Śrīmad-Bhāgavatam 10.22.25
Blended reading (Sanskrit + English inline)
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saṅkalpaḥ
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the motivation
Same word as verse 24. Now He names it back to them — your saṅkalpa is viditaḥ, known to Me. The gopīs' inner vow has been registered by the very Person it was aimed at.
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sādhvyaḥ
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O pious girls
Vocative plural feminine of sādhvī — a chaste, devoted woman. Kṛṣṇa names them sādhvī precisely after the cīra-haraṇa episode — pre-empting any worldly reading. They are not transgressors; they are sādhvīs because their bhāva is fixed on Him.
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mat-arcanam
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your worship of Me
Compound: mat (My) + arcana (worship). He reinterprets the whole month's Kātyāyanī-vrata as mat-arcana — worship of Him. Outward form, inward Person; this is the Gauḍīya reading of all sincere worship: it is taken up by Bhagavān.
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anumoditaḥ
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approved of
Past participle of anu-√mud (to consent, sanction). The Vedic word for divine ratification of a vrata. The līlā is sealed: the vow has succeeded because the One it was meant for has confirmed it personally.
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satyaḥ bhavitum arhati
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must become true
Phrase: satya (true) + bhavitum (to become) + arhati (must). Kṛṣṇa's word is itself the agency that makes the future come about. His promise here will become the rāsa-līlā in chapters 29–33.
Just as Kṛṣṇa is free of all impure desire, so are the gopīs. Their attempt to gain Kṛṣṇa as their husband was therefore motivated not by a desire for personal sense gratification but by their overwhelming desire to serve Kṛṣṇa and to please Him. Because of their intense love, the gopīs did not see Kṛṣṇa as God but rather as the most wonderful boy in all creation, and being beautiful young girls, they desired only to please Him by loving service. Lord Kṛṣṇa understood the pure desire of the gopīs and was thus satisfied. The Lord could certainly not be satisfied by ordinary lust, but He was moved by the intense loving devotion of the cowherd girls of Vṛndāvana.
"O chaste women! Though out of modesty, you have not spoke about your real desire (sankalpa) in worship of me to give me pleasure (mad arcanam). I know and I accept it. Because your desire was pure, , it must be fulfilled. What is not possible when it was done only for my pleasure--by prema , and when I am controlled by prema?" At this point, the krpa sakti made the Lord’s power more evident among the gopis, though the power was still under the control of prema, and subject to the pastimes. By this power, he knew the gopis’ austerities in worship of Katyayani to attain him, and gave them the results. According to the words of Garga that Krsna was similar to Narayana, but the gopis now took Krsna as Narayana.
He states in this verse that their desire has been fulfilled and with some special qualities. O saintly girls (sādhvyaḥ), endowed with form and qualities for activities of the highest prema! Because of that you desired only me. Or you have been related only to me. Your worship of me, your vow filled with prema to have me as your husband is known to me. It has been successful. Because your desires are fulfilled, I am pleased. You have done well. Because you desired only me and because I have agreed, it should not fail. It should come true. It is not necessary to ask for anything else. Arha means possibility, suitability, or determining. Arha means “suitability” according to the Kāśika commentary on Pāṇini’s sūtras. Sambhāvane’ lam and arhe krtā show the meaning of arha in the sūtras (Pāṇini 3,3.154 and3,3.169). In metaphors the meaning becomes “determining” or “attributing.” Supposition or imagining of great souls means that it will be true.
O saintly girls (sādhvyaḥ), having the highest vow, endowed with the best forms and qualities! Because of that, you desired only me. The vow is described. Your desire was to serve me with devotion as wives (mad-arcaṇam). That is the correct type of worship and thus will be successful.
A king certifying the petition: 'Your intention is correct, your worship has reached me, and what you have asked for will certainly happen.' The vow is sealed not by Kātyāyanī but by Kṛṣṇa Himself — anumoditaḥ, approved, with the same word the Vedas use for divine sanction.
My note
Source: vedabase.io