Statistical carver suggestions from the runic texts: 82 percent right among the confident suggestions in a locked blind test, against 44 percent for the nearest carver

Runologists attribute unsigned runestones to carvers from ornament, rune forms, spelling, formulas and place. Claiborne Thompson (1975) showed how spelling tells the Upplandic carvers apart. Jan Axelson (1993) listed the signed and attributed inscriptions of central Sweden, and most attributions in Rundata for Uppland, Södermanland, Västmanland and Gästrikland rest on his list. Per Stille (1999) attributed the stones of Fjädrundaland, and Magnus Källström (2007) has studied the carvers and their writing milieus across Scandinavia.

Statistical attribution is not new. In a method study with a modern carver, Laila Kitzler (1998) showed that the shape of the grooves in laser scans tells carvers apart with at least 70 percent accuracy, using cluster and discriminant analysis, and found that Öpir is probably at least two carvers. She has since applied the method to Viking-Age stones in Uppland and Östergötland (Kitzler Åhfeldt 2002) and on Bornholm (Kitzler Åhfeldt 2020). The method requires a scan of every stone.

We have found no method that suggests carvers for all runestones from what the runic-text database contains and that has been tested in a blind test locked in advance, against a simple comparison rule on the same stones. The aim here is to report such a test.

The plan was written and locked on 21 October 2026, before the blind test was computed. It is time-stamped in the project's version control and has the SHA-256 checksum 5ed0b2f3b147aad4… (see Data and code). The question in the plan reads: are the suggestions with the status new suggestion right clearly more often than a simple rule that suggests the carver of the nearest stone with a secure carver, on the same stones? Yes if McNemar's test gives p below 0.05. A no would be reported just as clearly. The plan forbids changes to weights, limits and rules after the results have been seen.

Two things were known before the plan was locked: how many stones without a carver received each status in the project's overview, and which stones have a carver in the Swedish National Heritage Board's register Runor (2020) but not in Rundata. The suggestion rule and the model were locked in the version tested. But they had been developed on the same material: the model's limit for "perhaps someone else" was chosen with stones by carvers left out of the model, and three details of the rule were adjusted on 11 October 2026 after examination of individual stones (U 92, U 735 and U 1026). The answer was thus hidden for every stone in the test, but not when the rule was designed. That is why the report is partially tested.

Sections 5.1 and 5.4 are the plan's tests. Sections 5.2 and 5.3 are additions beyond the plan.

• Source. The Scandinavian Runic-text Database (Rundata) 3.1, Department of Scandinavian Languages, Uppsala University: transliteration, normalisation, province, parish, place, carver, style group and rock type for each inscription.
• The stones in the test. All 769 Swedish Viking-Age runestones with a secure carver in Rundata, signed or attributed without a question mark. 636 have a carver who can be suggested. 133 have a carver who cannot be suggested; they cannot be right but are included, so that it shows how often a wrong carver is suggested.
• The carvers who can be suggested. 28: the 18 carvers the model is trained on (at least 8 secure stones) and the carvers who have a spelling profile (at least five secure inscriptions).
• Runestones only. Other objects with runes are not included.

4.1 The model. A random forest (Breiman 2001) with 500 trees, trained on 497 stones by 18 carvers. The variables are location and province, style group, cross and short-twig runes, eleven language traits, five formulas, the hundred most common rune pairs and nine content categories. The model is evaluated by fivefold cross-validation repeated three times, so that each stone's probabilities come from models that did not see it, and also with whole parishes and whole hundreds left out. If the first choice's probability is below 0.35, the model says perhaps someone else. Suggestions are given only for stones within 25 km of a training stone.

4.2 The spelling. Each inscription is compared with the carvers' spelling profiles: parts of words of two and three runes, word dividers and bind-runes, without proper names, so that a signature does not give the answer away. The stone itself is not counted in the profile.

4.3 The suggestion rule. The strength of a suggestion is computed from the model's probability and the spelling's first choice and lowered by four checks: whether the stone stands within the carver's area, whether the style group is among the carver's usual ones, whether the language traits agree and whether the rock type agrees. A new suggestion, here called a confident suggestion, is given at a strength of at least 0.5 and a possible suggestion at at least 0.3.

4.4 The blind test. For each stone in the test the carver is made unknown in a copy of the material, and the carvers' areas, style groups, rock types and language profiles are recomputed without the stone. The suggestion is compared with the rule nearest carver: the carver of the nearest other stone with a secure carver, all carvers if several stones stand at the same distance. The measures are the share right with Wilson's 95 % interval and the pairwise comparison with McNemar's exact test. An independent check recomputed 60 randomly chosen stones in a different way and got the same outcome for all of them.

4.5 Deviations and rerun. Three deviations from the plan. A coding error cut the list of the model's suggestions to the first 400 stones; it was corrected after the first run. That first run already gave 247 right of 300 confident suggestions, 82 percent, against 41 percent for the nearest carver. The nearest-carver rule was then made generous at equal distances, which makes the comparison harder for the suggestion rule. The breakdown by province and carver in 5.2 is an addition. On 31 October 2026 the test was rerun unchanged on today's version of the material; the model's probabilities are identical and the outcome is the same for every stone.

