• nārāyaṇasya — of Nārāyaṇa
  The crowd places Kṛṣṇa as expansion-of-Nārāyaṇa — the standard Vaiṣṇava genealogy. Gauḍīya correction: the order is in fact reversed, Kṛṣṇa is svayaṁ-bhagavān and Nārāyaṇa His Vaikuṇṭha-expansion (SB 1.3.28: kṛṣṇas tu bhagavān svayam). The crowd's reading is correct but incomplete; the Bhāgavatam itself will refine it.
• sākṣāt — directly
  'Directly' — not symbol, not metaphor. The Mathurā crowd reaches for the strongest available word: not 'like' Hari, not 'representing' Hari, but Hari sākṣāt. The Gauḍīya note: every Vraja-darśana is direct; Bhagavān has no veils for those who recognize Him.
• avatīrṇau — have descended
  Avatāra-vāda in dual. The doctrine of descent is articulated by the Mathurā citizens themselves, not by Vyāsa as commentary. Bhāgavata mode: revelation as overheard speech.
• vasudevasya-veśmani — in the home of Vasudeva
  The same household where Devakī was imprisoned (10.1–4) is now publicly named as Bhagavān's avatāra-bhūmi. The whole secret of Canto 10's prison-birth is suddenly common knowledge in the arena. A contiguous-token join of synonyms 'vasudevasya' and 'veśmani'.

• Radha Raman Sw SB 10-43-23-30 - 2014-06-03 ISKCON Alachua
  His Holiness Radha Raman Swami· 2014-06-03· English
• Ramai Sw SB 10-43-23 - 2006-11-29
  His Holiness Ramai Swami· 2006-11-29· English

• Where do you discount the spiritual perceptions of ordinary people?
• What if collective recognition is itself a form of evidence?

Mathurā, watching Kṛṣṇa enter, recognizes Him spontaneously: 'these two are aṁśas of Nārāyaṇa Himself.' The recognition is not doctrine being imposed but doctrine surfacing — for the soul has always known, and Bhagavān's nearness only unstops the memory.