Śivasaṃhitā 5.189

The haṃsa (swan/goose) in the sahasrāra is the Paramātman, the supreme self that floats on the waters of manifestation without getting wet. The mind resting in this abode (nivāsa) naturally breathes the divine mantra so’ham («I am That»): the inversion of haṃsa in the breath’s rhythm, the spontaneous mantra that every living being recites unconsciously.

Haṃsa is the sacred swan or goose (haṃ and sa are the two sounds of breath, also read reversed as so’ham), nivāsa the abode or residence, bhūta that which has become or is, niviṣṭa-cetāḥ one whose mind has entered/fixed itself (niviṣṭa = that has penetrated inside, cetas = mind/consciousness).

The identification of haṃsa with Paramātman has roots in the Upaniṣads: in the Chāndogya, the solar goose represents the ātman freely flying between the world and its source. In the Nātha tradition, haṃsa-yoga (the yoga of the swan) is the practice of following the breath as mantra until the distinction between «I» and «That» dissolves in direct perception of identity.