[Query] Please enlighten about differences between kadi, hadi and sadi vidyas?
In essence, there is no difference between kAdi, hAdi or sAdi as all three refer to the same brahma vastu called srI lalitA.
1. kAdi was taught by Sri Manmatha [sadAshiva – nArayaNa – Hayagriva – Agastya - Shankara bhagavatpAda etc are the Gurus], hAdi by Bhagavati Lopamudra [Parameshwara – Parashakti – Lopamudra – Kalatapanandanatha etc. are the Gurus] and sAdi by Sri Krodha Bhattaraka Durvasa Deshikendra [Mahadeva – Rudra – Durvasa – Dharmacharya etc are the Gurus].
2. kAdi invokes kAmeshwarAmka sthitA kAmeshwarI, hAdi invokes kAmeshwarI vibhUshitAnko kameshwaraH and sAdi invokes kAmakAmeshwarau shivau. In fact, Shadanvaya Shambhavi Krama described by Acharya in Saundaryalahari is chiefly for sAdi upAsakas. The subtle differences in these three visualizations should be learnt directly from one's Sadguru.
3. kAdi and hAdi panchadashi-s transform to laghu shodashi and maha/parA/guhya shodashi-s (in case of kAdi) and shuddha/hamsa shodashis (in case of hAdi). There is no shodashi in sAdi karma but the transformation is into saptadashI. Further, in the final step of karma system, all the three paths merge into aShTAdashaksharI.
4. Anga devatas differ for the three vidyAs.
5. The guru mandalas are different for the three. Oghatraya for kAdi and hAdi are well-known. Apart from its own oghatraya, paraugha, parAparaugha, aparaugha are worshipped in sAdi krama.
The best example of peaceful co-existence of hAdi and kAdi seems to be the household of Sri Agastya and Bhagavati Lopamudramba, who respectively were worshippers of kAdi and hAdi vidyAs. Sri Kamakshi Mahabhattarika is the confluence of the three chief vidyAs as she was worshipped by Agastya, Lopamudra and Durvasa.
gurumUrte tvAm namami kamAkShi