ऋत उत्

Operational rule vidhi

If a ऋकार or ऌकार is followed by the अकार of ङसिँ or ङस् प्रत्यय, then both of them combined to form an उकार.

Word by word (padaccheda)

Left context ऋतः pañcamī · ekavacanaSubstitute / term उत् prathamā · ekavacana

Left context Pañcamī (5th case): "after X", the operation applies to what follows (1.1.67 तस्मादित्युत्तरस्य). Also used for limits and sources.
Substitute / term Prathamā (1st case): in operational rules, the substitute or the thing introduced; in definitions, the term or its referent.

Full reading

ऋतः उत्

Pāṇini leaves out words that carry over from earlier sūtras. Expand to see the rule as a reader actually understands it.

Commentary

In the room of ऋ + अ of the case-affix अस् of the Ablative and Genitive singular, the single substitute is the letter short उ।
Thus होतृ + अस् = होतुर्स् (The उ must always be followed by र् 1.1.51 though this उ is not the substitute of ऋ only, but of ऋ + अ conjointly: on the maxim that a substitute which replaces two, both shown in the genitive case, as ऋतः and अकारस्य in this sutra, gets the attributes of every one of these separately as the son C of a father A and mother B (though both conjointly produce him) may be called indifferently the son of A or the son of B. So the उ may be called the substitute of ऋ or अ) II The final स् is then elided by 8.2.24 and we have होतुर् = होतुः ॥ Thus होतुरागच्छति, होतुः स्वम् ॥

Śrīśa Chandra Vasu, The Ashtadhyayi of Panini (1897), via ashtadhyayi.com.