Language and content order the runestones of Uppland in the same sequence as the stylistic chronology – rank correlation 0.54 without the ornament

The Viking-Age runestones of Uppland are dated relatively by their ornament, in Anne-Sofie Gräslund's style groups from RAK and Fp to Pr1–Pr5 (Gräslund 2006). The chronology rests on how the rune animal and the animal heads are shaped, not on the language or on what the text says. If language and content changed over the same time, the stones should fall in roughly the same sequence when ordered by them, and that would be support for the chronology not resting on the same observations. If two kinds of observation that have nothing to do with each other give the same order, it is hard to explain otherwise than that both follow time.

Seriation by correspondence analysis is a common method of relative dating in archaeology (Greenacre 2007). The aim here is to test whether language, formulas and content give the same sequence as the stylistic chronology, whether it holds in two halves of the material and whether it applies also outside Uppland, where the chronology was not built.

The seriation in Uppland was first made on 5 October 2026 as part of the project's survey, without a locked plan, and its value was known when the rest of the study was planned. It is therefore not pre-registered. The variants without crosses, without journeys abroad, without the traits that change over time and within hundreds and carvers (5.2) were computed at the same time and are exploratory.

On 31 October 2026 a plan for two tests was locked before they were run (SHA-256 checksum 454cacf9d8185a26…): the seriation in each half of the stones of Uppland on its own, and the same seriation on the stones of Södermanland, which had not been seriated on their own. The halves hold when Holm p is below 0.05 and rho at least 0.3 in both. Södermanland is replicated by the same limits; if the correlation with latitude held constant is below 0.3, the association is said to be possibly geographical. A trial run reproduced Uppland's known value exactly before the tests were run.

• Source. The Scandinavian Runic-text Database (Rundata), Department of Scandinavian Languages, Uppsala University. The material was frozen for the analysis on 29 October 2026. Runestones only.
• The traits. Language traits (the spelling of certain sounds and words), five formulas (sponsor formula, monument, word order, carver's signature, prayer), cross, short-twig runes and content categories, as presence or absence per stone. Traits found on fewer than 15 stones are not counted, nor stones with fewer than four traits. The style group is not included.
• Time is the style group's midpoint after Gräslund (2006).
• Uppland: 818 stones and 65 traits, 501 stones with a style group. Södermanland: 270 stones and 44 traits, 151 with a style group.
• The halves are the project's fixed division parish by parish.

4.1 The seriation. Correspondence analysis (the package ca; Nenadić & Greenacre 2007) of the table of stones and traits. The analysis places stones that have the same traits close together, and traits that tend to occur on the same stones close together; the first axis is the direction in the material that separates the stones most. The stones' position on the first axis is compared with the style group's midpoint by Spearman's rank correlation. The sign of the axis is arbitrary and is turned so that the correlation is positive.

4.2 The geography. Since language traits also differ between north and south, the partial correlation with latitude held constant is reported.

4.3 The halves and Södermanland. The same method, unchanged, on each half and on Södermanland, Holm-corrected over the three tests.

4.4 The variants (exploratory). The seriation without crosses, without journeys abroad, without the traits whose change over time is measured separately (dotted runes, the monophthong, the ós-rune) and without all of these, and the correlation within hundreds and within carvers with at least five dated stones.

4.5 Deviations. None from the plan.

5.1 Uppland and the halves. In Uppland rho = 0.54 (uncorrected p = 9.4 · 10⁻⁴⁰) and 0.54 with latitude held constant; latitude itself correlates only 0.09 with the axis. Half A: 264 dated stones, rho 0.51, with latitude held constant 0.51. Half B: 236 dated stones, rho 0.54, with latitude held constant 0.53. Both Holm-corrected p below 10⁻¹⁷: the halves hold. The style groups on average along the axis: RAK -0.79, Fp -0.89, Pr1 -0.46, Pr2 -0.18, Pr3 -0.01, Pr4 0.51, Pr5 0.80: the sequence is that of the stylistic chronology, except that RAK and Fp change places. In plain words: if one orders the stones only by what is written and how, they fall in roughly the same order as when one orders them by the ornament; the association is moderately strong and equally strong in both halves.

5.2 The variants (exploratory). Without crosses 0.55, without journeys abroad 0.54, without the traits that change over time 0.54, without all of these 0.53. Within hundreds (23 hundreds) 0.51; within carvers (13 carvers with at least five dated stones, 251 stones) only 0.25.

5.3 Södermanland (replication). 151 dated stones: rho 0.32, Holm-corrected p = 6.3 · 10⁻⁵; replicated by the plan's rule. With latitude held constant 0.29, below the plan's limit of 0.3, so the association may be partly geographical. Within hundreds 0.24 (11 hundreds).

5.4 Dating individual stones. If the axis is used to estimate years, the mean error is 21 years when each stone is estimated without itself, against 25 years for guessing the mean year: the seriation orders the stones, but it does not date a single stone much better than a guess.

What the finding says. Language, formulas and content changed in the same sequence as the ornament in Uppland, and it holds equally strongly in two halves of the material. Since the ornament is not included, it is support for Gräslund's relative chronology resting on other observations than her own. It also holds without the crosses, which are part of the picture, without the Ingvar and England stones, which could otherwise anchor the time, and without the spelling traits whose change is measured separately.

Against earlier research. The stylistic chronology is the basis on which most datings of Swedish runestones rest (Gräslund 2006). The result says that it is not only an ordering of ornament: language and content follow the same time. In Södermanland, where the chronology is applied but was not built, the same sequence is found but about half as strong.

Weaknesses, in order of weight.

1. The sequence runs between carvers. Within one and the same carver the correlation is only 0.25. Ornament and language both follow the carver, and the carvers worked at different times; part of the agreement may therefore be that the seriation orders carvers. Within hundreds it holds (0.51), so it is not an ordering of districts.
2. Not pre-registered. The seriation in Uppland was known when the plan for the halves and Södermanland was locked. The halves and Södermanland are therefore the actual test.
3. Södermanland may be geography. With latitude held constant the correlation is 0.29, below the plan's limit.
4. Not a dating. The mean error for years is only somewhat better than guessing the mean year.

What would overturn the finding. If the correlation disappeared within carvers also in a larger material with more carvers who worked long, or if a dating independent of both ornament and language gave another sequence.

Ordered by language, formulas and content, the runestones of Uppland fall in the same sequence as in the stylistic chronology, rho 0.54, and it holds in both halves. That is independent support for the relative chronology, but the order runs largely between carvers, and in Södermanland it is weaker and partly geographical. The next step is to test the seriation within carvers who worked over a long time, and in Östergötland and Västergötland when the dating there becomes more secure.