What is the evidence that indicates that the Quran has been completely preserved after the death of the Prophet, sallallaahu ‘alayhi wa sallam? Would you please provide logical and historical evidence, not textual ones (from the Quran and the Sunnah)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It is the duty of a Muslim to find the evidence from the Quran and the Sunnah more convincing than logical ones. However, out of belief in consistency between text and logic, and that each of them strengthens the other, and the impossibility of contradiction between sound logic and explicit text, it is admissible that when things are repeated, they are confirmed; and when they are spread, they are ascertained, and that having more than one proof in only one issue signifies certitude. That was exactly how the Quran was transmitted, and this is a fact known to all Muslims. Muslims inherited the Quran, one generation after the other. They studied it in their gatherings, recited it in their prayers and taught it to their children, and if it happened that a respected Shaykh made a mistake in one of its letters, the young, before the old, would hasten to correct him. That continuous process ensured that the Quran reached us free from addition or deletion and remained preserved from distortion.

Contemplating such proof, one has no alternative but to submissively surrender to its soundness; and whoever denies it risks being ridiculously ignorant. Even if we assume the possibility of denying this proof, then it would mean denying many other unquestionable facts, such as the existence of the Prophet, sallallaahu ‘alayhi wa sallam, the Companions and the prominent historical figures, and this, of course, is something that all wise people would reject.    

Further proof that the Quran is safeguarded from addition and corruption lies in its definite unquestionable inimitability. In this regard Allaah The Almighty challenges the polytheists to produce a single verse or more that would resemble the verses of the Quran, yet they have failed to do so.  Had something been added to the Quran or had it been distorted, it would have ceased to be inimitable, since it is possible to imitate the speech of humans. However, as long as it remains inimitable, this indicates that Allaah The Almighty has preserved His Book and safeguarded it from distortion or addition.

Allaah Knows best.