Background: Generative language models have transformed poetry writing into an iterative practice in which prompts, outputs, revisions, interfaces, and platforms jointly shape literary production. Objective: This study examines how prompting functions poetically, how creative agency is negotiated during human–AI collaboration, and how algorithmic literary voice emerges across documented digital writing practices. Method: A qualitative multiple-case corpus design analyzed 34 verified public documents, 41 text units, and 41 source-linked coding units through a Prompt–Rhetoric Coding Matrix, Human–AI Negotiation Sequence Analysis, and Algorithmic Literary Voice Profile. Results: Dialogic and evaluative prompting formed the largest prompting configuration, indicating that poetic composition depended on reformulation, assessment, and constraint rather than single-turn instruction. Human-directed control remained prominent across interaction sequences, although automation, platform mediation, and distributed participation produced several asymmetrical forms of collaboration. Hybrid and human-curated voice profiles exceeded purely model-conditioned patterns, demonstrating that literary voice developed through combined traces of prompting, editing, stylistic recurrence, attribution, code, and circulation. Implication: These findings reposition authorship as a traceable distribution of compositional decisions rather than a binary division between human and machine production. Novelty: This study integrates prompt rhetoric, interactional agency, and platform-mediated stylistics within one auditable framework for analyzing AI-assisted poetry in contemporary digital literary culture.