Sparse-Cue Reconstruction in Large Language Models: Two Controlled Experiments on Cue-Bound Regime Recovery

Can a weak signal alter the first inference of a language model by recovering a previously established interactional regime, or does the signal merely create a similar regime anew? The distinction is difficult to test in ordinary chat systems because a nominally fresh conversation may still receive summaries, memories, personalization, or other information-bearing state. This paper reports two prospectively specified, protocol-frozen synthetic experiments designed to separate persistence, reconstruction, and de novo induction at the level of first-turn behavior. Study 1 found no evidence that an accumulated reconstruction-favoring trajectory crossed into later ephemeral sessions, while visible target accumulation strongly shifted first inference. Study 2 found that an opaque cue was inert in fresh context but recovered the target regime when correctly bound in retained session history. A sparse relational cue transferred the target organization in fresh context, while a lexical scramble did so less reliably. The results support a substrate-bound account: sparse cues can selectively re-enter an established behavioral regime when an accessible cue-to-regime relation exists, while relationally informative cues can induce a comparable regime directly. The experiments do not support substrate-free persistence, weight change, or user-specific memory.