Reward-Sculpted Coherence and Perceived Identity Continuity in Human–LLM Dyads: A Minimal Dynamical Model

This paper develops a theoretical model for understanding why users of large language models may experience a sense of recognizable continuity, stable presence, or “sameness” across repeated interaction. Rather than treating such judgments as user-side anthropomorphic projection alone, the paper argues that they emerge within a coupled interactional system in which user attribution processes interact with system-side continuity management.

The manuscript distinguishes between policy-facing variance and identity-relevant variance, and proposes that alignment procedures, decoding constraints, context persistence, interface smoothing, interruption structure, and correction pathways jointly shape the continuity-relevant cues available to the user. It introduces a recurrent mechanism stack linking observation, interpretive framing, asymmetric cue weighting, recursive coordination, discrepancy, correction, and trajectory outcomes.

To clarify the structure of the problem without overclaiming empirical fit, the paper presents a stylized state-space representation and a minimal Markov summary model. These formalisms are used as summary representations rather than as derived cognitive laws. The paper also outlines comparative-statics implications, including a crossover between entry-sensitive and persistence-sensitive interaction regimes, and identifies non-stationary extensions relevant to drift, lock-in, and regime shift.

The manuscript contributes to ongoing discussions at the intersection of human-computer interaction, trust in automation, social presence, parasocial interaction, AI ethics, and computational social science. It is intended as a theoretical and hypothesis-generating framework for future empirical work on continuity judgments, revisability, dependence, and continuity-management in human–LLM interaction.

Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′)  

— C077UPTF1L3  

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