अष्टनः संज्ञायाम्

Operational rule vidhi

A long vowel is substituted for the final of अष्टन् before a second member, when the compound is a Name.

Word by word (padaccheda)

Target अष्टनः ṣaṣṭhī · ekavacanaRight context संज्ञायाम् saptamī · ekavacana

Target Ṣaṣṭhī (6th case): names what gets replaced, "in place of X" (1.1.49 षष्ठी स्थानेयोगा).
Right context Saptamī (7th case): "when X follows", the operation applies to what precedes (1.1.66 तस्मिन्निति निर्दिष्टे पूर्वस्य). Also a condition or domain ("in the sense of").

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Full reading

अष्टनः संज्ञायाम्

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

Commentary

A long vowel is substituted for the final of अष्टन् before a second member, when the compound is a Name.
Thus अष्टावक्रः, अष्टावन्धुरः अष्टापदम् ॥ But अष्टपुत्रः, अष्टभार्यः where the compounds are not names.

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