Vishnu’s Return to Brahmā and the Vāmana–Trivikrama Theophany
तमब्रवीत् प्रीतियुतः पितामहो वरं ममेहाद्य विभो प्रयच्छ रूपेण पुण्येन विबो ह्यनेन संस्थीयतां मद्भवने मुरारे
tamabravīt prītiyutaḥ pitāmaho varaṃ mamehādya vibho prayaccha rūpeṇa puṇyena vibo hyanena saṃsthīyatāṃ madbhavane murāre
Filled with affection, the Grandfather (Brahma) spoke to Him: 'O All-pervading Lord, grant me a boon here today. O Murari, please reside in my abode with this very auspicious form.'
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In the Puranic context, when a deity asks another to reside in their abode (Madbhavane), it signifies the unification of divine powers at a specific Tirtha. Since Brahma is the speaker, this often refers to a location like Pushkara, establishing that the holiness of a creator's site is amplified by the preserver's presence.
Brahma is not just asking for Vishnu's abstract presence, but for him to remain in that specific visible, meritorious form (likely the form he assumed during the specific narrative preceding this verse). This establishes the concept of 'Arca-avatara'—the deity incarnating in a specific image or form for worship.