Humans form cognitive maps that enable inferences beyond direct experience, relying on hexagonal grid-cell-like neural codes as a schema for two-dimensional (2D) spaces. However, how new experiences align with this schema remains unknown. We recorded intracranial activity from 42 epilepsy patients while they learned rank relations among feature objects, then combined these features into compounds occupying a 2D conceptual space. Hippocampal ripples during brief pauses between learning trials increased with experience, signaling integration of the learned ranks. Crucially, ripple activity during post-learning rest predicted the later appearance of grid-like codes in the entorhinal and medial prefrontal cortex (mPFC) when participants inferred unseen relations among compounds. Ripples synchronized with mPFC during rest were specifically associated with later schema-based inference rather than direct memory retrieval. These findings show that hippocampal ripples align new experiences with an existing grid-like schema, transforming discrete events into structured knowledge that supports flexible reasoning in human cognition.