The importance of saṅkalpa in every ritual – be it nitya, naimittika or kāmya, is well established in the śāstras. In terms of śrīvidyā, based on sampradāya-bēda, a specific saṅkalpa is prescribed.
In Kērala sampradāya, the saṅkalpa is performed thus:
केरलाख्ये सम्प्रदाये सङ्कल्पं शृणु सादरम् |
प्रीत्यर्थं देवतायास्तु सङ्कल्पः परिकीर्तितः ||
keralākhye sampradāye saṅkalpaṃ śṛṇu sādaram |
prītyarthaṃ devatāyāstu saṅkalpaḥ parikīrtitaḥ ||
Thus, the sankalpa here would be:
श्रीमहात्रिपुरसुन्दरी प्रीत्यर्थे जपे विनियोगः |
śrīmahātripurasundarī prītyarthe japē viniyogaḥ |
In the case of Kāśmīra sampradāya, the viniyōga is taught thus:
काश्मीराख्ये क्रमे देवि विनियोगं शृणु प्रिये |
प्रत्यक्षदर्शनार्थं हि देवताया महेश्वरि ||
kāśmīrākhye krame devi viniyogaṃ śṛṇu priye |
pratyakṣadarśanārthaṃ hi devatāyā maheśvari ||
Thus, the format for saṅkalpa would be:
श्रीमहात्रिपुरसुन्दर्याः प्रत्यक्षदर्शनार्थे जपे विनियोगः |
śrīmahātripurasundaryāḥ pratyakṣadarśanārthe japē viniyogaḥ |
In Gauḍa krama, the format prescribed is thus:
गौडक्रमे महेशानि सर्वसिद्ध्यर्थमेव तु |
देवताया यदा प्रीतिस्दता सर्वं प्रवर्तते ||
gauḍakrame maheśāni sarvasiddhyarthameva tu |
devatāyā yadā prītisdatā sarvaṃ pravartate ||
And this translates to:
सर्वसिद्ध्यर्थे जपे विनियोगः |
sarvasiddhyarthē japē viniyogaḥ |
These modes of saṅkalpa are indicative of the difference in approach between the three chief sampradāyas.