Is the order of the suras fixed by revelation or by the Companions' judgement?

The order of the suras in today's mushaf opens with al-Fatiha, then al-Baqara and Al Imran, although many Meccan suras were revealed before them. In the introduction to al-Jami' li-Ahkam al-Qur'an, al-Qurtubi devotes a chapter to the order of the suras and verses and to the Qur'an's vowelling, dotting and division, in which he reports two views on where the order of the suras comes from. ^{1 2 3}

Al-Qurtubi quotes the judge Abu Bakr ibn al-Tayyib: the early generations differed in the order of the suras; some wrote them in their codices in the order of revelation, putting Meccan before Medinan; some put al-Fatiha first; Ali's codex began with Surat al-Alaq, Ibn Mas'ud's with al-Fatiha, then al-Baqara, then al-Nisa', and Ubayy's with al-Fatiha, al-Baqara, al-Nisa', Al Imran, al-An'am, al-A'raf and al-Ma'ida — "with great variation". ^{1 2}

Ibn al-Tayyib answers that the present order of the suras may have been the Companions' own judgement. ² Al-Qurtubi reports from Makki that the order of the verses within the suras and the placing of the basmala at their heads came from the Prophet, and since he gave no such order for the head of Bara'a it was left without a basmala; al-Qurtubi says: "this is the soundest thing said on the matter". ² He reports from Ibn Wahb's Jami' that Rabi'a was asked why al-Baqara and Al Imran come first when some eighty suras were revealed before them, and answered that they were put first, that the Qur'an was arranged with knowledge by those who arranged it, and that they agreed upon it: "this is where we stop, and we do not ask about it". ²

Some scholars held that the arrangement of the suras as in our mushaf was fixed by the Prophet, and that the reported differences in the codices of Ubayy, Ali and Abd Allah predate the final review. ³ Yunus reports from Ibn Wahb that Malik said the Qur'an was arranged as they used to hear it from the Prophet. ³ Abu Bakr ibn al-Anbari wrote in al-Radd that the Qur'an was sent down whole to the lowest heaven and then in parts over twenty years, Gabriel showing the Prophet where each sura and verse belonged, "so the sequence of the suras is like the sequence of the verses and the letters"; he argued that whoever arranged the suras by their Meccan and Medinan stations would not know where to put al-Fatiha, since people disagree over where it was revealed. ^{3 4}

In al-Tafsir al-Wasit, Tantawi prefers that the order of the suras is fixed by revelation and that each sura has distinctive themes of its own, while criticising many of the correspondences claimed between neighbouring suras. ^{5 6}

Al-Qurtubi quotes Ibn Battal: those who hold the order fixed do not require it in recitation, in prayer or in study, but only in the written text; he cites Aisha's answer to a questioner, "it does not harm you which of it you read first", and the Prophet's reciting one sura in one cycle of prayer and, in the next, a sura other than the one that follows it; and he takes Ibn Mas'ud's and Ibn Umar's dislike of reading the Qur'an "inverted" to mean reading a single sura from its end to its beginning. ⁷