The distinction between 嫡子 and 庶子 was supposedly crucial in struggles for the Chinese imperial throne. It is often repeated (example) that only sons of the Empress were considered 嫡子。

Here it is stated explicitly, that the sons of 貴妃 were not 嫡子. And yet in the Zizhitongjian， scroll 238 , the son of a highest ranking concubine (貴妃) is referred to as 嫡子。

Relevant passage:

立遂王宥為太子，更名恆。恆，郭貴妃之子也。諸姬子澧王寬，長於恆。上將立恆，命崔群為寬草讓表。群曰：「凡推己之有以與人謂之讓。遂王，嫡子也，寬何讓焉！」

Partial translation attempt:

The King of Sui, You, was installed as crown prince. His Name was changed to Heng. He was the Son of Guo Guifei. The son of an ordinary consort, King of Li, Kuan, was elder than Heng. The Emperor wanted(?) to install Heng . He instructed Cui Qun to draft an abdication for Kuan. Qun said: […] „ The King of Sui is a 嫡子！ How could Kuan abdicate (i.e.: as he was not entitled to begin with)?

So, what was the precise definition of 嫡子？Was the above just a deliberate distortion of facts by Cui Qun? Or perhaps my understanding of the Ancient Chinese quote is crucially flawed?

Supplements

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Dictionaries Link 嫡子 to 正妻

My Hanyu Dacidian defines 嫡子 as the son of 正妻：

正妻所生之子

This is also repeated here:

嫡子（正妻所生之子）

Who is 正妻？

If we start out from this definition (that 嫡子 are precisely the sons of 正妻) the prevalent claim seems to be that only the Empress is 正妻. This source states:

皇帝的女人虽然多，但是正妻却只有一个，那就是“皇后”。/ Although the Emperor‘s women were many, there nonetheless was but one 正妻，namely the Empress.

Here is one more article that implicitly equates 皇后 with 皇帝的正妻 (“ “后”本来是君王的称呼。后来成为帝王妻子的专用名称，既然是皇帝的正妻，于是称“皇后”“).

Here one more that makes it explicit.

I see at least three possibilities:

1. Only the Empress is a 正妻，崔群 is not explained
2. The first properly wed wife is 正妻
3. Several wifes are 正妻 as it is alleged for pre-imperial China

Is the relevant maternal rank that at time of childbirth?

Based on the example of 商纣王 and brothers by the same mother here I assume mother‘s rank at birth to be relevant. Is this correct for 嫡子 in the Tang period?

Legal Situation (presumably not for royals)

Is very clearly set out in 唐律 159. After the primary wife reaches a certain age, an ordinary son (庶子）may be made 嫡子。