Structuring the AI-enabled home learning environment: a gatekeeper model of digital capital, trust, and relational support.

Introduction: As AI tools increasingly enter family life, parents function as gatekeepers who may shape whether AI becomes part of a governable learning ecology or remains an unregulated convenience. This study examined how family background, digital capital, AI-related beliefs, and relational support are associated with parental behavioral intention and willingness to pay in the AI-enabled home learning environment. Methods: We surveyed 585 Chinese parents of children from preschool through secondary school, and 567 valid responses were analyzed. An associational structural path model with observed composite variables was estimated, linking socioeconomic status, household AI use, parental digital literacy, cultural capital, AI trust, privacy concerns, algorithmic awareness, parental mediation, and home-school collaboration to behavioral intention and willingness to pay. Results: Household AI use was positively associated with parental digital literacy but did not consistently relate to broader digital capital or governance readiness. Socioeconomic status was associated with downstream support primarily through parental digital literacy, which was related to higher trust and, via relational supports, to behavioral intention. Willingness to pay was interpreted more cautiously as a financial-intention outcome. The model explained more variance in behavioral intention than in willingness to pay, and subgroup analyses indicated broadly comparable structural patterns across sample-defined lower- and higher-SES groups. Discussion: These findings suggest that equity-oriented AI-in-education initiatives should prioritize parents' digital capability, calibrated trust, and relational infrastructures that enable families to govern, not merely consume, AI in children's learning. Because the data are cross-sectional, the findings should be interpreted as associations rather than causal pathways.