कठचरकाल्लुक्

Operational rule vidhi

The affix denoting 'enounced by him' is elided by लुक्-substitution after the words कठ and चरक.

Word by word (padaccheda)

Left context कठ- चरकात् pañcamī · ekavacanaSubstitute / term 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.

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Full reading

कठ-चरकात्

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

Commentary

The affix denoting 'enounced by him' is elided by लुक्-substitution after the words कठ and चरक।
The word कठ would have taken णिनि as it is a वैशम्पायनान्तेवासी word: and चरक would have taken the affix अण् ॥ Both are elided. Thus कठाः 'who study the Chhandas enounced by Katha'. चरकाः &c.

The word 'Chhandas' qualifies this sutra. Observe काठाः चारकाः श्लोकाः ॥

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