5.1 The blind test. Of the 769 stones, 302 received a confident suggestion, 195 a possible one and 272 none.

• Confident suggestions: right on 248 of 302 (82 percent, 77–86). Nearest carver: 133 (44 percent). On 132 stones only the suggestion rule was right, on 17 only the simple rule: p = 3.1 · 10⁻²³. The answer to the plan's question is yes.
• Signed stones, where the answer key is the carver's own name: 72 of 100 (72 percent) against 42, p = 9.2 · 10⁻⁶.
• When the model gives a name: 213 of 254 (84 percent). When it says perhaps someone else: 35 of 48 (73 percent).
• Possible suggestions: 108 of 195 (55 percent) against 66 (34 percent).
• By strength: 0.5–0.6 right on 50 of 72; 0.6–0.7 on 56 of 65; at least 0.7 on 142 of 165.
• Carvers outside the 28: 23 of the 133 stones still received a confident suggestion, which is necessarily wrong; they are included in the figures above.

In plain words: when the rule gives a confident suggestion it is right about four times in five, and a guess by the nearest stone is right just over two times in five.

5.2 By province and by carver (beyond the plan). Uppland: 227 of 270 (84 percent) against 43 percent, p = 1.2 · 10⁻²³. Södermanland: 17 of 28 (61 percent) against 13 (46 percent), p = 0.39, so no clear difference. By suggested carver with more than three confident suggestions: Öpir 1: 68 of 104; Åsmund: 37 of 39; Balle: 34 of 37; Fot 2: 30 of 35; Gunnar: 21 of 22; Traen: 11 of 15; Erik: 14 of 14; Livsten: 10 of 10; Arbjörn: 7 of 7; Visäte: 6 of 6; Torbjörn 2: 4 of 4. Öpir has the lowest share right. All four errors for Traen (Sö 46, Sö 159, Sö 160, Sö 296) concern stones signed by other carvers in Södermanland.

5.3 The model on its own (the cross-validation). The model alone puts the right carver first on 72.8 percent of the training stones and among the first three on 86.7 percent; always guessing the most common carver gives 19 percent. With whole parishes left out: 68.8 percent; with whole hundreds: 58.6 percent.

• What carries the model. Language and content only: 61.4 percent; geography only: 43.9; style only: 33.0; rock type only: 18.9. With whole hundreds left out, language holds up better than geography, 50.1 against 30.2 percent. Language and content account for 72 percent of the variables' combined importance.
• The calibration. The model is cautious: when it gives about 25 percent to its first choice it is right in 51 percent of cases, at 45 percent in 81 and at 65 percent in 98. The probabilities thus underestimate the accuracy, and they should be read as a ranking rather than as odds.
• Perhaps someone else. The limit 0.35 flags 80 percent of the stones when their carver has been left out of the model, but also 41 percent of the known carvers' stones; among the stones not flagged, the first choice is right in 86.9 percent.
• The confusions. Most often Åsmund (10 stones), Gunnar (8) and Visäte (8) are taken for Öpir, and Tidkume for Balle (10).

5.4 External test (the plan's secondary). 19 runestones have a named carver in Runor (2020) but none in Rundata; 8 of them have a carver who can be suggested. None received a confident suggestion, 3 received a possible one, and 1 of those was right. That is too few stones to say anything, as the plan expected.

What the method can do. When the suggestion rule gives a confident suggestion, it has in the test been right about four times in five, twice as often as a guess by the nearest stone. That holds also for signed stones, where the answer key is not a judgement but the carver's own name. The 86 confident and 292 possible suggestions the rule gives for the 1,550 stones without a carver therefore carry a known error rate, and they can be put forward as hypotheses to be tested against the stones themselves.

Against earlier research. Kitzler Åhfeldt's method and this one measure different things. Hers rests on how the carver drove the chisel and requires a scan; this one rests on what the carver wrote and where the stone stands, and works for every stone in the database. That Öpir is the carver the rule hits least often, and the one other carvers are most often taken for, fits her observation that Öpir is probably at least two carvers (Kitzler 1998). The two methods are independent of each other, and where both can be used they test each other.

Weaknesses, in order of weight.

1. The answer key is largely judgements of the same kind. Of the 769 stones, 523 are attributed, not signed, and the attributions rest on style, spelling and place, in central Sweden largely via Axelson (1993). The test therefore partly measures how well the rule reproduces the runologists' judgements. The signed stones are the independent test, and there the share right is lower: 72 percent.
2. The rule was set on the same material. Weights and limits were locked before the test but chosen with the material in view (section 2). That probably gives a somewhat too high accuracy. A test on stones attributed only after the rule was locked would remove this; today there are only 8 such stones.
3. Only 28 carvers. A stone by another carver can only receive a wrong suggestion. 23 such stones received a confident suggestion. Among the stones without a carver there are surely many by carvers the rule does not know.
4. Södermanland. The advantage is not clear there (17 of 28 against 13), and almost all confident suggestions concern Uppland.
5. Öpir. The largest carver in the model attracts stones by other carvers, and the share right is lowest for him (68 of 104).

Where the method should not be used. Outside Uppland, for stones more than 25 km from a stone with a known carver, to decide between neighbouring stones in one and the same carving milieu, and as proof of an attribution. A suggestion is a hypothesis.

What would overturn the method. If the share right fell to the nearest-carver level on stones attributed after the rule was locked, or if groove analyses of scanned stones contradicted the confident suggestions.

A statistical suggestion rule that uses only what the runic-text database contains suggested, in a locked blind test, the right carver for 82 percent of the stones where it gave a confident suggestion, against 44 percent for the nearest carver, and for 72 percent of the signed stones. It works as a way of sorting out testable attributions in Uppland. The next step is a test on stones attributed after the rule was locked, and a comparison with groove analyses of the scanned stones.