Tibetan Empire

བོད་ཆེན་པོ

Began 618Ended 842Tibet and the Himalaya

The plateau empire that fought the Tang and the caliphate at the same time, and briefly held both Chang'an and the Silk Road oases.

Reach
4,600,000 km²
Lasted
224 yrs
Population
No cited figure
Rating
69th pct

Facts

Core region
The Tibetan plateau and the Tarim basin
Capitals
  • Lhasaལྷ་སfrom 618
Founder
Songtsen Gampor. 618–649
Peak-era ruler
Trisong Detsenr. 755–797
Last ruler
Langdarmar. 838–842
Administration
Tibetan
Writing system
Tibetan
How it ended
fragmentation842Beckwith, The Tibetan Empire in Central Asia (1987)

How it was governed

0 of 4 coded
Army raised byHow the fighting force was recruited, not how it fought.
No cited figure
Revenue fromWhat the state lived on. The values are unranked: the field cannot express which mattered most.
No cited figure
Succession byThe rule in force, not the outcome. A rule repeatedly violated is still the rule.
No cited figure
Right to rule fromThe ground publicly asserted — on coins, in the khutba, in titles.
No cited figure

Each line is drawn from a source that addresses the question directly. A line reads No cited figure where no source consulted does — never because the answer seemed obvious.

Turning points

No dated event is recorded as having changed this polity’s course. Not every history has one: a hinge is something some polities turn on and others simply do not.

Chapters

8 in order

The golden goose

Drafted from Bushell, The Early History of Tibet, from Chinese Sources (1880)formation

The Tibetan empire enters the written record in the seventh century as a frontier problem in a Chinese archive, and the way the Tang historians tell it is worth reading exactly, because they are describing a man they thought they had absorbed.

How to obtain a princess

Songtsen Gampo — Lungtsan, in Bushell's transcription of the Tang text — asked for a marriage alliance and was refused. So he invaded, carried off the herds of a neighbouring people, and stayed in the field for several years without going home; his chief ministers begged him to return, and when he would not listen, eight of them killed themselves.

Then he sent a mission to apologise for his misdeeds and asked again, with five thousand ounces of gold and several hundred precious articles. In 641 the emperor gave him the Princess Wencheng.

That is a Chinese court history admitting, in its own words, that a marriage alliance was extracted by force and then paid for.

What he did with her

The account of what followed is the part a Chinese historian is least likely to have invented, because it is flattering to China and factually specific.

He met her escort in person and received the presiding prince with the rites due from a son-in-law. Afterwards, the history says, he praised the costume of the great empire, and the perfection of their manners, and was ashamed of the barbarism of his own people. He told his relatives that no ancestor of his had ever been allied to the sovereign empire, and that he would build a walled city for the princess to proclaim his glory to later generations — and did, with a palace for her inside the walls.

She disliked the Tibetan custom of painting the face red, so he ordered his people to stop, and they stopped. He put off felt and skins and put on brocade and silk. He sent the sons of his chiefs and his rich men to ask admission to the Chinese national schools to study the classics, and invited scholars from China to compose his official despatches to the emperor.

The goose

The despatches were worth having. When Taizong came back from campaigning in Korea, Songtsen Gampo's minister was sent with congratulations and this:

The wild goose flies most swiftly, but not when compared with the speed of the emperor. His slave and unworthy son-in-law, rejoicing a hundred-fold above ordinary barbarians, in that the common goose is not unlike the wild goose, has made a gold goose, and respectfully offers it.

The goose was moulded of pure gold, seven feet high, and held about ten gallons of wine.

Read the letter and the object together and they are not the same document. The letter is elaborately abject — his slave and unworthy son-in-law, above ordinary barbarians — in the precise register a Chinese chancery expects, which is exactly what you would produce if you had hired Chinese scholars to write your despatches. The gift is a seven-foot wine vessel of solid gold from a country the Tang had just refused a princess.

What he was actually building

Within seven years of the marriage, in 648, a Chinese envoy on his way to India was robbed there, and it was Tibetan troops who marched into India with him, defeated the offenders and sent word of the victory to the Chinese emperor. The next emperor gave Songtsen Gampo the title Prince of the Western Sea and two thousand pieces of silk. He replied offering to lead his warriors into China personally to punish any officer who proved disloyal.

