Questioning Authenticity of works attributed to Adi Sankara

Are all the works attributed to Adi Sankara bhagavadpAda actually his compositions?

There are over 400 different works attributed to Adi Sankara. Many eastern and western scholars have raised their concerns about the works which are attributed to Adi Sankara are actually composed by the great acharya. There are several reasons for these assumptions. Hymns, stotras, stutis, etc are not voluminous works. Westerners may not have any hidden motives, but researchers, by nature, are extrovert unless they are Self Realized. An extrovert person who believes in logical reasoning cannot imagine something that their mind cannot comprehend, nor they can accept things that do not seem to be practically possible, comparing their ability and the extraordinary effort and time needed to compose those hymns.  Genuine enquiry is welcome. 
It is not in my capacity to find the truth behind the authenticity of works attributed to Adi Shankara. This page is created to know the reasons behind such doubts, so that at least we can understand the basis on which the doubt is created. Attempts are made to give simple logical explanation in support of works attributed to our AchArya Adi Sankara bhagavadpAda.

Critical analysis of Adi Sankara's authorship over vast works attributed to him can be broadly classified into two reasons

1. A person cannot change writing style and thinking pattern (this includes the main philosophy taught by him as he cannot change his basic philosophy, which has become a part of his life itself).
2. In short life span, a person cannot compose around 400 hymns, stotra-s, independent grantha-s and commentaries. Hence later AchArya-s who hold the title of SankarAcArya must have composed them.

We will try to understand these objections and give possible answers.
Let us now try to understand what methods are used to determine authenticity of attribution of works attributed to Adi Shankara Bhagavadpada

Methods of evaluation for determining authenticity
There are certain parameters and rules according to which works are tested. There are three types of works 

• Commentaries / Sub-commentaries 
• Independent hymns, stuti-s and stotra-s, which includes those related to his biography. 
• prakaraNa grantha-s 

Methods of evaluation mostly include 

• Colophon (Introduction to a chapter e.g. intro of different chapters in Gita BhASya) 
• Writing style, Chanda, Meter, Terminology, Grammar, etc used 
• Sub-commentaries by famous successors of Advaita tradition citing reference of his works. E.g. Siddhanta bindu is a commentary by Madhusudan Sarasvati on dasasloki, manasollasa is commentary by sureSvarAcArya on daxINAmUrty stotra 
• Historical facts relating to incidents in his life as mentioned in Adi shankara’s biographies like Sankshepa Madhaviya Digvijay or Ananadgiri’s PrAcina-Sankara-vijaya 

Major works are of westerners who just think logically without meditating and so they do not get proper insight. Some critics have biased mind. Natalia Isayeva’s work is published in a book titled 'Shankara and Indian Philosophy' (found here, refer pg 101 [1]), Reading 5-10 pages gives you an idea on the way of analysis. On page 101 (110 in pdf file), she mentions three types of debates, vAda, jalpa and vitaNDa. She declares that it is vitaNDa that appears to have been particularly prevailed in advaita polemics. One can understand the mindset of these type of critics. For the sake of understanding, let us under what these three words mean, as explained by Kanchi Paramacharya. (sanskrit words are not spelled as per transliteration)

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