Srimathe Ramanujaya Namaha,
Sri Velukkudi Krishnan Swami Guruvae Namaha,
Here is an article which states about the verses/quotes about classification of puranas into Satva,Rajas,Tamas.
https://narayanastra.blogspot.com/2013/05/vishnu-supreme-brahman-according-to-all.html#h.jpsmv0y5s5sd
Swami Ramanujar “Vedhartha Samgraham” states:
agneḥ śivasya māhātmyaṃ tāmaseṣu prakīrtyate /
rājaseṣu ca māhātmyam adhikaṃ brahmaṇo viduḥ //
sāttvikeṣu ca kalpeṣu māhātmyam adhikaṃ hareḥ /
teṣv eva yogasaṃsiddhā gamiṣyanti parāṃ gatim //
The same is found in Matsya Purana as:
sāttvikeṣu purāṇeṣu māhātmyamadhikaṃ hareḥ /
rājaseṣu ca māhātmyam adhikaṃ brahmaṇo viduḥ // MatsP_53.68 //
tadvadagneśca māhātmyaṃ tāmaseṣu śivasya ca /
Also, In Vishnu Puranam Upanyasam as below link, Swami says in the beginning that, depending up on Brahma’s which of the 3 guna’s are predominant at that time, He chants either Sathvik Purana or Rajasik Purana or Tamasik Purana. If Swami is saying about 3 types of classification of Puranas, then that itself is the shastric formal evidence, so we dont need to worry about actual shastric references.
https://www.youtube.com/watch?v=W3MUlhJtToU
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Bhaktas another question, “do all sects of sanatana dharmis accept this classification”. The Answer is already there in above Swamis clippings, same as Brahmas situation. It will depend up on the individual persons which guna is predominant, depending up on that, they will read related puranas. So accepting this 3 classification in right sense happens only if the persons Satva Guna is predominant, like how Bhakta is accepting this classification.
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Also adiyens understanding with Swami/Senior Bhagavatas anugraham is, Finally knowing which Puranas are which category, and what does these puranas/BhagavAt Gita says, doesn’t give us Moksham. Reading granthams or listening upanyasams only does “Chitta Shuddhi” (cleanising our karmas), so we could have a CLEAR MIND, which leads us to PERFORM “Sharanagathy (Athma Samarpanam)” on Para-Devathai ‘Perumal-Thayar’ ThiruvAdi through Swami Ramanujar ThiruvAdi, which gives us Moksham in same birth for those who has desire to reach SriKrishna lokam in SriVaikuntam. If not, we will keep reading all puranas/Gita in next janma also, like how were doing it in the past janma without doing Sharanagathy on Acharyan lotus feet. We have to stop our birth-death cycle at some point by doing Sharanagathy on Acharyans lotus feet, so Thayar-Perumal could their property ‘JeevAthma’ back, is what adiyen understood.
Adiyen Sri Velukkudi Krishna Dasan,
Uyya Oraey Vazhi UdayavAr ThiruvAdi,
Sarvam SriKrishnarpanam Asthu.