That is not a client. That is a power positioning itself as the guarantor of a neighbour's order, in the vocabulary of a son-in-law, six years after being told it was not good enough for a princess.

Under the same reign an alphabet was devised for Tibetan on an Indic model, and the country acquired the ability to write itself down — which is the more consequential of the two things Songtsen Gampo imported, and the one the Tang historians do not mention.

Fifteen days in Chang'an

Drafted from Bushell, The Early History of Tibet, from Chinese Sources (1880)expansion

In the tenth month of 763 a Tibetan army walked into the capital of the Tang empire, deposed the dynasty, appointed a new emperor with a new reign title and a full slate of ministers, and went home a fortnight later.

The Tang histories record all of it, because they had to.

How it happened

The empire was still broken from the An Lushan rebellion. Tibetan forces took Jingzhou, whose governor Gao Hui surrendered to them; the next month they invaded Binzhou. The great general Guo Ziyi was sent west to hold them, and had to turn back when two hundred thousand Tuyuhun and Tangut troops came in from another direction.

Then the emperor's carriage left for Shangzhou and the capital was abandoned. The surrendered governor led the Tibetans in.

Inside the city, with the Tibetan commander-in-chief, they raised the Prince of Guangwu to the throne, gave his reign the title Dashe, and appointed the various officers of state.

What the empire looked like that autumn

Bushell's translation keeps the detail, and the detail is the humiliation.

When the emperor first went east, the officers and their families fled south or went into the mountains to hide, and the soldiers of the imperial armies broke up into armed bands blocking the roads. Guo Ziyi — the most celebrated soldier of the dynasty — was in a mountain valley with a few hundred followers, his wives, children and slaves, and some hundreds of camels, horses, carts and oxen, not knowing which way to turn, until two of his officers came and told him he ought to be ashamed of himself.

He agreed, and took a back road because the main one would be watched. His column of a thousand men was strung out over a hundred li because the mountain track was too narrow, and two of his officers left by a different route in case of pursuit, since in a defile the van could not help the rear.

Meanwhile the general of the six armies had fled the capital with his own standard and spent several days plundering the fleeing court officials and robbing the townspeople of money, saddles and horses, until he too was talked into behaving.

That is the strongest empire in the world, described by its own historians, in the fortnight after a Tibetan army took its capital.

Then they left

The Tibetans occupied the city fifteen days and retired, and the imperial army came back.

It is easy to read the withdrawal as a failure of nerve, and it was not. An army of this kind could not garrison Chang'an: it was months from its own supply, in a river valley in autumn, with a hostile countryside and no interest in administering a Chinese province. What it could do was demonstrate — publicly, in front of every polity in Inner Asia — that the Tang could be reached.

That demonstration is why the empire spent the following century holding the Gansu corridor and the Tarim oases at Chinese expense, and why the Uyghurs could charge the price they charged for cavalry.

Three powers, not two

The period between about 660 and 840 is usually told twice, once from Chang'an and once from Baghdad, and each account has a frontier that stops where the other begins. Between them was a third empire fighting both.

Tibetan armies took Tang oases in the Tarim, met the caliphate's forces in the Pamirs and Transoxiana, and at different moments allied with each against the other. The Karluks, Türgish and Uyghurs in between made and unmade arrangements with all three.

Neither surviving imperial tradition has an obvious place for that, which is why a fortnight in 763 tends to appear in accounts of the Tang as a raid, and in accounts of Islam not at all.

The third power

Drafted from Beckwith, The Tibetan Empire in Central Asia (1987)peak

At its height the empire held the Tarim basin oases, the Gansu corridor, much of what is now Qinghai and the approaches to the Pamirs, and fought both of the great settled powers of the age at once.

The Abbasid frontier in Central Asia was not simply the far edge of the caliphate; it was one face of a three-cornered contest, and the Karluk, Türgish and Uyghur groups in between made and unmade alliances with all three. The period is usually narrated twice — once from Chang'an, once from Baghdad — and each version has a frontier that stops where the other begins.

The empire's other creations are a script and a religion. Songtsen Gampo's reign saw an alphabet devised for Tibetan on an Indic model — a writing system made for a language that had none. Trisong Detsen made Buddhism the religion of the court.

It broke apart after Langdarma's assassination in 842, and nobody conquered it.

