The Akal Takht faces the Harmandir Sahib across the causeway, and the fact that they look at each other is the doctrine.
Miri and piri
Guru Hargobind wore two swords: miri, temporal authority, and piri, spiritual authority.
The two buildings express the same claim. The temple is the seat of spiritual authority; the Takht is the seat of temporal authority. Each was placed where it looks directly at the other, so that neither can be considered without the other.
The position it rejects is that religion should confine itself to the inner life and leave power alone. Sikh tradition holds the opposite: that spiritual authority carries obligations in the world, including the obligation to resist.
Higher than a throne
Guru Hargobind founded it in the early seventeenth century as the Akal Bunga, raising a platform higher than any seat a subject of the Mughal emperor was permitted.
That was not an oversight. It was a deliberate assertion that the community's authority did not derive from the emperor's.
Sources differ on whether the founding year was 1606 or 1609.
What a hukamnama is
Edicts issued from the Akal Takht, hukamnamas, bind the whole Sikh community worldwide. They can settle disputed questions of practice, and they can excommunicate, which is the sanction that gives the office its force.
The Jathedar of the Akal Takht is the highest temporal authority in Sikhism and speaks for Sikhs globally.
1984, and the rebuilding that was rejected
The Indian Army destroyed the building during Operation Blue Star in June 1984.
The government then had it rebuilt within weeks, by a Nihang leader, Baba Santa Singh, working under state sponsorship. The work was completed quickly and the building stood.
The community rejected it, precisely because the state had paid for it. A seat of authority independent of the government could not be reconstructed by that government without forfeiting the thing it stood for.
Santa Singh was excommunicated. The new structure was demolished in January 1986 and rebuilt by kar seva, voluntary labour.
Most of the nineteenth-century frescoes were lost in the process, destroyed in 1984, and what survived did not survive the demolition and rebuild.
The unresolved question
Who may appoint and remove the Jathedar has never been settled.
Rival claimants have been recognised by the Shiromani Gurdwara Parbandhak Committee on one side and by Sarbat Khalsa assemblies on the other. The committee is an elected statutory body under the Sikh Gurdwaras Act 1925; the Sarbat Khalsa is a traditional general assembly with no statutory basis.
Underlying it is a genuinely open question: whether the highest temporal office in Sikhism can be independent of the committee that funds it and appoints to it.