Which surah starts without “Bismillah” ?

According to Imam al-Qurtobi in his tafsir five reasons for the lack of al-Basmalah (Bismillahi ar-Rahmani ar-Rahim) in surath bara’ah براءة or at-Taubah (at-Tawbah) have been quoted by scholars:

It was said that the Arabs in al-Jahiliya if they had a treaty with others and wanted to refute it they addressed them a Letter which didn’t start with al-Basmalah. When the surah bara’ah was revealed and refuted the treaty between Mohammad () and the pagans the Prophet () has sent his cousin Ali () who recited or read it out aloud in an occasion (or feast) and he didn’t read al-Basmalah following this custom.
He quoted this hadith which is compiled in sunan abi-Dawod, Jami’ at-Tirmidhi and also in al-Mustadrak of al-Hakim, sahih ibn Hebban and Musnad Ahmad. Which emphasizes two facts and an assumption: that the order of the surahs in the Quran is at least to some extent a matter of ijtihad (of the sahaba) and the fact that Qiyas is indeed a valid legal source (as they made Qiyas (deductive analogy) to order surat at-Tawbah after surat al-Anfal because of the similarity of the stories or narrations). And as the sahaba seemed to have a doubt whether these two surahs were different they didn’t put the basmalah between them (this is the assumption).
The Basmalah was not mentioned in the beginning of this Surah because the Companions did not write it in the complete copy of the Qur’an (Mushaf) they collected, following the Commander of the faithful, Uthman bin Affan, may Allah be pleased with him. (From tafsir ibn Kathir)

The 3rd opinion is based on the fact that some sahaba said that this surah before the abrogation of some verses had the length of surat al-Baqarah and has also an origin in a statement of ‘Othman ():

وقال مالك فيما رواه ابن وهب وابن القاسم وابن عبد الحكم : إنه لما سقط أولها سقط ” بسم الله الرحمن الرحيم ” معه
(My own translation take it carefully) – – –
Imam Malik has said according to what has been narrated on the authority of (his students) ibn Wahb, ibn al-Qassim and ibn ‘Abdalhakam: When its beginning has been taken away (abrogated) also “Bismillahi ar-Rahmani ar-Rahim: In the name of Allah , the Entirely Merciful, the Especially Merciful.” has been left aside.

Some of the scholars of the tabi’yn like Kharijah خارجة (one of the 7 scholars of Medina) and abu ‘Ismah أبو عصمة said: When they compilled the moshafs (written copies of the Quran) at the time of ‘Othman the sahaba had a difference on whether at-Tawbah and al-Anfal are different surahs or the same so they kept a space between both as a compromise between both parties.

The fifth view is based on a statement of ibn ‘Abbas ()(which is quoted in al-Mustdrak of al-Hakim)

قال عبد الله بن عباس : سألت علي بن أبي طالب : لم لم يكتب في ( براءة ) ” بسم الله الرحمن الرحيم ” ؟ قال : لأن ” بسم الله الرحمن الرحيم ” أمان و ( براءة ) نزلت بالسيف ليس فيها أمان . (My own translation take it carefully) – – –
Abdullah ibn ‘Abass said: I’ve asked Alib ibn abi talib: Why they didn’t write in Bara’ah “Bismillahi ar-Rahmani ar-Rahim”? He answered: Because “Bismillahi ar-Rahmani ar_Rahim” is a gurantee (or safety ) while Bara’ah has been revealed with the sword (meaning in order to make an end to the treaty of al-Hudaybiyah) without any (promise of) safety.