I offer my respectful obeisances unto the internal potencies of the Lord, of whom Śrī Gadādhara Prabhu is the foremost.
(CC Adi 1.41)
Gadādhara Paṇḍita, the fourth branch, is described as an incarnation of the pleasure potency of Śrī Kṛṣṇa. No one, therefore, can equal him.
PURPORT
In the Gaura-gaṇoddeśa-dīpikā (147-53) it is stated, “The pleasure potency of Śrī Kṛṣṇa formerly known as Vṛndāvaneśvarī is now personified in the form of Śrī Gadādhara Paṇḍita in the pastimes of Lord Caitanya Mahāprabhu.” Śrī Svarūpa Dāmodara Gosvāmī has pointed out that in the shape of Lakṣmī, the pleasure potency of Kṛṣṇa, she was formerly very dear to the Lord as Śyāmasundara-vallabhā. The same Śyāmasundara-vallabhā was present in Lord Caitanya’s pastimes as Gadādhara Paṇḍita. Formerly, as Lalitā-sakhī, she was always devoted to Śrīmatī Rādhārāṇī. Thus Gadādhara Paṇḍita is simultaneously an incarnation of Śrīmatī Rādhārāṇī and Lalitā-sakhī. In the Twelfth Chapter of this part of the Caitanya-caritāmṛta there is a description of the descendants or disciplic succession of Gadādhara Paṇḍita.
(CC Adi 10.15)
Lord Śrī Caitanya Mahāprabhu is the Supreme Lord, and Nityānanda Prabhu and Advaita Prabhu are manifestations of the Supreme Lord. All of Them are viṣṇu-tattva, the Supreme, and are therefore worshipable by the living entities. Although the other two tattvas within the category of Pañca-tattva—namely, śakti-tattva and jīva-tattva, represented by Gadādhara and Śrīvāsa—are worshipers of the Supreme Lord, they are in the same category because they eternally engage in the transcendental loving service of the Lord.
(CC Adi 7.15 purport)
No one can describe the characteristics and ecstatic love of Gadādhara Paṇḍita. Therefore another name for Śrī Caitanya Mahāprabhu is Gadādhara-prāṇanātha, "the life and soul of Gadādhara Paṇḍita."
(CC Antya 7.163)