Which Buddhism

Drafted from Beckwith, The Tibetan Empire in Central Asia (1987)aside

Trisong Detsen made Buddhism the religion of the Tibetan court in the second half of the eighth century and founded the monastery at Samye in the 770s. Then he had to decide whose Buddhism it was going to be, and the choice was between his two largest neighbours.

The question

Tibet sat between India and China and could have taken the religion from either. The Chinese route was the obvious one: the empire had been dealing with the Tang for a century and a half, it had captured Chinese territory full of Buddhist establishments, and Chan teachers were already in the country. The Indian route meant bringing scholars over the Himalaya and working in a language nobody in Tibet had grown up speaking.

The tradition records a debate at Samye, placed in the 790s, between an Indian monk arguing the gradual path of study and accumulated merit and a Chinese Chan master arguing sudden enlightenment. The Indian side is recorded as winning.

Whether it happened as a single staged event is doubted, and the sources for it are Tibetan and later and have an interest in the outcome. That a choice was made in that direction is not in doubt at all, because everything downstream of it is visible.

What a king was choosing

It is worth being clear that this was not only a doctrinal question, because the doctrinal question is the part that has survived and the political one is the part that would have decided it.

Trisong Detsen was at war with the Tang for most of his reign; his armies took Chang'an in 763 and he spent decades holding the Gansu corridor against Chinese attempts to recover it. Adopting the religious establishment of the state he was fighting, staffed by its clergy and reading its commentaries, would have put a Chinese-trained institution at the centre of his court.

India was not a rival. There was no Indian empire on his frontier, no Indian army he was going to have to fight, and no Indian court whose prestige his own nobility might prefer to his. Importing from India meant importing scholars without importing a patron.

What it committed the state to

Everything that followed was expensive.

Taking the religion in Sanskrit rather than in Chinese translation meant a translation programme built from nothing: Indian panditas brought in and maintained, Tibetan translators trained in a language with no prior tradition of scholarship in it, and — the decision that made the whole thing work — a standardised technical vocabulary decreed by the court, so that a given Sanskrit term produced the same Tibetan word in every text by every translator.

A state deciding by edict what words mean, and enforcing it across a body of translation running to thousands of volumes, is an administrative act on the scale of a tax reform. It was paid for out of the same revenue as the armies in the Tarim basin.

Nobody involved was buying an institution that would outlast the court. That is simply what they got.

Like unto these victims

Drafted from Bushell, The Early History of Tibet, from Chinese Sources (1880)aside

The Tang histories carry a description of how the Tibetan state worked, compiled by people who had to deal with it and who wrote down the parts a foreign ministry needs to know. It is the only account of the empire's institutions written while it existed by anybody who was not inside it.

The machinery

The sovereign is the tsanpo — from tsan, a famous hero, and pu, a man. His consort is the momeng. Under him are ministers styled great lun and small lun, and the histories set out the whole establishment: a chief minister and his assistant, a commander-in-chief, a chief minister of the interior with an assistant and a lesser minister, a chief consulting minister with the same two grades under him, the whole body named collectively in one Tibetan phrase the Chinese transcribe and do not translate.

Then the observation that a Chinese archivist would find worth making:

Although there are officers, they are not constantly employed, being only appointed when there is stress of business.

An establishment that exists on paper and is staffed when required is a description of a state run by an aristocracy rather than a bureaucracy, from the point of view of the most bureaucratic government on earth.

The communications are the part they admired. A gold arrow seven inches long served as a sign of office and was used to call warriors out. There was a post station every hundred li; if the war was important the courier carried a silver hawk on his breast, and if it was urgent, several hawks. When the country was invaded, smoke-fires were lit from towers a hundred li apart.

No writing

The same passage states, flatly, that the Tibetans have no written characters, and that notched pieces of wood and knotted strings are used in covenants.

That cannot be true of the empire the Tang were fighting. An alphabet was devised for Tibetan on an Indic model under Songtsen Gampo; the treaty of 821 was cut in Tibetan on a stone pillar; and the imperial chancery was producing documents in Tibetan that survive.

What the sentence preserves is an earlier notice, copied forward into an account of a later state — which is how these compilations were made, and a useful warning about the rest of the description.

Punishment and hospitality

Two details sit next to each other and are worth keeping together.

