कलापिवैशम्पायनान्तेवासिभ्यश्च

After the words denoting the pupils of कलापि and वैशम्पायन , the affix णिनि is used in the sense of 'enounced by him'.
Karika

हरिद्रुरेषां प्रथमस्ततश्छगलितुम्बुरू ।
उलपेन चतुर्थेन कालापकमिहोच्यते ॥
आलम्बिश्चरकः प्राचां पलङ्गकमलावुभौ ।
ऋचाभारुणिताण्ड्याश्च मद्ध्यमीयास्त्रयो ऽपरे ॥
श्यामायन उदीच्येषु उक्तः कठकलापिनोः ।

This debars अण् and छ ॥ There are four words which express pupils of Kalapa: as, हरिद्रु, छगली, तुम्बुरुः, उलपः ॥ There are nine words expressing pupils of Vaisampayana: as, आलम्बि, पलङ्ग, कमल, ॠचाभ, आरुणि; ताण्ड्य, श्यामायन, कठ, कलापी ॥

Thus हारिद्रविणः 'those who study 4.2.64 the works enounced by Haridru.' तम्बुरविणः, औलपिनः and छगली takes dhinuk 4.3.109॥ आलम्बिनः, पालङ्गिनः, आरुणिनः, आर्च्चाभिनः, कामलिनः, ताण्डिनः, श्यामायनिनः ॥ The affix is elided after कठ 4.3.107, and is replaced by अण् 4.3.108 after कलापी ॥

The pupils must be direct ones, and not pupil of pupils. For had that been the meaning, Kalapi being a pupil of Vaisampayana, the words 'pupils of Vaisampayana' would have included the 'pupils of Kalapi.' But that is not so, the word Kalapi being separately mentioned in the sutra. So also Katha is a pupil of Vaisampayana, and Khadayana is a pupil of Katha and had the sutra applied to pupil's pupil also, then the affix णिनि would have applied to खाण्डायन also. But that is not the case, Khadayana being mentioned in Saunakadi class. 4.3.106.

The word चरकः means वैशम्पायनः, hence चरकाः means pupils of वैशम्पायनः ॥