesch, P. 2004. “How many grains are needed for a provenance study?” Earth and Planetary Science Letters 224: 441–451. https://doi.org/10.1016/j.epsl.2004.05.037
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