Their punishments are most severe, and even for small crimes the eyes are scooped out, and the nose cut off, or stripes inflicted with a leather whip. They differ according to caprice, there being no fixed code. They imprison men in holes several tens of feet under the ground, and release them only after two or three years.

And:

When they entertain envoys from foreign countries, they always bring out a yak for the guest himself to shoot, the flesh of which is afterwards served at the banquet.

The first is an accusation — a Chinese historian's standard complaint about a government that has punishments without a written code, which is the thing his own state most prided itself on having. The second is a piece of protocol somebody experienced and reported, and it is the only glimpse anywhere of what being received at a Tibetan court was like.

The oath

The central institution, and the one the Chinese describe at most length, is a ceremony.

Once a year the officers were assembled for the lesser oath of fealty. Sheep, dogs and monkeys were sacrificed — their legs broken first, then killed, the intestines exposed and cut into pieces. The sorcerers were summoned and called on the gods of heaven and earth, of the mountains and rivers, of the sun, moon, stars and planets:

Should your hearts become changed, and your thoughts disloyal, the gods will see clearly and make you like these sheep and dogs.

Every third year came the great ceremony. All assembled in the middle of the night on a raised altar spread with savoury meats. The victims were men, horses, oxen and asses, and the prayer ran:

Do you all with one heart and united strength cherish our native country. The god of heaven, and the spirit of the earth, will both know your thoughts, and if you break this oath they will cause your bodies to be cut into pieces like unto these victims.

What that is a description of

Not barbarism, whatever the compiler thought. It is a constitutional mechanism.

An empire with no standing bureaucracy, whose officers are appointed when there is business and whose army is summoned by sending out a gold arrow, is held together by the personal obligation of a few hundred aristocrats to one man. The Chinese state bound its servants with an examination system, a code and a salary. The Tibetan state assembled them once a year and, every third year at midnight, showed them what they would look like if they broke their word.

For two centuries it worked better than the alternative. When it stopped working — when the great families took their own regions after 842 and stopped taking orders — there was nothing underneath it, because the oath was the administration.

A horse with no bit

Drafted from Bushell, The Early History of Tibet, from Chinese Sources (1880)contraction

The two empires swore treaties at each other for two centuries. The Tang histories record the ceremonies in detail, including the negotiations about what to kill and the occasion on which the ceremony was an ambush.

What to sacrifice

At the peace of 783 the two delegations agreed the shape of the thing in advance: two thousand men each, half armed and drawn up two hundred paces from the altar, half unarmed below it; seven men a side in court costume to go up and swear.

It had been agreed that the Chinese would sacrifice an ox and the Tibetans a horse. Then the Chinese envoy, Zhang Yi — who, the history says, was ashamed of his part in the ceremony and wanted to depreciate the rites — proposed a substitution:

The Han cannot cultivate the ground without oxen, the Fan cannot travel without horses, I propose therefore to substitute a sheep, pig and dog as the three victims.

The Tibetan minister agreed. But there were no pigs to be had outside the frontier, so he took a wild ram instead and the Chinese took a dog and a sheep. They were killed on the north side of the altar, the blood mixed in two vessels and smeared on the lips of the swearers.

An envoy embarrassed to be treating with barbarians downgrades the victims on a pretext about agriculture, and the other side, being on the wrong side of a frontier with no pigs, improvises. That is what two empires negotiating as equals looked like from close up.

Pingliang

Four years later they arranged to swear again, and the Chinese chose the ground carefully.

The Tibetan minister had proposed a valley called Tulishu. The general Ma Yulin reported that the Tulishu country was full of difficult passes and that he feared a secret ambush; Pingliang, by contrast, was a plain open on every side and close to a Chinese garrison town. The court agreed and moved the ceremony there, and had to send after the Tibetan envoy, who had already left, to tell him.

At Pingliang the two commanders agreed three thousand men a side drawn up east and west of the altar, four hundred unarmed men below it, and mounted scouts on both sides to watch each other.

Then the Tibetan minister massed several tens of thousands of picked horsemen west of the altar. His scouts rode through and through the Chinese ranks. When the Chinese general sent sixty horsemen into the middle of the Tibetan army they were seized and bound on the spot.

Hsien had provided for nothing.

A message came across asking that the minister and his subordinates put on their official robes and hats, swords and jewels, and wait for instructions — this was to induce them to dismount from their horses so that they might be captured. They went into the tent together, calm and unsuspecting. The Tibetan commander had the drums beaten three times and his army came on shouting.

