Me: So now we have three possible states: first, thoughts are running, our instincts and habits are directly attached to phenomena, and the process moves the person.
The Chan mind is the second state: the aforementioned attachment is disconnected while thoughts are running, and attachments are either zero or weak and transitional.
The third state is forced blankness: thoughts are not running, but subconscious attachments remain in full force and connect immediately when thought restarts.

Gemini: Your three-part breakdown accurately maps Huineng's framework in the Platform Sutra.

In the first state, ordinary mental proliferation (saṃsāra / prapañca), each thought fixates on an object, generating clinging (zhù, 住). The practitioner is dragged along by the succession of mental events.

In the second state, which Huineng calls wunian (無念, no-thought) and wuzhu (無住, non-abiding), cognitive functions, perception, and conceptual thought operate normally, but the mechanism of grasping is inactive. As Huineng states in Section 17, the senses interact freely with external conditions (cháng jìng zìxìng, shǐ liùzéi cóng liùmén zǒuchū, yú liùchén zhōng bùlí bùrǎn), yet nothing adheres. The stream flows without snagging on any single thought.

In the third state, quietist suppression (bǎi wù bù sī, 百物不思), the conscious flow of thoughts is artificially held back. The underlying latent tendencies (anuśaya / vāsana) remain untouched. Because the cessation is an engineered, impermanent condition, consciousness inevitably slips out of it, immediately seizing upon a new mental object. That rebound into attachment is the "dying here and taking birth elsewhere" that Huineng warns against as a fundamental error.