The ride

The Chinese commander Hun Jian got out of the back of the tent, caught a loose horse and rode.

The horse had no bit in its mouth, and Hsien had to lean over its mane to guide it with his hands, and it was only after he had ridden for several miles that he got the bit into its mouth, and it was owing to this that the arrows of the pursuing horsemen passed by without wounding him.

One of his generals collected a few hundred men on a hillock to the north and fought until the whole army surrounded him. The treaty officials were taken.

Why the record kept it

A court history is not obliged to preserve an episode in which its own side chooses the ground for safety, agrees the numbers, walks into the tent, and is taken. The Tang histories preserve this one in circumstantial detail, down to the horse's missing bit.

Part of the reason is that Hun Jian survived to report it and somebody had to be blamed; the sentence about providing for nothing is a verdict. But the larger part is that the treaty system itself mattered. The Tang had been making sworn agreements with the Tibetans since the seventh century and would make another thirty-five years later — the one cut on stone in Lhasa, with its two sovereigns and its single border. A record of what happened when the ceremony was used as a trap is exactly what a chancery preserves, and reads.

The stone outside the temple

Drafted from Bushell, The Early History of Tibet, from Chinese Sources (1880)end

In 821 and 822 the Tibetan empire and the Tang concluded the last of their sworn treaties, and the text is the clearest statement anyone made of what the two centuries of fighting had established.

The terms

The oath was sworn on an altar in the western suburb of the Chinese capital, with a pit dug on the north side; the victims were sacrificed and buried with the written text.

What the Chinese now rule shall have the Tang as the sovereign, and the country of their western race shall have the great Fan as ruler. From this time henceforward both shall put by weapons and armour, forget their differences and old grievances, and respect the honoured kinship of their sovereigns and the ancient bonds of mutual aid. The frontier guard-houses shall be left ungarrisoned, and the watch-fires no longer lighted... the barrier stations and fortifications shall be disused and invasion and plunder shall cease.

And then the verse the ministers proclaimed:

The frontier mountains are lofty, the River flows on unceasingly: on a propitious day and favourable season have we fixed the two boundaries, the west to belong to the great Fan, the east to be ruled by the grand Tang: the great ministers, holding up the sworn treaty, proclaim it afar to the autumn country.

Two sovereigns, two territories, one border, no tribute either way. That is not how the Tang concluded arrangements with frontier peoples. It is how two empires conclude a peace.

The treaty was ratified in Tibet and cut on a stone pillar, which was set up in Lhasa outside the Jokhang temple and is still standing.

Twenty years

The empire had about twenty years left.

What ended it is domestic and badly documented. Langdarma was assassinated in 842; the succession was disputed between two claimants and never resolved; the great families that had supplied the empire's ministers took their own regions and stopped taking orders; a revolt of the common people in the 860s finished whatever central administration was left, and the imperial tombs were dug up.

There is no conquering power in it. Nobody took Tibet in 842 or afterwards. The Tang, which had spent two hundred years failing to, was itself sixty years from its end and in no condition to try. The Uyghur khaganate on the northern steppe had collapsed two years earlier, in 840, for reasons of its own.

What went with it

The state religion went. Buddhism had been made the court religion by Trisong Detsen and endowed on an imperial scale, and imperial endowment is what monasteries live on. When the court stopped, the monastic establishment stopped with it, for something over a century.

The empire's other creation did not stop. The translation programme had already produced a library, and libraries do not need a government.

What came back in the eleventh century was built on the books the empire had paid for, by men who no longer had any idea how to raise an army.

What the library did

Drafted from Beckwith, The Tibetan Empire in Central Asia (1987)afterlife

The empire fell apart in the 840s and Tibet did not become a state again for four hundred years. What the empire had built that survived the empire was a translation.

What the vocabulary did

The decreed vocabulary is the unglamorous part and it is the reason the whole enterprise worked. It made the body of translation internally consistent across thousands of volumes and hundreds of translators, and it made the Tibetan versions reversible: a scholar can often reconstruct the Sanskrit from the Tibetan word by word, because the same term was never rendered two ways.

Korea and Japan received their Buddhism through Chinese translations, which are not reversible in that way, having been made by many hands over centuries with no authority standardising them.

Why that turned out to matter to everybody else

Buddhism disappeared from India. Over the centuries after the empire fell, the monastic universities were destroyed, patronage went elsewhere, and a very large part of Indian Buddhist literature was lost in its original language.

The Tibetan canon has it. For a great many Indian Buddhist works — including central texts of Madhyamaka and Yogacara philosophy, and much of the tantric literature — the Tibetan translation is the only complete version that exists, and it is exact enough to be used as evidence for what the Sanskrit said.

So a decision taken by a Tibetan king in the eighth century about which of two neighbours to import a religion from is the reason a substantial part of Indian intellectual history is recoverable at all. It is not a Tibetan legacy in the ordinary sense. It is an Indian legacy that Tibet happens to be holding.

The four hundred years

The intervening period is usually called the era of fragmentation and it is badly served by the name, which suggests nothing happened.

The imperial line did not end; a branch of it went west and founded the kingdom of Guge in Ngari, which in the eleventh century paid for the second wave of translation and invited Atisha from Bengal. The monastic orders that dominate Tibetan history afterwards — Kadam, Sakya, Kagyu — all form in that period, out of the second transmission, working from and adding to the books the empire had paid for.

What did not come back was the state. When Tibet next appears as a political unit under a single authority, in the thirteenth century, it is as a territory administered for the Mongols by the abbots of Sakya — a monastery governing a country on behalf of a steppe empire.

That is the empire's real afterlife and its strangest one. It had made Buddhism the instrument of the Tibetan state; four centuries later the Buddhist establishment was the Tibetan state, and the arrangement lasted, in one form or another, until 1959.

Succession

What led here

  • Tibetan Empireabsorbed remnants ofZhangzhung

    The kingdom of the upper Sutlej and Ngari in western Tibet, with its own language, its own script and the Bon tradition attached to it. Songtsen Gampo married its ruler's sister, and the kingdom was absorbed into the empire during or shortly after his reign; its language survives in a handful of Dunhuang documents and in Bon texts.

What led away

  • the kingdom of Guge, and the second transmission

    No power took Tibet in 842 and none replaced the empire for four hundred years. A branch of the imperial line went west and founded Guge in Ngari, which paid for the second wave of Buddhist translation and invited Atisha from Bengal in the eleventh century; the monastic orders that dominate Tibetan history afterwards all form in that period, out of the books the empire had commissioned. When Tibet is next governed as a unit, in the thirteenth century, it is by the abbots of Sakya on behalf of the Mongols.

Contemporaries

46 overlapping

The 12 that overlapped longest, in date order.

Show the remaining 29

Derived from cited spans, not from a separate source. Where both spans are ranges and they meet only on the widest reading of each, the pair is listed as possible rather than resolved to one answer. Unlinked entries are here for scale and are not written up.

Extent

An illustration, not a measurement
Tibetan Empire — border precision 1, approximate

Snapshot year

800

This is the nearest available snapshot to the cited peak of 800. It is not the peak.

Cited extent

4,600,000 km²

The area of the shape on the left will not match this figure. That is expected. The cited figure is the figure; the map is an illustration, and the two are never reconciled.

Tibetan Empire, as the snapshot draws it
Everything else on the same snapshot

Edges are blurred from the dataset’s own border-precision field. Every feature in this period is marked 1, approximate, so every border here dissolves.

The dataset author’s caveat, which belongs here rather than in the footnotes: territorial boundary as a concept is meaningful in Europe only after Westphalia, ancient polities overlap, and old vector borders drawn on modern coastlines mislead because rivers and shorelines move. Boundaries from historical-basemaps, CC-BY-4.0.

Rating

Four axes, all computed from cited numbers and never from editorial judgement. Percentiles are against every polity written up here — 280 of them — plus 50 more included for scale. Absolute figures. A missing axis is excluded from the total rather than counted as zero.

Reach

4,600,000 km²

66th percentile

Longevity

224 years

54th percentile

Demographic weight

No cited figure

Influence

Three separate counts. This site never publishes a single influence number of its own; the sliders on the rankings view fuse them only in your view.

Descendant scripts

1

Tibetan script

Religions carried

1

Tibetan Buddhism

Successor claims

No cited figure

Weighted total

69th percentile

computed from 3 of 4 axes, renormalised across the axes that have figures. A polity with two documented axes is not penalised against one with four.